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For DXJ Writer: I would appreciate...

For DXJ Writer:

I would appreciate it if you would review the information below, and try to have it back to me late Friday night! I will more than likely have another one for you that will be due ealier in the week. I will let you know, but I will send you a copy of the entire assignment, just so you know what it will pretain and I will let you know what part you will have to be concerned with, but for now here is the info. for friday!

You are interested in conducting research concerning police officers and their jobs. The information you want to gather, including job satisfaction or job hazards, is up to you as long as you clearly state the goal of your research. The method you use should be appropriate for the goal of your research.

Develop a 1,050- to 1,750-word paper addressing what you have learned about criteria for criminal justice research, specifically with regards XXXXX XXXXX research method is appropriate in your proposal.

Address the following questions:

• What is the goal or purpose behind your proposed research?

• What type of interview structure would you use? Why?

• What would be some questions you would ask? Why?

• What are some distinct advantages of a qualitative data-gathering strategy, such as participant observation, over more quantitative approaches?

• When conducting survey research, how important is informed consent and confidentiality?

Include at least two references.

Format your paper consistent with APA guidelines

I would appreciate it if you would review the information below, and try to have it back to me late Friday night! I will more than likely have another one for you that will be due ealier in the week. I will let you know, but I will send you a copy of the entire assignment, just so you know what it will pretain and I will let you know what part you will have to be concerned with, but for now here is the info. for friday!

You are interested in conducting research concerning police officers and their jobs. The information you want to gather, including job satisfaction or job hazards, is up to you as long as you clearly state the goal of your research. The method you use should be appropriate for the goal of your research.

Develop a 1,050- to 1,750-word paper addressing what you have learned about criteria for criminal justice research, specifically with regards XXXXX XXXXX research method is appropriate in your proposal.

Address the following questions:

• What is the goal or purpose behind your proposed research?

• What type of interview structure would you use? Why?

• What would be some questions you would ask? Why?

• What are some distinct advantages of a qualitative data-gathering strategy, such as participant observation, over more quantitative approaches?

• When conducting survey research, how important is informed consent and confidentiality?

Include at least two references.

Format your paper consistent with APA guidelines

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DXJWriter :

Hi! Thanks for your request! This could work!

DXJWriter :

Please let me know if you have any ideas for this, as well! DXJ

Customer:

This is reaffirm what's due on friday, instructor reposted - can you check it for any changes!

Customer:

You are interested in conducting research concerning police officers and their jobs. The information you want to gather, including job satisfaction or job hazards, is up to you as long as you clearly state the goal of your research. The method you use should be appropriate for the goal of your research.

**Develop** a 1,050- to 1,750-word paper addressing what you have learned about criteria for criminal justice research, specifically with regards XXXXX XXXXX research method is appropriate in your proposal.

**Address** the following questions:

What is the goal or purpose behind your proposed research?

What type of interview structure would you use? Why?

· What would be some questions you would ask? Why?

· What are some distinct advantages of a qualitative data-gathering strategy, such as participant observation, over more quantitative approaches?

When conducting survey research, how important is informed consent and confidentiality?

**Include** at least two references.

**Format** your paper consistent with APA guidelines

DXJWriter :

Hi! We can confirm this! Did you have a topic preference? DXJ

Customer:

No, not really...to be honest I haven't had a chance to really review it. I am taking three classes this session, so I am really relying on to pick what you feel comfortable with...if you don't mind!!! I am just be real!

DXJWriter :

:-) Well, we could *trade* homework- LOL (Just Kidding, but I hope it made you smile!) DXJ

Customer:

![IMAGE][SRC][/SRC][ALT][/ALT][WIDTH]100[/WIDTH][HEIGHT]100[/HEIGHT][STYLE][/STYLE][/IMAGE]

DXJWriter :

?

Customer:

It was a smilely face!

DXJWriter :

Oh, I wish I could see it! Maybe because we're in chat mode I can't.

DXJWriter :

I would have liked the smiley face!

DXJWriter :

(I not only taught all day but had a test tonight:-)

DXJWriter :

Thanks!

Customer:

Well, I sincerely XXXXX XXXXX do as well on your test, as you do on the things you've have done for me!

DXJWriter :

:-) We'll see! There were only two Chinese characters I did not know:-) That test was on 4 chapters! THanks so much for the good wishes! I really appreciate them and you! DXJ

Customer:

Your welcome, and the feeling is mutual! Let me ask you do you have any suggestions on what our total team assignment should be on? The team is struggling on a topic!

DXJWriter :

Hi! What is the team project again?

DXJWriter :

Sorry, I don't remember if that's on another question:-)

Customer:

**Begin** working on the Research Proposal, due in Weeks Three and Five.

**Post **your team’s proposed hypothesis for facilitator approval. One team member for each team should submit a 1 page discussion of the reason for the choice of subject, and the hypothesis you’re your team seeks to prove through research. Also include a brief discussion of what you intend to prove in order to further explain your hypothesis. There is no need to follow APA formatting, but please have a heading, list of team members, and use proper grammar, spelling, and punctuation

Customer:

Team Project: DUE Week 3:

DXJWriter :

Well, it depends on what you're interested in. What is the class title or the parameters of the class? There are too may topics you could investigate! Looking forward to your repsonse! DXJ

Customer:

Research Methods in criminal justice.

DXJWriter :

Yes I know that, but I thought the topic had to be more focused:-)

DXJWriter :

What interests you in that field?

DXJWriter :

Let's see if we can find something together............

DXJWriter :

For example, you coulf take this week's individual paper topic and find an area within it.

DXJWriter :

You could look at certain job hazards...........

DXJWriter :

For example, likelihood of injury on the job in certain districts compared with another one or the national average.

DXJWriter :

Job satisfaction in a world of interagency cooperation

DXJWriter :

The role of ethics training and/or cross cultural training in lessening officer injury

DXJWriter :

After all, the latter would be theoretically reduced by cultural competency, correct?

DXJWriter :

Do any of these suggestions help?

DXJWriter :

To research them you could do a traditional research method/ data exploration and construct a survey for longer answers.

Customer:

Oh, yes you are so very right! I have a couple of ideas now, but there are five others who have to agree/or have strong interest as well. So, I will see whos suggestion will prevail. Thank you very much!

DXJWriter :

:-) Glad I could help! Sometimes, it just takes a spark to get the brainstorming going!

Customer:

IF I HAVEN'T TOLD YOU BEFORE, I'M TELLING YOU NOW! YOU ARE A GOD SENT TO ME AND I COULDN'T BE MORE BLESSED TO HAVE - HAD YOU COME INTO MY LIFE!

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:-) Thanks so much! That made my day! DXJ

DXJWriter :

working through this:-) (Borrowing a cup of internet today!)

Customer:

Can you work on this? I'm having a problem with getting it answered.

Customer:

WEEK 1 DQ2?

What is a research/target population? What is a research sample? Please provide an example that incorporates each concept.

ANSWER: JANICE

According to the text, a research target or population is the subject, or the key focus of the research. An example of a research target, or population, pertaining to the Criminal justice field could be anything from prison(s) population or a specific criminal type. In other words, the target or populations have to have the same, or similar, characteristics. A research sample, according to the text, is a sampling of the research target or population. In most circumstances, researchers cannot interview or get information from every single person or individual in the specific research target group. It really is not possible. They use the data they receive from the sampling they take and make a deduction off of that. It is basically a strategy for obtaining information about a certain group. Although it cannot be said to be completely accurate without taking samples from every individual, it is a good deduction of the research target or population.

Customer:

same 50 to 75 words

DXJWriter :

Sure! I'll get it to you shortly!

DXJWriter :

Any progress on the group topic?

Customer:

NO< BUT I have a call out to the lead this week!

DXJWriter :

:-)! Well, I can hope!

DXJWriter :

Try this response to your DQ:

DXJWriter :

While a research/a target population is the population defined by the characteristics or shared experiences or parameters established by the researchers, studying every single person in this group is costly and almost impossible. Therefore, a research sample of the group might include persons meeting the requirements set forth by the study and also representative of the group itself. For example, a broad sample or large target population might contain several races and minorities. It might contain certain socioeconomic statuses, etc. Therefore, research might select participants that meet the requirements and do in ways that mirror the percentages and composition of the overall target population. For example, researchers might examine the effects of low socioeconomic status and residence in certain neighborhoods and hypothesize this has a positive relationship with criminal activity and/or certain types of crimes. Depending on the composition of the neighborhood, the researchers would try to recruit a sample population that mirrors the ethnic and racial composition. Even though it is smaller, it *should *prove valid.

Customer:

THank you!

DXJWriter :

Does that help you understand it better?

Customer:

yes

I'm glad!

About halfway through the other part for today.............. DXJ

Customer reply replied 9 years ago

Ok, don't stress it.....you have done the other question for me without hesitation and it wasn't on the schedule for today. So, if you want to wait til the morning it will be ok!

Almost finished!

Customer reply replied 9 years ago

Thanks for fininshing it tonight anyway! :-)

You're welcome! DXJ

Customer reply replied 9 years ago

Tomorrow I will.....Rather, later today I will finish sending you the remaining 3 or 4 chapters of this 5 week session! Do remember exactly the last chapter I sent you? If don't remember I will just start with chapter 9!

not sure.............wherever you think........

Hi!

Did you understand the study design? Please let me know if you have any questions! Thanks! DXJ

Customer reply replied 9 years ago

H A P T E R

10 Scaling and Index Construction

Levels of Measurement

Scaling Procedures

Arbitrary Scales

The Uniform Crime Reports

as an Arbitrary Scale

Attitude Scales

Thurstone Scales

Likert Scales

Guttman Scales

Other Scaling Procedures

Q Sort

Semantic Differential

Other Variations

Crime Seriousness Scales

Sellin-Wolfgang Index

Types of Crime Seriousness Scales

Prediction Scales

The Salient Factor Score

Greenwood's "Rand Seven-Factor Index"

Career Criminal Programs

Advantages of Scales

Disadvantages of Scales

Summary

Key Concepts

Review Questions

Useful Web Sites

LEVELS OF MEASUREMENT

Variables may be measured on four levels:

Nominal Interval

Ordinal Ratio

Nominal level variables represent the simplest level of measurement. Objects are usually

placed into mutually exclusive categories or types, and there is often no necessary quantitative or

statistical meaning to numbers assigned to these categories, except as a convenience in distinguishing

groups. Thus, any numbers assigned are merely qualitative descriptions, or labels, that

enable us to keep track of differences. Demographic variables such as sex, race, religion, and city

are examples of nominal variables. Values might be assigned, such as 1 to Protestant, 2 to

Catholic, 3 to Jewish, and 4 to other. Three Protestants, however, do not equal one Jewish.

The numbers merely assist in categorizing qualitative distinctions. Another example of this

Nominal

variables

ISBN 0-558-58864-6

Research Methods in Criminal Justice and Criminology, Eighth Edition, by Frank E. Hagan. Published by Prentice Hall. Copyright © 2010 by Pearson Education, Inc

Chapter 10 • Scaling and Index Construction **253**

would involve writing down five telephone numbers of friends and calculating the "average"

telephone number from this data, then calling it and waiting for an "average" friend to answer

(Dowdall, Babbie, and Halley, 1997, p. 185). Many variables that should take on higher scale

value may be treated as nominal level, although information is lost as a result. In criminal justice,

numbers could be arbitrarily assigned to different types of crimes in order to categorize them,

for instance:

1. Homicide

2. Assault

3. Robbery

4. Burglary

Obviously, as in the previous example, the actual numbers assigned have no mathematical

meaning. That is, a homicide (1) plus a robbery (3) does not equal a burglary (4), nor do four

homicides equal one burglary. Other qualitative or nominal categories to which numbers are

assigned are telephone numbers, social security numbers, room numbers, addresses, and officer

badge numbers. Any reduction in the level of measurement of a variable from higher level to

nominal measurement involves a loss of precision or detail. Similarly, any increase in the level of

measurement to ordinal, interval, or ratio involves an increase in information, or precision, over

the previous categories.

Table 10.1 ranks data on violent criminal victimization. In a representation of the same

data using only nominal level information, the cities would be classified as either Eastern or

Western, for example:

1. Eastern cities 8

2. Western cities 5

Another nominal means of assigning values to the data in Table 10.1 would be to consider

scores above fifty-four as high, and assign them a value of 1, and scores of fifty-four or below as

low, and assign them a value of 2.

TABLE 10.1 Violent Criminal Victimization Rates in Thirteen Selected

Cities (per 1,000 Residents 12 and Older)

Rank Location

Detroit 68 1 Eastern

Denver 67 2 Western

Philadelphia 63 3 Eastern

Portland 59 4 Western

Baltimore 56 5.5 Eastern

Chicago 56 5.5 Eastern

Cleveland 54 7 Eastern

Los Angeles 53 8 Western

Atlanta 48 9 Eastern

Dallas 43 10 Western

Newark 42 11.5 Eastern

St. Louis 42 11.5 Western

New York 36 13 Eastern

Source: *National Crime Panel Surveys. *Law Enforcement Assistance Administration, 1974.

ISBN 0-558-58864-6

Research Methods in Criminal Justice and Criminology, Eighth Edition, by Frank E. Hagan. Published by Prentice Hall. Copyright © 2010 by Pearson Education, Inc.

254 Chapter 10 • Scaling and Index Construction

For instance, weight, which could be measured in pounds and inches, could be reduced to

simply heavy and light. Similarly, "sentence imposed," which could be measured in months,

might be reduced to simply "long" and "short."

Ordinal level variables contain all the properties of nominal variables, but they also

enable the placement of objects into ranks, that is, highest to lowest. In Table 10.1, the city with

the highest victim rate was assigned a rank of 1, the city with the second highest a rank of 2, and

so forth to 13 for the lowest.

For cities that were tied, the average of the ranks that would have been assigned is given

to each of the tied values. Most attitudinal scales used in the social sciences and criminal justice

are ordinal in nature. They enable us to rank respondents, but they must not be mistaken

for real numbers. For example, a person whose attitudinal scale score is 50 is higher than a

person who scored 30, which is again higher than one who scored 10. Thus, we know that

each is higher than the next. We do not know by how much each is higher; the ranks are not

comparable to meters or dollars. As another example, although we know that a student with a

3.6 quality point average in college is 0.6 higher than one with a 3.0, we would have no idea

of the unit differences in points among students who ranked first, fifth, and tenth unless the

actual averages were provided.

Interval level variables contain all the elements of nominal and ordinal data and also

assume equal distance between objects on a scale. It not only provides a ranking of objects, but

also reflects equal intervals or a standard unit between scale scores. Thus, the distance between

scores 2 and 4 is exactly the same as the distance between 8 and 10. Using our victimization

rate example from Table 10.1, the assignment of nominal level measurement to the data merely

resulted in mutually exclusive categories of east-west or high-low, whereas ordinal assignment

ranked the cities from highest to lowest. Interval level data, the actual rates, give us this same

information plus the unit differences between each value. That is, we now know not only which

city ranks higher or lower, but how much higher or lower. Interval level measurement also contains

an arbitrary zero point.

Ratio level variables not only assume the interval quality of data, but they also have a

fixed meaningful zero point. Such data enable one to show how many times greater one value is

than another. Some examples of ratio variables are variables such as age, weight, income, education,

number of children, and frequency of crime commission. Although it is possible to have

zero income or education, one would not have zero IQ or attitude toward crime. Each scale is

more complex and takes on the properties of the preceding.

Upon waking in the morning, a typical American may "hit the scales" and discover that he

or she has gained three pounds. While reading the morning newspaper one discovers that the

Gross Domestic Product has increased by only 2 percent, whereas the Dow Jones Industrial

Average is up three points, the Consumer Price Index is 1.2 percent for the previous month, and

the FBI reports that the crime rate for the first six months is up 6 percent. In addition, the pollution

index is 65 (which is in the fair range), and an earthquake in California registered 3.6 on the

Richter scale. Without realizing it, most of us are quite familiar with the use of scales to measure

degrees of change in factors affecting our lives.

Chapter 1 pointed out how meaningful concepts or abstractions of reality are created to

provide insight and useful tags with which to manipulate and understand reality. Previously,

variables were described as operationalized concepts or concepts that vary or take on various

values. Scales reflect levels of measurement or various degrees of quantitative value that a variable

can take on. As we shall see in this chapter, each level of measurement has appropriate

corresponding statistical measures.

Ordinal

variables

Interval

variables

Ratio

variables

ISBN 0-558-58864-6

Research Methods in Criminal Justice and Criminology, Eighth Edition, by Frank E. Hagan. Published by Prentice Hall. Copyright © 2010 by Pearson Education, Inc

Chapter 10 • Scaling and Index ConstructionSCALING PROCEDURES

The purpose of measurement is to make connections between concepts and numbers. Mere

observation, measurement, and assignment of numbers to responses are not the same as a proper

measure. Scales can be viewed as calibrated instruments with which to interrogate concepts

(Wright, 1980). Thus, there is a difference between scaling and scoring of test items. The level of

measurement of a variable is very important in the utilization of various statistical procedures.

Many statistical procedures, for instance, require interval variables and are inappropriate if used

with nominal or ordinal variables.

Although many of the scaling procedures discussed in this chapter can be calculated by

hand, the increased availability of inexpensive computer hardware and "canned" or prewritten

computer programs makes these procedures easier to perform.

Scaling procedures involve attempts to increase the complexity of the level of measurement

of variables from nominal to at least ordinal and hopefully interval/ratio. They build more

complex, composite indicators of phenomena. A great many well-constructed scales already

exist and should be consulted and analyzed before construction of a new scale. Established scales

may be used as they are or modified to fit the special needs of a specific study. Such scales have

an established track record.

Various excellent handbooks that catalog scales exist. These not only classify scales by the

concept to be measured, but report reliability, validity, previous studies that employed the scale

where one could obtain the instrument, as well as usual sample items from the scale.1 Strong

consideration of previously developed scales is important because *replication*, the repetition of

measures with different populations, enables establishment of a comparative and universal social

science.

Although some writers attempt to make major distinctions between scales and indexes, in

reality they are referred to quite interchangeably. One distinction is that a scale is generally

concerned with only one attribute of a concept, whereas an index involves many dimensions or

scales. With an index, the researcher combines or averages the results for more than one

phenomenon. It is this writer's preference to view the terms *scale *and *index *as synonyms.

Scales are useful for a number of reasons but primarily because they avoid reliance on any

single response alone as an indicator. For example, the response to any single item may be an

error, may be misclassified or misinterpreted by subjects, or may not adequately tap the full

dimension of the idea being measured (Orenstein and Phillips, 1978, pp. 258-259).

ARBITRARY SCALES

Arbitrary scales are developed by the researcher and are based primarily on face validity (the

scale appears to be measuring what one intends to measure) and professional judgment. They

are intended to measure relative degrees of a concept or provide a rough estimate. A simple way

of developing arbitrary scales is to begin with ordinal or interval scales of phenomena that lend

themselves readily to accepted measurement, for example, income, education, and attendance.

Scaling

1 Some examples of excellent reference handbooks for scales include: Miller, Delbert C., ed.Design and Social Measurement, 5th ed. New York: Longman, 1991; Brodsky, Stanley and O'Neal Smitherman, eds.

Handbook of Scales for Research in Crime and Delinquency. New York: Plenum Press, 1983; and Robinson, J. P.,

P. R. Shaver, and L. S. Wrightsman, eds. *Measures of Personality and Social Psychological Attitudes*, San Diego:

Academic Press, 1991.

Arbitrary

scales

ISBN 0-558-58864-6

Research Methods in Criminal Justice and Criminology, Eighth Edition, by Frank E. Hagan. Published by Prentice Hall. Copyright © 2010 by Pearson Education, Inc

.256 Chapter 10 • Scaling and Index Construction

Figure 10.1 presents a hypothetical example of the construction of a social class index using

three subscales-income, education, and occupation. In reality, it would make far better sense

previously than to construct a new scale.

It might be quite misleading for a researcher to use one of the three subscales alone as a

measure of social class; however, use of an index that takes into account all three measures overcomes

this. But how might an index be constructed using this arbitrary scale of social class?

Suppose we have a respondent who earns $40,000, is a college graduate, and has a career in sales.

Such a case would score 14 out of a possible 15 on our scale. One might arbitrarily decide that

scores of 1 to 5 represent lower class, 6 to 10 middle class, and 11 to 15 upper class. Thus, according

to our operationalization of social class, our respondent would be upper class.

Because the construction of arbitrary scales rests primarily on the judgment of the

researcher, they are easily criticized. For this reason, attitudinal scaling procedures have been

developed that permit logical and methodological defenses for scale operationalization.

THE UNIFORM CRIME REPORTS AS AN ARBITRARY SCALE

A lengthy exposition of the UCR was presented in Chapter 4. Using the original UCR, a simple

summation of the eight index offenses is made. The **UCR index ***offenses *are those crimes that are

considered serious and that the police feel are fairly accurately reported and uniformly measured:

Homicide

Larceny

Forcible rape

Car theft

Robbery

Burglary

Aggravated assault

Arson (not actually calculated in index due to unreliability of measurement)

Although arson is listed as part of the index, the unreliability of such data prevents it from

being included in any calculations. As discussed in Chapter 4, the crime index is the total number

of such offenses recorded by police per 100,000 population. Table 10.2 presents a typical

FIGURE 10.1 An Arbitrary Social Class Scale.

Income (annual) Education *Occupation *(using U.S. Census Ratings)

$40,000 and over 5 College Graduate 5 Higher Professional, Managerial 5

$30,000-$39,999 4 Some College 4 Less Professional, Managerial,

$20,000-$29,999 3 High School Graduate 3 Technical & Sales 4

$10,000-$19,999 2 Some High School 2 Services 3

Under $10,000 1 Grade School or Less 1 Skilled Labor 2

Unskilled Labor 1

FIGURE 10.1 An Arbitrary Social Class Scale.

Income (annual) Education *Occupation *(using U.S. Census Ratings)

$40,000 and over 5 College Graduate

Figure 10.1 presents a hypothetical example of the construction of a social class index using

three subscales-income, education, and occupation. In reality, it would make far better sense

previously than to construct a new scale.

It might be quite misleading for a researcher to use one of the three subscales alone as a

measure of social class; however, use of an index that takes into account all three measures overcomes

this. But how might an index be constructed using this arbitrary scale of social class?

Suppose we have a respondent who earns $40,000, is a college graduate, and has a career in sales.

Such a case would score 14 out of a possible 15 on our scale. One might arbitrarily decide that

scores of 1 to 5 represent lower class, 6 to 10 middle class, and 11 to 15 upper class. Thus, according

to our operationalization of social class, our respondent would be upper class.

Because the construction of arbitrary scales rests primarily on the judgment of the

researcher, they are easily criticized. For this reason, attitudinal scaling procedures have been

developed that permit logical and methodological defenses for scale operationalization.

THE UNIFORM CRIME REPORTS AS AN ARBITRARY SCALE

A lengthy exposition of the UCR was presented in Chapter 4. Using the original UCR, a simple

summation of the eight index offenses is made. The **UCR index ***offenses *are those crimes that are

considered serious and that the police feel are fairly accurately reported and uniformly measured:

Homicide

Larceny

Forcible rape

Car theft

Robbery

Burglary

Aggravated assault

Arson (not actually calculated in index due to unreliability of measurement)

Although arson is listed as part of the index, the unreliability of such data prevents it from

being included in any calculations. As discussed in Chapter 4, the crime index is the total number

of such offenses recorded by police per 100,000 population. Table 10.2 presents a typical

FIGURE 10.1 An Arbitrary Social Class Scale.

Income (annual) Education *Occupation *(using U.S. Census Ratings)

$40,000 and over 5 College Graduate 5 Higher Professional, Managerial 5

$30,000-$39,999 4 Some College 4 Less Professional, Managerial,

$20,000-$29,999 3 High School Graduate 3 Technical & Sales 4

$10,000-$19,999 2 Some High School 2 Services 3

Under $10,000 1 Grade School or Less 1 Skilled Labor 2

Unskilled Labor 1

UCR index

ISBN 0-558-58864-6

Chapter 10 • Scaling and Index Construction **257**

UCR crime index summary. In addition to all of the shortcomings presented in Chapter 4,

a principal difficulty with the UCR as an index of crime in the United States is that it is an

unweighted index. That is, each crime incident, whether it is homicide or auto theft, is added to

the total index without any consideration of its relative seriousness. No monetary or differential

psychological value is attached. A city with fifty burglaries per 100,000 and a city with fifty

homicides per 100,000 would actually have the same UCR crime index. Similar problems exist

with unweighted victimization rates. Later in this chapter, we discuss attempts to develop crime

seriousness scales to measure not only the quantity, but also the severity of crime.

ATTITUDE SCALES

Three major types of attitude scales that have been developed in the social sciences are used in

criminology and criminal justice:

Thurstone scales

Likert scales

Guttman scales

Thurstone Scales

Thurstone scales were the first to be developed (Thurstone and Chave, 1929). Thurstone had

judges to select items. "Judges" are individuals whose expertise is respected and who might be in

a position to help in the determination of the most useful items.

The earliest method developed by Thurstone was the *method of paired comparisons.*

A number of judges are presented with all possible pairs of items to be used in a scale. Items or

questions are then rated by the judges as to which of each pair is more favorable to the issue in

question. Such a procedure tends to be quite tedious and time consuming.

As a judgmental technique, Thurstone's method of **equal appearing intervals **is superior

to the paired comparisons method in that it requires only one judgment per item. Each judge is

TABLE 10.2 The UCR Crime Index*

Offense Number

Murder and nonnegligent manslaughter 23,400

Forcible rape 102,560

Robbery 639,270

Aggravated assault 1,054,860

Burglary 3,073,900

Larceny-theft 7,945,700

Motor vehicle theft 1,635,900

Arson -

Index total 14,475,600

Index rate 5,820.3 (per 100,000)

*Offenses may not add to index total because of rounding.

Source: U.S. Department of Justice, *FBI Uniform Crime Reports: Crime in the United States*, 1990.

Washington, D.C.: U.S. Government Printing Office, August 11, 1991, p. 50.

258 Chapter 10 • Scaling and Index Construction

Judge No. Item 1 Item 2 Item 3

1 9 2 2

2 10 3 3

Median 3 10 3 9

4 11 3 10

5 11 4 11

FIGURE 10.2 Method of Equal Appearing Intervals: Five Judges

Assign an Eleven-Point Scale to Three Items.

required to sort the items into a predetermined number of categories so that the intervals between

them are subjectively equal. Figure 10.2 illustrates the rating of three items by five different

judges using an eleven-point scale in which 1 indicates that the item is a positive measure of the

entity being measured, and 11 indicates a negative measure.

The ratings for item 1 by five judges were 9, 10, 10, 11, and 11; that is, the judges generally

agreed that the item was a negative measure of the entity in question. On item 2 the judges were on

basic agreement that the item was positive, whereas they disagreed on item 3. According to

Thurstone's procedure, the third item would be eliminated because of the conflicting interpretations

of the judges. Sometimes investigators assign weights to the items on the basis of the median scores

of the values assigned by the judges. The logic of *weighting *assumes that responses to the first item

carry a more negative meaning (a weight of 10) than those to item 2 (a weight of only 3). The final

form of the scale is made up of those agreed-upon items that provide even intervals on the scale

from high to low.

An interesting application that partly involved Thurstone methods was the development

of police assessment centers (Dunnette and Motowidlo, 1976). As part of the procedure to

develop a police career index that would permit police departments to predict likely successful

candidates for both hiring and promotion, a group of psychologists and senior police

officials reviewed a series of items, including simulations that had been constructed by the

researcher. Those items deemed most promising and on which there was the greatest agreement

were then pretested.

The following is a *summary of the Thurstone scaling procedure*:

A large number of questions believed to be related to the concept under investigation are

constructed.

A number of judges are asked to assign weight to each item using a predetermined scale

ranging from favorable to unfavorable.

The median (midpoint) of the values assigned to each item is taken as its score or weight.

Those items on which there was significant disagreement by the judges are eliminated.

Selected items with weights spread at intervals along the scale are retained for the final

scale which can now be administered to respondents (Miller, 1991, p. 88).

Likert Scales

Likert scales, the scales most commonly used in attitudinal research, are named for Rensis

Likert who developed the procedure (Likert, 1932). Figure 10.3 illustrates a typical Likert

scale. **Likert scales **consist of a simple summation of usually a five-point bipolar response

FIGURE 10.2 Method of Equal Appearing Intervals: Five Judges

Assign an Eleven-Point Scale to Three Items.

Likert scales

ISBN 0-558-58864-6

required to sort the items into a predetermined number of categories so that the intervals between

them are subjectively equal. Figure 10.2 illustrates the rating of three items by five different

judges using an eleven-point scale in which 1 indicates that the item is a positive measure of the

entity being measured, and 11 indicates a negative measure.

The ratings for item 1 by five judges were 9, 10, 10, 11, and 11; that is, the judges generally

agreed that the item was a negative measure of the entity in question. On item 2 the judges were on

basic agreement that the item was positive, whereas they disagreed on item 3. According to

Thurstone's procedure, the third item would be eliminated because of the conflicting interpretations

of the judges. Sometimes investigators assign weights to the items on the basis of the median scores

of the values assigned by the judges. The logic of *weighting *assumes that responses to the first item

carry a more negative meaning (a weight of 10) than those to item 2 (a weight of only 3). The final

form of the scale is made up of those agreed-upon items that provide even intervals on the scale

from high to low.

An interesting application that partly involved Thurstone methods was the development

of police assessment centers (Dunnette and Motowidlo, 1976). As part of the procedure to

develop a police career index that would permit police departments to predict likely successful

candidates for both hiring and promotion, a group of psychologists and senior police

officials reviewed a series of items, including simulations that had been constructed by the

researcher. Those items deemed most promising and on which there was the greatest agreement

were then pretested.

The following is a *summary of the Thurstone scaling procedure*:

A large number of questions believed to be related to the concept under investigation are

constructed.

A number of judges are asked to assign weight to each item using a predetermined scale

ranging from favorable to unfavorable.

The median (midpoint) of the values assigned to each item is taken as its score or weight.

Those items on which there was significant disagreement by the judges are eliminated.

Selected items with weights spread at intervals along the scale are retained for the final

scale which can now be administered to respondents (Miller, 1991, p. 88).

Likert Scales

Likert scales, the scales most commonly used in attitudinal research, are named for Rensis

Likert who developed the procedure (Likert, 1932). Figure 10.3 illustrates a typical Likert

scale. **Likert scales **consist of a simple summation of usually a five-point bipolar response

FIGURE 10.2 Method of Equal Appearing Intervals: Five Judges

Assign an Eleven-Point Scale to Three Items.

Likert scales

ISBN 0-558-58864-6

Research Methods in Criminal Justice and Criminology, Eighth Edition, by Frank E. Hagan. Published by Prentice Hall. Copyright © 2010 by Pearson Education, Inc.

Chapter 10 • Scaling and Index Construction **259**

For each of the following questions, circle the response that best represents your attitude:

SA A DK D SD

SA A DK D SD

SA A DK D SD

SA A DK D SD

SA A DK D SD

SA

Strongly

Agree

A

Agree

DK

Don't

Know

D

Disagree

SD

Strongly

Disagree

The best way to handle people is to tell them what they

want to hear.

When you ask someone to do something for you, it is

best to give the real reasons for wanting it rather than

giving reasons which might carry more weight.

It is hard to get ahead without cutting corners here

and there.

Barnum was wrong when he said, "There's a sucker

born every minute."

It is wise to flatter important people.

All in all, it is better to be humble and honest than

important and dishonest.

1.

2.

3.

4.

5.

6.

Note: Those circled represent hypothetical response

FIGURE 10.3 A Likert Scale: Adaptation of the Machiavellianism Scale. *Source*: Christie, Richard,

and Florence L. Geis. *Studies in Machiavellianism. *New York: Academic Press, 1970.

ranging from "strongly agree" to "strongly disagree." Figure 10.4 portrays the scoring key for

Figure 10.3, the six Machiavellianism2 items in which the more manipulative orientation is

given the higher score or +5.

According to the scoring system in Figure 10.4, our hypothetical respondent scored 24 on

a scale that ranged from 6 (low Machiavellianism) to 30 (high Machiavellianism). The low or

high numbers are arbitrarily assigned by the researcher. Low scores could have been assigned to

high orientations or vice versa, as long as the investigator remembers the assignment for later

analysis. The even items, questions 2, 4, and 6, are examples of *reversal items*, in which the

substance of the question is worded in a negative fashion relative to the orientation being

2 Machiavellianism takes its name from the sixteenth-century Italian philosopher Niccolo Machiavelli, whose classic

work *The Prince *(1952) has often been described as a "handbook for dictators" in its espousal of the "end justifies the

means" in obtaining power. Socially, Machiavellianism refers to a manipulative orientation toward others.

FIGURE 10.3 A Likert Scale: Adaptation of the Machiavellianism Scale. *Source*: Christie, Richard,

and Florence L. Geis. *Studies in Machiavellianism. *New York: Academic Press, 1970.

FIGURE 10.4 Scoring for a Likert Scale: the Machiavellianism Scale in

Figure 10.3 (hypothetical response).

For each of the following questions, circle the response that best represents your attitude:

SA A DK D SD

SA A DK D SD

SA A DK D SD

SA A DK D SD

SA A DK D SD

SA

Strongly

Agree

A

Agree

DK

Don't

Know

D

Disagree

SD

Strongly

Disagree

The best way to handle people is to tell them what they

want to hear.

When you ask someone to do something for you, it is

best to give the real reasons for wanting it rather than

giving reasons which might carry more weight.

It is hard to get ahead without cutting corners here

and there.

Barnum was wrong when he said, "There's a sucker

born every minute."

It is wise to flatter important people.

All in all, it is better to be humble and honest than

important and dishonest.

1.

2.

3.

4.

5.

6.

Note: Those circled represent hypothetical response.

"Handle People"

"Give Real Reasons"

"Cut Corners"

"Barnum"

"Flatter"

"Better to Be Honest"

1.

2.

3.

4.

5.

6.

SA A DK D SD

+5 +4 +3 +2 +1

+1 +2 +3 +4 +5

+1 +2 +3 +4 +5

+5 +4 +3 +2 +1

+1 +2 +3 +4 +5

+5 +4 +3 +2 +1

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260 Chapter 10 • Scaling and Index Construction

measured; that is, "strong agreement" is assigned a low score or denotes low *Machiavellianism.*

Such reversals are standard in Likert scales to avoid *response sets*-patterns of consistent

responses in which the respondent reads only the first few items and, on the basis of these

responses, merely circles the remaining responses in a similar pattern. Such response sets can

be spotted by noting straight vertical patterns or widely inconsistent extreme responses that are

highly unlikely. If response sets appear despite reversals, the analyst may decide to discard the

case entirely because the subject did not act in good faith by providing his or her true feelings.

Standardized examinations such as the Scholastic Aptitude Test (SAT) or Graduate Record Exam

(GRE) discourage test takers from merely guessing the answers to questions as time runs out by

deducting two points for incorrect items, while giving only one point for correct ones.

The Thurstone procedure for discarding weak questions was based on the disagreement

by the judges on the scoring weight to be assigned. Likert procedures skip this step of using

judges and accomplish the same thing by analyzing the responses after the fact. In the Likert

method, the respondents do the job that the judges do in the Thurstone procedure. Basically,

item analysis asks whether both high and low scorers answered particular items the same way.

If so, these items are considered nondiscriminating and therefore are eliminated from the scale.

By nondiscriminating, we mean that the responses to these questions add nothing to the final

scale measurement because they do not distinguish between high and low scores. For example,

if both high Machiavellians (scores over 20) and low Machiavellians (scores under 20) agreed

that "There's a sucker born every minute," then perhaps that question is not measuring manipulative

orientations and should be eliminated from the scale. It would be as if everyone got a

question correct or incorrect on a competitive test; such items do nothing to predict who will do

well or poorly and therefore should be eliminated. The final scale then would consist of only

those items that appeared to have variability or distinguish between high and low scores.

In the process of developing a scale, researchers begin with a much larger number of items

than they expect to employ in the final score. On the basis of elimination, the final scale is

trimmed down to the most useful items. Table 10.3 illustrates a hypothetical item analysis.

Taking the first item in Table 10.3, we find that the highest scorers (those that fell into the

top 25 percent of all respondents) scored 3.6, while the lowest scorers (bottom 25 percent) scored

3.2. Little difference was exhibited between high and low scorers, and therefore, this item is

dropped from the final scale. Items 2 and 3 show large differences between high and low scorers

and thus are discriminating items to be retained. Item 4 shows little ability to distinguish high

from low scorers and is also eliminated.

A major shortcoming of Likert scaling is that on the basis of the total scale score it is

impossible to predict the exact endorsement of each individual item. Suppose a person's

Machiavellianism score from Figure 10.4 was 20. On the basis of this score, can we predict how the

individual responded to item 4, "Barnum was very wrong when he said, ‘There's a sucker born

TABLE 10.3 Hypothetical Item Analysis

Item

Average Score

of Top Quartile

Average Score

of Low Quartile

1 3.6 3.2

2 4.1 1.7

3 3.9 1.2

4 2.6 2.2

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Chapter 10 • Scaling and Index Construction **261**

every minute' "? No, such a total score could be obtained with a person circling any of the response

categories supplied.

The following is a *summary of Likert scaling procedures.*

A large number of items are selected and about evenly expressed as either positive or

negative statements regarding the subject of investigation.

For each item, the respondent is asked to respond using usually a five-point scale (strongly

agree, agree, don't know, disagree, and strongly disagree).

The total score for each individual is the simple sum of all items although the researcher

should exercise caution in identifying and scoring appropriate reversals or items that were

negative.

Items that lack variability or fail to distinguish between high and low scores are eliminated

from the final scale.

Only those items retained in the final index are scored and used in the final analysis.

Handling Missing Data in Likert Scale Construction. Even with the provision of "don't

know" categories, some respondents may answer all but a few items in a scale. If a large number

of respondents fail to answer a particular item, then that item should be eliminated from the

scale. If the missing item is one of a series of measures of the same basic dimension, we could

assign to that item the average score for the items answered. For example, if an individual

answers nine of ten questions on the same subject and the nine scores average 2.5, then a score

of 2.5 can be assumed for the missing response. Obviously, if too many nonresponses exist, it

may be necessary to drop the respondent from analysis. Although there is no universal rule, it

would seem reasonable that if more than three of ten responses are not ascertained, the individual's

responses for the entire set of scale items should be dropped from the analysis. Another

alternative to substituting the average score from the items answered is to assign an intermediate

score to missing responses (Orenstein and Phillips, 1978, p. 268). For instance, if the scoring for

the item ranges from 1 to 5, a three would be assigned. Although simpler than the other procedure,

such assignment tends to reduce or inflate the total scores of high and low scorers.

Guttman Scales

Guttman scales were developed as one outcome of a research series conducted by social scientists

during World War II (Guttman, 1944, 1950). Sometimes referred to as scalogram analysis, but

more often referred to by the name of its developer, Louis Guttman, **Guttman scaling **insists

that an attitudinal scale be based on **unidimensionality**; that is, it should measure one and only one

dimension or concept. In our Machiavellianism example, it may appear that the items are measuring

things other than Machiavellianism, for instance, cynicism, honesty, and practical judgment.

Guttman procedures provide a quantitative procedure by which to approach this issue.

The major advantage of Guttman scaling over Likert scaling is that from the final scale

score one should be able to predict the exact pattern of item endorsement. As in our previous

example, a score of 20 on the Machiavellianism scale (Figure 10.3) would enable a fairly accurate

prediction that a person scored, let us say, 2 on the "Barnum" question. Before going into the

quantitative aspects of the Guttman procedure, let us first provide some examples and follow the

logic of the procedure. Figure 10.6 presents two hypothetical examples.

In examining each of the scales in Figure 10.5 , note that the items are progressively more

difficult. Additionally, endorsement of the more difficult items almost presupposes that one

Unidimensionality

Guttman scale

ISBN 0-558-58864-6

Research Methods in Criminal Justice and Criminology, Eighth Edition, by Frank E. Hagan. Published by Prentice Hall. Copyright © 2010 by Pearson Education, Inc.

262 Chapter 10 • Scaling and Index Construction

Mathematical Ability Scale Spelling Ability Scale

1. Can you *add *and *subtract? *1. Can you spell *CAT?*

YES NO YES NO

2. Can you do *long division? *2. Can you spell *CATTLE?*

YES NO YES NO

3. Can you *solve equations *with one unknown? 3. Can you spell *CATASTROPHE?*

YES NO YES NO

262 Chapter 10 • Scaling and Index Construction

FIGURE 10.6 Hypothetical Guttman Scales. *Source*: The Theft Scale is from Hirshi and Selvin

(1973, p. 64) and the Fear of Crime Scale was suggested by Baumer and Rosenbaum (1980).

FIGURE 10.5 Hypothetical Guttman Scales. *Source*: The Mathematical Ability Scale is from

Cole (1972, p. 52).

Theft Scale Fear Of Crime Scale

Have you ever taken: Are you afraid:

1. Things of little value? YES NO In the city? YES NO

2. Things of moderate value? YES NO Down the block? YES NO

3. Things of large value? YES NO Outside own house? YES NO

Inside own house? YES NOQuestion #1 Question #2 Question #3

(Add & Subtract) (Long Division) (Simple Equation)

(Cat) (Cattle) (Catastrophe)

1.

2.

3.

Response 4.

Patterns 5.

6.

7.

8.

would have affirmatively answered the previous items. Figure 10.7 presents a Guttman analysis

of the possible response patterns for these scales. There are eight possible combinations of

responses to these items. Assume that these scales measure spelling or mathematical ability, and

that anyone who can do the more difficult problems can do the less difficult ones and that the

opposite is seldom true. Which response patterns are unlikely? Patterns 3, 5, 6, and 7 are unlikely

or are considered errors in the predictability of the scales. Because no scale can be completely

accurate, Guttman suggests that a 90 percent coefficient of reproducibility is the minium

FIGURE 10.7 Possible Response Patterns in the Guttman Scales: , Ability to Perform;

, Inability to Perform.

Chapter 10 • Scaling and Index Construction **263**

nature of scoring, that Guttman attempted to build into his scaling procedure.

The *coefficient of reproducibility *is calculated in the following manner:

That is, on the basis of the scale score, one should be able to predict the exact pattern of

response, although as much as 10 percent of the time one could be in error in doing so. The "Spelling

Ability Scale" in Figure 10.7 ranges from 0 (no spelling ability) to 3 (very good spelling ability).

Although a score of 2 could be obtained by means of response patterns 2, 3, and 5, only response

"cat" and "catastrophe" but not "cattle," as in response 3 or be able to spell the latter two without

knowing how to spell "cat," as in response 5. Thus, if the scale is unidimensional, a score of 2 should

enable you to predict with at least 90 percent accuracy that the individual endorsed items 1 and 2 but

not 3. If greater than 10 percent error were introduced by anomalies with regard to item 2, "cattle," the

scale would need to be reconstructed with "cattle" dropped in favor of a more workable substitute.

Although Guttman scaling has a distinct advantage over Likert scaling in that it provides the

facility to predict a fairly precise pattern of response to each item given the final scale score, its

insistence on unidimensionality may be too rigid a demand. Many concepts, particularly abstract

ones, may be multidimensional in nature and therefore not amenable to Guttman scaling.

A different series of complex traits may feed together to provide similar composite scores.

For example, perhaps in a scale measuring counselor effectiveness, it is discovered that people

scoring above average on a hypothetical scale are most effective; however, such a score could be

obtained by those rated excellent in knowledge but average in empathy, as well as those rated

only average in knowledge but excellent in empathy. An insistence on unidimensionality in this

instance would be inappropriate. Many important concepts are multidimensional. The insistence

on Guttman scaling procedures may become a "fetish" (Hirschi and Selvin, 1973, p. 209) similar

to the misuse of some statistical tests of significance.

The following is a *summary of Guttman scaling procedures*:

Construct a large number of items that appear on face validity to measure the concept.

Pretest the instrument by administering it to a sample of people.

Any item with greater than 80 percent agreement or disagreement should be discarded

from the analysis and final scale.

Order respondents from highest score (most responding "yes" to each item) to lowest score

(fewest "yes" responses).

Also order items from left to right, from most favorable to least favorable responses.

After discarding those items that fail to discriminate between high and low scorers,

calculate the coefficient of reproducibility where errors are defined as those responses

that are out of the predictable pattern.

If the coefficient of reproducibility equals 0.90 or higher, then scalability or unidimensionality

is assumed.

The respondent's final score is calculated by simply summing the number of favorable

items (Miller, 1991, p. 90).

Reproducibility = 1 -

Numbers of errors

Numbers of responses

Customer reply replied 9 years ago

Chapter 10 • Scaling and Index Construction **263**

nature of scoring, that Guttman attempted to build into his scaling procedure.

The *coefficient of reproducibility *is calculated in the following manner:

That is, on the basis of the scale score, one should be able to predict the exact pattern of

response, although as much as 10 percent of the time one could be in error in doing so. The "Spelling

Ability Scale" in Figure 10.7 ranges from 0 (no spelling ability) to 3 (very good spelling ability).

Although a score of 2 could be obtained by means of response patterns 2, 3, and 5, only response

"cat" and "catastrophe" but not "cattle," as in response 3 or be able to spell the latter two without

knowing how to spell "cat," as in response 5. Thus, if the scale is unidimensional, a score of 2 should

enable you to predict with at least 90 percent accuracy that the individual endorsed items 1 and 2 but

not 3. If greater than 10 percent error were introduced by anomalies with regard to item 2, "cattle," the

scale would need to be reconstructed with "cattle" dropped in favor of a more workable substitute.

Although Guttman scaling has a distinct advantage over Likert scaling in that it provides the

facility to predict a fairly precise pattern of response to each item given the final scale score, its

insistence on unidimensionality may be too rigid a demand. Many concepts, particularly abstract

ones, may be multidimensional in nature and therefore not amenable to Guttman scaling.

A different series of complex traits may feed together to provide similar composite scores.

For example, perhaps in a scale measuring counselor effectiveness, it is discovered that people

scoring above average on a hypothetical scale are most effective; however, such a score could be

obtained by those rated excellent in knowledge but average in empathy, as well as those rated

only average in knowledge but excellent in empathy. An insistence on unidimensionality in this

instance would be inappropriate. Many important concepts are multidimensional. The insistence

on Guttman scaling procedures may become a "fetish" (Hirschi and Selvin, 1973, p. 209) similar

to the misuse of some statistical tests of significance.

The following is a *summary of Guttman scaling procedures*:

Construct a large number of items that appear on face validity to measure the concept.

Pretest the instrument by administering it to a sample of people.

Any item with greater than 80 percent agreement or disagreement should be discarded

from the analysis and final scale.

Order respondents from highest score (most responding "yes" to each item) to lowest score

(fewest "yes" responses).

Also order items from left to right, from most favorable to least favorable responses.

After discarding those items that fail to discriminate between high and low scorers,

calculate the coefficient of reproducibility where errors are defined as those responses

that are out of the predictable pattern.

If the coefficient of reproducibility equals 0.90 or higher, then scalability or unidimensionality

is assumed.

The respondent's final score is calculated by simply summing the number of favorable

items (Miller, 1991, p. 90).

Reproducibility = 1 -

Numbers of errors

Numbers of responses

264 Chapter 10 • Scaling and Index Construction

Judy Andrews et al. (1991) used Guttman scaling procedures to construct an Adolescent

Substance Use scale. The scale was constructed using the following progression:

1. Had never used substances

2. Had used alcohol

3. Had used cigarettes

4. Had used marijuana

5. Had used at least one hard drug during the previous six months

The coefficient of reproducibility for the scale was approximately 0.96, which exceeded

the 0.90 limit for a Guttman scale.

Some examples of the use of Guttman scales in criminal justice research are found in Scott

(1959), Arnold (1965), Nye and Short (1957), and Dentler and Monroe (1961). One of the earliest

pieces of research in the social sciences that exhibited cumulative qualities was Bogardus'

"Social Distance Scale" (1933). Each respondent was asked to indicate the closeness of relationship

they were willing to accept with a variety of ethnic groups. The response categories were:

1. Would exclude from my country

2. As visitors only to my country

3. To citizenship in my country

4. To employment in my occupation

5. To my street as neighbors

6. To my club as personal chums

7. To close kinship by marriage

With 7 indicating highest acceptance or least social distance and 1 indicating the converse,

index scores could be devised to rate the relative acceptance of various groups. Similar

criminal justice applications in which types of criminals are substituted for ethnic groups

seem possible.

In their excellent review of delinquency research, Hirschi and Selvin (1973) indicate an

element of Guttman scaling that may be overlooked by those analyzing self-report data.

Guttman scaling of items such as Figure 10.6 is appropriate only if the period during which the

acts could have taken place is relatively long. If the time span were short, it would be possible

that an individual committed a more serious act and not less serious ones, during the specified

period, thus making a Guttman scale inapplicable (see also Dentler and Monroe, 1961). In measuring

delinquent acts, it makes more sense to concentrate on more recent acts rather than acts

over an extended time period. "Suppose the boy with three delinquent acts committed all of

them within the preceding year, while the boy with five delinquent acts committed none in that

period. At the time of the study, which boy is more delinquent?" (Hirschi and Selvin, 1973,

p. 65). A more valid measurement would be gained by restricting the time period and thus not

using Guttman scaling because it makes sense to concentrate on more recent acts, rather than

those that may have occurred at any time.

OTHER SCALING PROCEDURES

The three types of attitude scales that we have discussed-Thurstone, Likert, and Guttman-are

the key generic classifications of such scales; most others can be viewed as variations.

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Chapter 10 • Scaling and Index Construction **265**

1. painful :__:__:__:__:__:__:__: pleasurable

2. orderly :__:__:__:__:__:__:__: disorderly

3. trivial :__:__:__:__:__:__:__: important

4. masculine :__:__:__:__:__:__:__: feminine

5. popular :__:__:__:__:__:__:__: lonely

6. poor :__:__:__:__:__:__:__: wealthy

7. individualistic :__:__:__:__:__:__:__: conformist

8. mature :__:__:__:__:__:__:__: childish

9. right :__:__:__:__:__:__:__: wrong

10. lonely :__:__:__:__:__:__:__: well liked

Q Sort

Q sort methodology is a newer variation of the Thurstone process; the respondents rather than

the judges place a series of statements into previously predetermined categories (Stephenson,

1953). The individual's sorting is scored and summed into an index. Farrington (1973) had a

group of English juveniles place thirty-eight cards on which various crimes were printed in

two different piles-"have done it" and "have not done it." In investigating attractiveness and

juvenile delinquency, Cavior and Howard (1973) had a group of college students sort pictures

of delinquents and nondelinquents into five categories ranging from 1 (very attractive) to

5 (very unattractive).

Semantic Differential

The **semantic differential **usually consists of a seven- or nine-point bipolar rating scale in

which individuals are asked to indicate their perception of a tag or description that is provided.

Originally developed in the field of linguistics as a nondirective means of measuring the subjective

meaning of words to respondents (Snider and Osgood, 1969; Osgood et al., 1957), it has

been found to be an exceptionally versatile tool in attitudinal research. In particular, the semantic

differential has been found to be useful in cross-cultural research and with a wide cross

section of the population with broad ranges in education and vocabulary level. An illustration of

the use of the semantic differential in research related to criminal justice would be an examination

of labeling theory-seeing whether people are viewed as being what they do. That is, a

person who has an alcohol problem is viewed as an alcoholic, or one with a drug problem as

a drug addict. Figure 10.8 illustrates a typical semantic differential scale.

Suppose our sample scale were to be used in this study: Subjects would be asked to

respond to their interpretation of the term *heroin *using the scale and then *heroin addicts *using a

second page containing the same scale. Subjects asked to fill out a semantic differential scale

typically say, "What is it that I am to do?" or "I do not see where some of the things we are to rate

are applicable to the subject." The monitor should merely reply: "Do the best you can."

Each respondent checks off the point on the scale for each item that corresponds to their

reaction to that concept. One obvious advantage of the semantic differential is that the researcher

need not tediously prepare a large series of statements but rather merely add the concept to be

Q Sort

methodology

Semantic

differential

FIGURE 10.8 Semantic Differential Scale.

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266 Chapter 10 • Scaling and Index Construction

rated to a previously constructed scale as in Figure 10.8. Obviously, the bipolar descriptors must

be altered so that they are appropriate for the evaluation of the concept under analysis.

In an interesting use of the semantic differential scale, Thielbar and Feldman (1978) had

subjects rate different forms of deviant behavior and those who perform such activities on an

eleven-point scale featuring twenty-four bipolar adjectives for each type, such as kind-cruel,

good-bad, and honest-dishonest. Of the eleven types of behavior evaluated, rapists and child

molesters were the most negatively regarded and welfare recipients and marijuana smokers the

least negatively regarded.

In a Chicago study, Short and Strodtbeck (1965) asked black and white gangs to rate various

forms of conduct by means of the semantic differential. They found that gang boys tended to rate

such middle-class values as school, saving, and reading as high, as did nongang middle-class boys;

however, these same gang boys tended to rate pimping, fighting, and similar behavior higher than

did the nondelinquent nongang boys. Nevertheless, that nongang nondelinquent and gang boys

gave the same ratings to middle-class values has important implications with respect to some leading

subcultural theories of juvenile delinquency (Cohen, 1955; Cloward and Ohlin, 1961).

Other Variations

There are perhaps an infinite variety of scales depending on subject matter. In addition to consulting

handbooks that review scales used in previous studies, researchers should examine useful

literature that discusses scaling procedures (Edwards, 1957; Maranell, 1974; Oppenheim, 1966;

Shaw and Wright, 1967; Torgerson, 1958; Summers, 1970).

Brodsky and Smitherman, in theirDelinquency (1983), have performed a real service for researchers in criminology and criminal

justice by collating hundreds of scales and indexes applicable to these fields. This handbook

outlines the scales available to measure a particular concept, describes their development and

scoring, and generally assesses their reliability (consistency/stability) and validity (accuracy). The

scales are organized by topical area, and references to sources are provided. In some cases, actual

scale items are included. The scales are also classified by target and purpose. The *research targets*

of criminal justice scales are law enforcement/police, courts/the law, corrections, delinquency,

offenders, crime/criminality, and general scales/citizens. *Scale purposes *include attitudes, behavior

ratings, personality assessment, milieu ratings, prediction, and description. The following list

is a sample of the scales described:

Niederhoffer Cynicism Scale

Police Job Stress Interview

Attitude Toward Law Scale

Competency Screening Test

Judicial Role Perception Scale

Attitude Toward Death Penalty

Prison Adjustment Index

Prisoner-Therapist Q Sort

Parole Adjustment Scale

Recidivism Prediction Scale

Prison Guard Job Perception

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Chapter 10 • Scaling and Index Construction **267**

Delinquency Attitude Scale

Nye and Short Self-Reported Delinquency Scale

Compulsive Masculinity Scale

Rokeach Dogmatism Scale

Delinquency Proneness Scale

Teenage Slang Test

Differential Association Questionnaires

Sellin-Wolfgang Delinquency Index

Severity of Offense Scale

Criminally Insane Attitude Scale

Inmate Personality Survey

I-Level Classification

Perception of Addicts Scale

Attitude Toward Violence Scale

Legal Dangerousness Scale

Crime Seriousness Ratings

Authoritarianism Scale

F Scale (Fascism)

Alienation Scale

Instead of developing their own measurements, researchers should review available measures

and, unless theirs are clearly superior, consider using or modifying an existing index. By utilizing an

available measure, a researcher is also replicating findings, an important feature of maturing sciences.

Below is a list of useful handbooks of scales in the social sciences:

S. Brodsky and H. O'Neal Smitherman.Delinquency. New York: Plenum Press, 1983.

A. L. Comrey, E. Baker, and M. Glaser. *A Sourcebook for Mental Health Measures. *Los

Angeles: Human Interaction Research Institute, 1973.

B. A. Goldman and J. L. Saunders.Measures. New York: Behavioral Publications, 1974.

O. G. Johnson. *Test and Measurements in Child Development: Handbook II. *Volumes 1

and 2. San Francisco: Josey Bass, 1976.

D. G. Lake, B. Miles, and R. B. Earle, Jr. *Measuring Human Behavior. *New York:

Columbia University, 1973.

S. B. Lyerly. *Handbook of Psychiatric Rating Scales. *2nd ed. Washington, D.C.: U.S.

Government Printing Office, 1973.

D. C. Miller. *Handbook of Research Design and Social Measurement. *4th ed. Thousand

Oaks, CA: Sage, 1987.

J. L. Price. *Handbook of Organizational Measurement. *Lexington, MA: D.C. Heath, 1972.

J. P. Robinson and R. Shaver. *Measures of Social Psychological Attitudes. *Ann Arbor, MI:

Institute for Social Research, 1971.

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268 Chapter 10 • Scaling and Index Construction

M. E. Shaw and M. Wright. *Scales for the Measurement of Attitudes. *New York:

McGraw-Hill, 1967.

A. Simon and E. G. Boyer. *Mirrors for Behavior III: An Anthology of Observation Instruments.*

Wyncote, PA: Communication Materials Center, 1974.

M. A. Straus. *Family Measurement Techniques: Abstracts of Published Instruments*,

1935-1965. Minneapolis, MN: University of Minnesota Press, 1969.

Murray Straus' measurement of domestic violence serves as an example of a popular scale.

Straus, in 1975 and again in 1985, conducted some of the first national surveys of domestic

violence in the United States. Using face-to-face interviews in 1975 and telephone surveys in

1985, Straus and associates developed a "conflict tactics scale" that consisted of the following

items (Straus and Gelles, 1986):

Types of Violence

A. Minor

1. Threw something

2. Pushed/grabbed/shoved

3. Slapped/spanked

B. Severe

4. Kicked/bit/hit with fist

5. Hit, tried to hit with something

6. Beat up

7. Threatened with gun or knife

8. Used gun or knife

The violence indices were overall (1-8), severe (4-8), and very severe (4, 6, 8).

Sherman et al.'s Scientific Methods Scale (SMS)

The Scientific Methods Scale (SMS) was developed as part of the evaluation of "What Works?"

commissioned by the U.S. Congress and carried out by the University of Maryland's Department

of Criminology and Criminal Justice in 1997 (Sherman et al., 1997). The Maryland Report, as it

became known, was later updated (Sherman et al., 2002). The SMS is a five-point scale that evaluates

the methodological rigor and type of research design of studies. The SMS scores were

awarded and determined as follows:

1. A relationship exists between a crime prevention program and a measure of crime or crime

risk factors.

2. A temporal sequence or time order exists between the program and the crime or risk outcome,

or a comparison group is present without demonstrated comparability to the treatment group.

3. A comparison between two or more units of analysis, one with and one without the

program, is present.

4. A comparison of multiple units with and without the program, controlling for other factors

or a nonequivalent comparison group, has only minor differences evident.

5. Random assignment and analysis of comparable units to the program and comparison

groups take place.

Programs with scores of "1" to "4" are considered "nonexperiments," while those with a score of

"5" are considered randomized controlled experiments (Lum and Yang, 2005).

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CRIME SERIOUSNESS SCALES

Previous criticism of the UCR crime index indicated that one of its major shortcomings is that it

represents an unweighted index. No consideration is given to the type of crime; that is, a homicide

and a petty theft have equal weight. **Crime seriousness scales **attempt to assign weight to crimes

in terms of their relative severity.

Sellin-Wolfgang Index

Despite early work by Thurstone and Chave (1929), the pioneering work in the area of crime

seriousness ratings was performed by Sellin and Wolfgang (1966), who had a group of respondents

(police officers, juvenile court judges, and college students) rate descriptions of criminal

incidents on the basis of amount stolen, method of intimidation, and degree of harm inflicted.

They actually employed two different types of measures: an eleven-point rating scale and a

magnitude scale (to be discussed shortly). On the basis of a relatively complex methodology

(see their book for greater detail), they were able to develop a crime seriousness scale or weighting

system for crime based on bodily injury, property theft, and damage. Thisindex tries to account for both the quality (seriousness) and the quantity of an act. For example,

a robbery involving no injury but a loss of $5 because of verbal intimidation would receive

a crime seriousness score of 3: no points for lack of injury, 1 point for economic loss of $5, and

2 points for verbal intimidation. These scores were arrived at on the basis of analysis of respondents'

previous seriousness ratings of descriptions of various crimes. The following are some of

the scores (weights) produced by the Sellin-Wolfgang index:

Crime

seriousness

scales

Sellin-

Wolfgang

index

Assault (death) 26

Forcible rape 11

Robbery (weapon) 5

Larceny ($5,000) 4

Auto theft (no damage) 2

Larceny ($5) 1

Assault (minor) 1

An extensive literature has since developed on crime seriousness measures, and although

some cross-cultural and subcultural differences have been found (Akman et al., 1967; Hsu, 1973),

various replications have demonstrated striking similarities (Rossi and Henry, 1980). Blumstein

(1974) assigned similar seriousness weights to UCR data and came up with results similar to the

Sellin-Wolfgang index, and the index was found useful in a Prosecutor's Management

Information System (PROMIS) in which prosecutors set prosecution priorities on the basis of

various factors, including crime seriousness (Jacoby, 1975).

Types of Crime Seriousness Scales

There are two basic types of crime seriousness (severity) scales: simple rating scales and magnitude

scales. Simple rating scales of crime seriousness ask respondents to rate crime usually on a

scale ranging from 1 (not serious at all) to 9 (extremely serious). In surveys of residents of

Baltimore, Maryland (Rossi et al., 1974; Rossi and Henry, 1980), and Macomb, Illinois (Cullen,

Link, and Polanzi, 1982), respondents were asked to rate roughly 140 descriptions of crime using

the nine-point scale. The average score for each crime is used as the measure of crime seriousness.

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270 Chapter 10 • Scaling and Index Construction

Such simple rating scales are ordinal (result in relative rankings) and are unable to take

into account the magnitude of the differences between scale scores. For example, is a planned

killing only about three times more serious than loitering? They cannot be used to weight crime

seriousness, although they are useful in examining relative changes in public ratings (rankings of

crime seriousness) over time. This problem becomes apparent when almost all of the 140 crimes

rated were given scores above the theoretical midpoint of 5.

Magnitude scales measure public rankings of the degrees of relative seriousness of various

crimes. They are an attempt to develop interval/ratio level scores that can be assigned to various

criminal acts. Our description of the Sellin-Wolfgang index was such an example. Another is the

following case of the *National Survey of Crime Severity*, which was designed by Wolfgang et al.

(1985) and conducted in 1977 as a supplement to the NCS. As you may recall, the NCS surveys

60,000 households and thus is the *largest crime seriousness study ever conducted. *Similar to the

methodology employed in the Sellin-Wolfgang index, respondents were

Each given a description of a crime, "A person steals a bicycle parked on the street,"

and told that the seriousness of this crime was 10. They were then given a list of other

crimes and told to compare them in seriousness to the bicycle theft. If a crime seemed

to be twice as serious, they were to rate it at 20. If it were four times as serious, they

were to rate it 50, and so on. Each person rated twenty-five crimes, but not everyone

had the same twenty-five. Overall, 204 items, each of which was illegal in at least one

state, were rated.

Combining the ratings given by each of the 60,000 respondents, a single severity

score was developed for each of the 284 items (crimes). (Klaus and Kalish, 1984, p. 2).

Table 10.4 reports some of the scores of the 204 events measured in the NCS crime seriousness

study.

The present emphasis on "just desserts"-"let the punishment fit the crime"-suggests

that research on crime seriousness scales and other attempts to quantify dangerousness and

career criminals will continue.

PREDICTION SCALES

A rich tradition exists in the field of corrections of attempting to develop **prediction scales**, or

experience tables, as they are sometimes called. Such scales attempt to assign scores that hopefully

predict the likelihood of an individual committing crime or being a success or failure on

probation or parole (Hood and Sparks, 1971, pp. 171-192; Simon, 1971, p. 1015; Gottfredson

and Ballard, 1966). Some of the earliest work in this area was performed by the Gluecks (1960)

and Mannheim and Wilkins (1955). The Gluecks attempted to develop a Social Prediction Table

Planned killing for a fee 8.9

Forcible rape of a neighbor 8.4

Armed bank robbery 8.2

Child battering 8.0

Armed robbery ($200) 7.6

Loitering in public place 3.5

Strong relative agreement is found among the Rossi and Cullen studies and similar studies. Some

examples of scores (rounded) from Cullen, Link, and Polanzi (1982, pp. 88-90):

Chapter 10 • Scaling and Index ConstructionTABLE 10.4 The National Survey of Crime Severity: How People Rank

the Severity of Crime*

Severity

Score Offense

72.1 A person plants a bomb in a public building. (highest score)

52.8 A man forcibly rapes a woman. As a result of physical injury, she dies.

47.8 A parent beats his young child with his fists. As a result, the child dies.

33.8 A person runs a narcotics ring.

30.0 A man forcibly rapes a woman. Her physical injuries require hospitalization.

21.2 A person kidnaps a victim.

18.3 A man beats his wife with his fists. She requires hospitalization.

16.9 A legislator takes a bribe of $10,000 from a company to vote for a law favoring

the company.

14.6 A person, using force, robs a victim of $10. The victim is hurt and requires

hospitalization.

9.0 A person, armed with a lead pipe, robs a victim of $1,000. No physical harm occurs.

6.2 An employee embezzles $1,000 from his/her employer.

3.1 A person breaks into a home and steals $100.

1.6 A person is a customer in a house of prostitution.

0.8 A person under 16 years old runs away from home.

0.8 A person is drunk in public.

0.5 A person takes part in a dice game.

0.2 A person under 16 years old plays hooky from school.

*This represents only a selection of 204 items rated.

Source: Wolfgang, Marvin E., et al. *The National Survey of Crime Severity. *Washington, D.C.: U.S. Department

of Justice, 1985, pp. vi-x.

that would forecast the risk of a child becoming delinquent. An index was developed based on

the scores assigned to such items as family togetherness, parental love, disciplinary policies, and

supervision (Glueck and Glueck, 1950). Mannheim and Wilkins developed statistical prediction

tables attempting to forecast parole success. These are often referred to as experience tables or

base expectancy tables, because they are based on the experience of those who have already

undergone treatment. Risk groups are usually developed on the basis of past probabilities of failure

using items such as past record of offenses, seriousness of offenses, family conditions, age,

and work record. Mannheim and Wilkins used techniques such as multiple regression to choose

the most predictive variables and the relative weights to be assigned to each. Wilkins also assisted

the California Department of Corrections in developing similar "base expectancy tables"

(Hood and Sparks, 1971, p. 183). Ohlin (1951) developed parole prediction scales based on case

records, personality assessments, and more traditional items.

In criminal justice, prediction scales may be employed to assess probation/parole risk, to

establish sentencing guidelines, to predict "dangerousness," and to establish a scoring system for

targeting and incapacitating "career criminals."

Statistical predictions are based on the behavior patterns of an individual compared with

others of similar background. This is common in insurance or actuarial predictions. *Clinical predictions*,

on the other hand, are based on professional evaluation of individual behavior.

Farrington and Tarling (1983) indicate that actuarial predictions of human behavior have been

more successful than the individualized clinical element.

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272 Chapter 10 • Scaling and Index Construction

The Salient Factor Score

The **Salient Factor Score **has been used by the U.S. Parole Commission since the early 1970s to

objectively assess the likelihood of a prisoner's recidivism on parole. Six items are used to construct

a ten-point scale, which ranges from 0 (poor risk) to 10 (very good risk) (Hoffman, 1985):

1. The offender's prior criminal convictions

2. The offender's prior criminal commitments for longer than thirty days

3. The offender's age at the time of the new offense

4. How long the offender was at liberty since the last commitment

5. Whether the prisoner was on probation, parole, or escape status at the time of the most

recent offense

6. Whether the prisoner has a record of heroin dependence

The Salient Factor Score is combined with the seriousness of the current offense in a grid

to establish a guideline range for sentencing (see Table 10.5).

The example in Table 10.5 shows that an offender with a very low Salient Factor Score

may serve a sentence two or three times as long for the same offense as an offender with a high

score. Although problems exist with any prediction efforts (see Hoffman, 1984, 1985), the

Salient Factor Score has demonstrated clear differences in recidivism rates between categories,

although perfect prediction within categories is perhaps impossible.

Greenwood's "Rand Seven-Factor Index"

Greenwood's "**Rand Seven-Factor Index**" was aimed at *selective incapacitation*, individualization

of sentences on the basis of predictions that particular offenders are likely to commit serious

crimes at a high rate if not incarcerated (Blumstein et al., 1986; Cohen, 1983a, p. 1). A self-report

survey of inmates in which robbers and burglars admitted crime commission during the two years

preceding incarceration yielded an index that came up with predictive results quite similar to those

Salient Factor

Score

TABLE 10.5 Salient Factor Score Grid*

Salient Factor Score

Offense Severity

Category Example

Very good

(10-8)

Good

(7-6)

Fair

(5-4)

Poor

(3-0)

1 Low Minor theft 6-10 8-12 10-14 12-14

2 Low/moderate Forgery/fraud (under $1,000) 8-12 12-16 16-20 20-25

3 Moderate Motor vehicle theft 12-16 16-20 20-24 24-30

4 High Robbery (no weapon) 16-20 10-16 26-32 32-38

5 Very high Robbery (weapon) 24-36 36-48 48-60 60-72

6 Greatest Willful homicide (scores vary because of extreme variations

in cases)

*This is a compilation and abridgement for illustration purposes, as the Salient Factor Scores undergoes revision

over time and may not reflect current sentencing guidelines. (All figures are months for a given sentencing

guideline range.)

Source: Compilation of Hoffman, Peter. "Predicting Criminality." *Crime File Series*, Washington, D.C.: National

Criminal Justice 11 (1984): 539-547.

Rand Seven-

Factor Index

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Chapter 10 • Scaling and Index Construction **273**

of the Salient Factor Score (Hoffman, 1985, p. 3; Greenwood and Abrahamse, 1982). Seven

variables were selected to form a simple additive scale from 0 (low risk) to 7 (high risk):

1. Prior conviction for same charge

2. Incarcerated more than 50 percent of preceding two years

3. Convicted before age 16

4. Served time in state juvenile facility

5. Drug use in preceding two years

6. Drug use as a juvenile

7. Employed less than 50 percent of preceding two years

Although space prohibits a full detailing of such predictive efforts (see Cohen, 1983b),

the forecasts of such scales are probabilistic, that is, not 100 percent accurate for each score.

The Greenwood scale had a 45 percent rate of "true positives" (sometimes called "hits") or correctly

identified that percentage of high-rate offenders; however, the "false-positive" ("misses"

or inaccurate prediction) rate was 55 percent, which was similar to findings by Monahan (1981)

who analyzed scales that attempt to predict potential violence or dangerousness. Kratcoski

(1985) points out that in the use of such instruments to decide probation supervision, it should

not be assumed that recidivism will be reduced at all supervision levels; instead, these instruments

should be used to ensure efficiency and productive allocation of resources within supervision

levels. Vito (1986) points out that in using different measures of the success of such

efforts, multiple outcomes of success must be employed: "The goals of intensive supervision

must be clearly specified and measured so that we avoid the premature crucifixion of intensive

supervision upon the cross of recidivism" (p. 24).

Career Criminal Programs

The police have had much less experience in using prediction devices to target police resources on

"repeat offenders" or "career criminals." The ROP (Repeat Offenders Project, pronounced "rope") of

the Washington, D.C., Metropolitan Police uses criminal informants and other sources of information

on criminals to concentrate police efforts on those most active in crime (Sherman, 1985; Martin and

Sherman, 1985). A similar program in Minneapolis combines formal and informal methods reviewing

"nominations" (of criminals to target) from many sources and extensive information and established

criteria in focusing on a small group of active criminals. Validation of the criteria employed in

both programs is incomplete, but the evaluation of the ROP targets by the Police Foundation noted

that all had criminal histories, all had been arrested the previous year, and, as a result of the program,

all were five times more likely to be arrested than were those randomly assigned to a control group

(Sherman, 1985). Officers assigned to the ROP program had a smaller number of arrests, but more

"quality arrests" of more serious, active criminals with records. The Police Foundation study was not

able to determine the impact of the program on reducing crime in the District of Columbia.

Prediction criteria employed by prosecutors (district attorneys) tend to be more formal

than those used by the police. A system employed in Charlotte, North Carolina, assigns weight to

such factors as alcohol or drug abuse, age, and length of criminal career to create a scale for

deciding which cases are most likely to be successfully prosecuted (Sherman, 1985).

An important caution in the utilization of prediction tables is that the administrator should be

careful that the group to be rated does not differ significantly in experience from the group on which

the base expectancy table was calculated. It is important that the table be validated or tested on samples

other than the original on whose experience it was developed (Simon, 1971; Wilkins, 1969).

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274 Chapter 10 • Scaling and Index Construction

Related to the prediction table tradition are numerous psychological studies that use

personality inventories and scales to discover a distinctive criminal personality. Tennenbaum

(1977), in an update of earlier reviews by Scheussler and Cressey (1950) and Waldo and Dinitz

(1967), reviewed studies employing various personality scales that attempt to distinguish criminal

from noncriminal personalities. Although 80 percent of the studies claimed to have found

personality differences, they failed to identify the complex, multidimensional nature of these

differences. The majority had greater variation within groups than between groups, and thus no

significant differences can be claimed (Tennenbaum, 1977, p. 19).

ADVANTAGES OF SCALES

The development of scale measurement *enables more exact measurement of phenomena *from

simple nominal to ordinal or interval level. Rather than vaguely suggesting that City A has a

bigger problem than City B, one could indicate that, according to the 1980 victimization index

for eight specific crimes, the rate of crime was 30.6 per 1,000 in City A and 21.2 per 1,000 in

City B. Thus, more quantitatively precise measurement can be obtained by means of scales.

Scales lend themselves to replication and the longitudinal measurement of even small

changes in the phenomena under investigation. For example, the index offense crime rate

may increase from 30.6 to 30.8 per 1,000. The construction of scaled measurementmore rigorous thinking in that the researcher is involved in a systematic approach to operationalization.

DISADVANTAGES OF SCALES

A principal critique of the use of scales is a philosophical one and relates to an anti-quantitative

approach to research. Those who oppose the scaling tradition question whether it really measures

what it is claimed to measure ora five- or seven-point scale. In the same light, there may be little relationship between a scaled

measurement and the entity being measured. Some antiempiricists feel that rather than speak of

errors in measurement we should speak of the *"error of measurement." *As with any measurement,

scales are subject to problems of unreliability and invalidity.

Despite these and other criticisms, scaling is widely used in the social sciences and criminal

justice and has been found useful in measuring a variety of concepts such as personality, occupational

aptitude, authoritarianism, self-concept, cost of living, urbanization, industrialization,

anomie, alienation, social class, crime, marital satisfaction, and job satisfaction.

These problems are not by any means exclusive to the development of scales in criminal

justice. In the field of economics, the widely used Consumer Price Index (CPI) has been

under attack despite the fact that it is generally considered one of the best price measures in

the world. This index represents the composite average increase in prices consumers pay for

such items as shelter, food, utilities, clothing, furnishings, upkeep, transportation, health, and

entertainment. With the double-digit inflation of the early 1980s being fired primarily by

high housing costs, interest, and gasoline prices, critics charged that the CPI tended to exaggerate

the inflation rate for those consumers whose spending pattern differed from the average

pattern. That is, consumers who already owned their home or car in that given year may

have been unaffected by as much as 40 percent of the rise in the inflation rate (Fritz, 1980,

p. 86; Samuelson, 1974, pp. 34-35).

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Chapter 10 • Scaling and Index Construction **275**

Item analysis

Summary

Scaling is the process of attempting to develop composite

measurement or ranked or unit measurement of

phenomena. The *levels of measurement *are nominal,

ordinal, interval, and ratio. *Nominal *measurement is

the simple placement of objects into categories in

which the actual numbers assigned have no mathematical

meaning. *Ordinal *measurement entails the

ability to assign ranks, higher to lower. *Interval *measurement

assumes equal units or distances between

the scores. *Ratio *measurement assumes, in addition to

equal units, a meaningful zero point.

Arbitrary scales are constructed on the basis

of the judgment of the researcher. The Uniform

Crime Report (UCR) is an arbitrary scale that, in the

opinion of those who constructed it, reflects most

serious crimes as well as those crimes for which

police departments generally have the best records.

A major limitation of the UCR is that it fails to take

into account the relative seriousness of the crimes,

which are simply summated into an index.

There are *three major types of attitude scales*:

Thurstone, Likert, and Guttman. Other scaling procedures

covered in this chapter are Q sort, semantic differential,

factor analysis, and prediction scales.

Thurstone scales make use of a series of judges to

decide on appropriate scale items. A *Likert scale *is a

simple summated scale of items usually containing a

five-point response category ranging from "strongly

agree" to "strongly disagree." Likert scales typically

make use of reversal items to eliminate response sets.

In addition, **item analysis **is employed to eliminate

nondiscriminating items. *Guttman scales *insist on

unidimensionality-that one and only one dimension

be measured by a particular scale. The cumulative

nature of such a scaling procedure ensures a reasonable

(if proper reproducibility) ability to predict the

exact pattern of responses on the basis of an individual's

scale score.

Q sort methodology is a variation of the

Thurstone procedure in which the respondents place

statements written on cards into assigned scale categories.

The *semantic differential scale*, originally

developed in the field of linguistics, is a seven- or

nine-point bipolar rating system in which respondents

are asked to indicate their perception of a concept

or subject. *Factor analysis *is a procedure that

identifies underlying dimensions among a series of

scale items. Because many concepts are multidimensional,

factor analysis not only is useful in identifying

subscales, but also assigns factor loadings or weights

to items. Thus, the relative importance of each item is

taken into account in calculating scale scores.

The Scientific Methods Scale is a five-point

scale that measures the methodological rigor and

type of research design.

Crime seriousness scales attempt to measure

the gravity, or seriousness, of crime by means of

public ratings using either simple rating scales (e.g.,

a zero-to-nine scale) or magnitude ratings (e.g., the

Sellin-Wolfgang index or National Survey of Crime

Severity). *Prediction scales*, sometimes called experience

or base expectancy scales, are constructed on

the basis of past experience to predict future performance

usually in probation and parole. TheFactor Score is used by the U.S. Parole Commission

in assessing the likelihood of prisoner recidivism

and in the determination of sentencing. The Rand

Seven-Factor index and career criminal programs

represent similar prediction efforts.

The relative *advantages *of using scales is that

they provide more composite and exact measurement.

They lend themselves to longitudinal assessment

and replication studies, and they force more

rigorous thinking on the part of the investigator.

Disadvantages, on the other hand, point to the artificiality

of such measurement and the question as to

whether people really think in scale patterns.

Scaling is by no means a substitute for good theoretical

and substantive knowledge of the subject under

investigation.

There is no mysterious, magical, mechanized process that will ensure adequate indicators

for concepts. In this sense, scaling procedures and methodological wizardry are no substitute for

creative, logical, and sensitive theoretical conceptualization.

276 Chapter 10 • Scaling and Index Construction

Key Concepts

Nominal variables *252*

Ordinal variables *254*

Interval variables *254*

Ratio variables *254*

Scaling *255*

Arbitrary scales *255*

UCR index *256*

Thurstone scales *257*

Equal appearing intervals *257*

Likert scales *258*

Guttman scales *261*

Unidimensionality *261*

Q sort methodology *265*

Semantic differential *265*

Crime seriousness scales *269*

Sellin-Wolfgang Index *269*

Prediction scales *270*

Salient Factor Score *272*

Rand Seven-Factor Index *272*

Advantages/disadvantages

of scales *274*

Item analysis *275*

Review Questions

1. Discuss the three major types of attitude scales. What

are the unique features of each?

2. In a recent journal, find an example of a study employing

a scale. Describe the characteristics, scoring, reliability,

and validity of this measure.

3. What are the two types of crime seriousness scales and

of what utility are they in criminal justice research?

4. Discuss and give examples of the use of prediction

scales in criminology and criminal justice.

Useful Web Sites

Eric Clearinghouse on Assessment and Evaluation

www.ericae.net

converted/Measurement/

Identifying and Locating Mental Measurements

www.lib.auburn.edu/socsi/docs/measurements.htm

Developing Performance Measures for Criminal Justice

Programsmeasures.html

faculty,ncwc.edu/toconnor/308/308links.htm

fastmail.usf.edu/ugrads/mmc4420/guidelines%20for%

20writing%20likert%20items.htm

textbook/streliab.html

garson/pa765/standard.htm

Sample Test on Types of Reliability and Validity

www.selu.edu/academics/education/edf600/cw7d.htm

edu/classes/jerryb/rvc.html

ISBN 0-558-58864-6

**THIS IS THE END OF CHAPTER 10**

C H A P T E R

11 Policy Analysis and Evaluation

Research

Policy Analysis

Evaluation Research

Policy Experiments

Policy Analysis: The Case of the National

Institute of Justice Research Program

NIJ Mission Statement

NIJ Research Priorities

A Systems Model of Evaluation Research

Types of Evaluation Research

Will the Findings Be Used?

Is the Project Evaluable?

Who Can Do This Work?

Steps in Evaluation Research

Problem Formulation

Design of Instruments

Research Design

Data Collection

Data Analysis

Utilization

What Works in Criminal Justice?

Exhibit 11.1 Preventing Crime: What Works,

What Doesn't, What's Promising

The Campbell Collaboration (C2)

Obstacles to Evaluation Research

Researchers and Host Agencies

Summary

Key Concepts

Review Questions

Useful Web Sites

In the introductory chapter, we addressed the criticism that much criminological and criminal

justice research is either common sense or impractical. This chapter focuses on the latter concern:

"So what; of what practical use are these research findings?" We will apply what we have

learned to the tasks of policy analysis and evaluation research-the cutting edge of governmentsponsored

criminal justice research today.

POLICY ANALYSIS

Policy analysis is the "study of whatever governments choose to do or not to do," "the description

and explanation of the causes and consequences of government behavior" (Dye, 1995, pp. 3-4).

Jones (1977, p. 4) views policy analysis as the study of proposals (specified means for achieving

goals), programs (authorized means for achieving goals), decisions (specified actions taken to

implement programs), and effects (the measurable impacts of programs). Policy analysis is an

Policy

analysis

ISBN 0-558-58864-6

278 Chapter 11 • Policy Analysis and Evaluation Research

Evaluation

research

applied subfield of economics, political science, public administration, sociology, law, and statistics.

It involves the identification and description of social problems, the development of public

policies that may alleviate these problems, and determination of whether these policies work (Dye,

1995, p. 17). Although there are many models, perspectives, and approaches to policy analysis, the

policy process could be viewed as a series of political activities consisting of the following:

Identifying problems Demands are expressed for

government action.

Formulating policy proposals Agenda is set for public discussion.

Development of program proposals

to resolve problem.

Legitimating policies Selecting a proposal.

Building political support for it.

Enacting it as a law.

Implementing policies Organizing bureaucracies.

Providing payments or services.

Levying taxes.

Evaluating policies Studying programs.

Reporting "outputs" of government programs.

Evaluating "impacts" of programs on

target and nontarget groups in society.

Suggesting changes and adjustments

(Dye, 1995, p. 21).

Thus the policy process involves identification, formulation, legitimation, implementation, and

evaluation.

EVALUATION RESEARCH

Evaluation research is the last stage of the policy process; questions such as the following are

asked:

Do the programs work?

Do they produce the desired result?

Do they provide enough benefits to justify their costs?

Are there better ways to attack these problems?

Should the programs be maintained, improved, or eliminated?

Evaluation research is an applied branch of social science that is intended to supply scientifically

valid information with which to guide public policy. Historically, research in the social

sciences had its origins in the physical sciences and was oriented toward development of theories

and utilization of the experimental model to test those theories. Its concern was much more akin to

pure or basic research discussed in Chapter 1-the acquiring and testing of new knowledge.

Evaluation research as a type of applied research has different roots as well as intentions.

It evolved from the world of technology rather than science and emphasizes mission

or goal accomplishment and product/service delivery rather than theory formation.

Evaluation research aims to provide feedback to policy makers in concrete and measurable

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terms. Although such an approach has existed informally since early times, the introduction

of computer technology in the 1950s and its successful application to "defense systems" and

"space systems" have led to the application of evaluation research to "social systems" such

as the "criminal justice system." Much of this thinking grew out of the "Planning,

Programming, Budgeting Systems" (PPBS) approach originally employed by the U.S.

Department of Defense in the 1960s, a method of policy evaluation widely adopted by other

government agencies. PPBS attempts to specify (by clearly defining program objectives)

and quantify (by developing measures of accomplishments) the output of a government

program and to analyze the relative costs and benefits of the program (see Rossi and

Freeman, 1993).

As billions of dollars were poured into social programs in the 1960s, the following questions

were increasingly asked: Do the programs work or make a difference? Are they cost effective? Are

they the most efficient method of providing services? With fewer funds available at the turn of the

century, the same questions are still relevant: How can the best use be made of limited resources to

accomplish maximum program benefits?

Other than its very practical bent and some relatively esoteric techniques such as cost-

benefit analysis, many of the methodological procedures employed in evaluation research have

already been covered earlier in this text in Chapters 1-10. Thus, rather than viewing it as a different

type of research, readers can confidently assume that they can master the essentials of evaluation

research on the basis of knowledge of many of the issues we have already described. Quite

simply,of its specific goals, outcomes, or particular program criteria. Weiss (1972, p. 4) states that the

purpose of evaluation research is "to measure the effects of a program against the goals it set out

to accomplish as a means of contributing to subsequent decision making about the program and

improving future programming." It is essential to this purpose that the research methodology we

have discussed be used to measure program outcomes in terms of specifically identified criteria

in order to accomplish an applied or practical research objective-better programs. Similar to a

scientific experiment, the research methodology is applied to evaluate social action programs to

accomplish more efficient programs (Schwarz, 1980).

The National Advisory Committee on Criminal Justice Standards and Goals feels very

strongly about the importance of evaluation research:

A high quality evaluation is expensive and time-consuming. Indeed, it may be many

times more expensive than the operational program it is designed to test. Viewed in

the context of that single program, such an expenditure may appear absurd. But in

the context of advancement of knowledge, this type of concentration of funds is

more likely to be fruitful than the same expenditure on a large number of inadequate

evaluations would be. Progress does not depend on every program being evaluated;

in fact, with limited resources for evaluation, it may be retarded by such a practice.

(National Advisory Committee, 1976, p. 52)

Some workers involved in administering applied or action programs in criminal justice

may have either little understanding of evaluation, past exposure to poor evaluations, or perhaps

little regard for the necessity of evaluation as they are already committed to a particular programmatic

strategy. The logic of the National Advisory Committee statement would argue that a few

expensive, well-designed evaluations are in the long run more cost-effective in revising or eliminating

unnecessary treatments or procedures. The last point-elimination-is perhaps at the

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280 Chapter 11 • Policy Analysis and Evaluation Research

Policy

experiments

crux of the resistance to evaluations. Similar to early applications of social, scientific, and managerial

studies in industry, many of those to be studied obviously have an understandably vested

interest in maintaining a favorable image of the current procedures, practices, and staffing of

their organizations.

Policy Experiments

A close link between experimental methods and the assessment of public policy programs has

increased dramatically since 1970 (Fagan, 1990, p. 108). **Policy experiments **are applied field

experiments that address themselves to immediate practical policy questions. The National

Research Council's Committee on Research on Law Enforcement and the Administration of

Justice summarized the following steps in designing policy experiments (Garner and Visher,

1988, pp. 7-8):

1. Choose an interesting problem-a policy question that people really care about or an existing

procedure that clearly needs improvement.

2. Do some creative thinking to solve legal and ethical issues that may arise.

3. Rigorously maintain the random assignment of persons, cases, or other units into treatment

and control groups throughout the experiment.

4. Choose a design and methods of investigation that are appropriate both to the questions to

be answered and to the available data.

5. Adopt a team approach between researchers and practitioners and keep working in close

cooperation.

6. Put as much into your experiment as you want to get out of it.

7. Use an experiment to inform policy, not to make policy.

8. Understand and confront the political risks an experiment may involve.

9. Insofar as possible, see that the experiment is replicated in a variety of settings before

encouraging widespread adoption of experimentally successful treatments.

Before exploring evaluation research more thoroughly, let us first provide an example of a

policy analysis program that utilizes evaluation research.

POLICY ANALYSIS: THE CASE OF THE NATIONAL INSTITUTE

OF JUSTICE RESEARCH PROGRAM

Although policy analysis and evaluation research in criminology and criminal justice are not

restricted solely to government-funded research of primarily government-funded projects, and

the National Institute of Justice (NIJ) is not the only agency sponsoring criminal justice research,

NIJ does utilize the largest, most ambitious policy-oriented program of its type and has been

heralded by the National Academy of Sciences as a pioneer and model for other programs. For

this reason, we explore the philosophy, aims, and research program plan of the NIJ.

NIJ Mission Statement

The NIJ is a research branch of the U.S. Department of Justice. The Institute's mission is to

develop knowledge about crime, its causes, and methods of controlling it. Priority is given to

policy-relevant research that can yield approaches and information that state and local agencies

can use in preventing and reducing crime. The decisions made by criminal justice practitioners

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and policymakers affect millions of citizens, and crime affects almost all our public institutions

and the private sector as well. Targeting resources, assuring their effective allocation, and developing

new means of cooperation between the public and private sector are some of the emerging

issues in law enforcement and criminal justice that research can help illuminate.

Carrying out the mandate assigned by Congress in the Justice Assistance Act of 1984, the

NIJ aims to:

- Sponsor research and development to improve and strengthen the nation's system of

justice with a balanced program of basic and applied research.

- Evaluate the effectiveness of criminal justice and law enforcement programs, and identify

those that merit application elsewhere.

- Support technological advances applicable to criminal justice.
- Test and demonstrate new and improved approaches to strengthen the justice system.
- Disseminate information from research, development, demonstrations, and evaluations

(NIJ, 1994, p. 1).

In establishing its research agenda, the Institute is guided by the priorities of the Attorney

General and the needs of the criminal justice field. The Institute actively solicits the views

of police, courts, and corrections practitioners as well as the private sector to identify the

most critical problems and to plan research that can help resolve them. Recent priorities

include:

- Reducing violent crime
- Reducing drug and alcohol-related crime
- Reducing the consequences of crime
- Improving the effectiveness of crime prevention programs
- Improving law enforcement and the criminal justice system
- Developing new technology for law enforcement and the criminal justice system

Studies that involve the use of randomized experimental designs are encouraged, as are

multiple strategies for data collection and well-controlled, quasi-experimental designs and

equivalent comparison group designs. Qualitative studies, including ethnographic data collection,

are also encouraged (NIJ, 1994, p. 2).

NIJ Research Priorities

Some recent research priorities of NIJ (NIJ, 2004) include:

Violence and other criminal behavior

Sex offenders/offenses

Crime and delinquency prevention

Child abuse and neglect

Juvenile delinquency

Policing practices, organization, and administration

Terrorism or counterterrorism

Drugs, drugs and crime/alcohol, and drug testing

Drug treatment

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Systems

model

White-collar crime/cybercrime

Transnational crime, organized crime

Justice systems

Courts, prosecution, and defense

Corrections

Offender programs and treatment

Crime mapping and spatial analysis

Other thematic areas

A SYSTEMS MODEL OF EVALUATION RESEARCH

Although a variety of terms and competing models of evaluation research exist, the "systems

model" is presented here to acquaint the reader with a general evaluation approach. A *model *is a

simplified schema that outlines the essential points of a theory. A **systems model **assumes that all

parts of an organism, organization, or program are interrelated and could be represented in basic

computer language as a system of inputs into an existing system, processing of these inputs, and

subsequent outputs (or outcomes). Figure 11.1 presents a systems model for evaluating programs

in the criminal justice system.

The project components to be evaluated in this model are inputs, activities, results, outcomes,

and feedback (Schneider, 1978, pp. 3,23-3,31):

Inputs Resources, guidelines, rules, and operating procedures provided for a

program, for example, funds for personnel, equipment, operating costs, and

authorization to introduce new policies (often an experimental treatment)

Inputs Activities Results Outcomes

The Project

Feedback

(inputs) The Criminal Justice System (outcomes)

The Social System

FIGURE 11.1 A Systems Model of Evaluation Research: System and Project Components. *Source*:

Schneider, Anne L., et al. *Handbook of Resources for Criminal Justice Evaluators. *Washington, D.C.:

U.S. Department of Justice, 1978, pp. 3-24.

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Chapter 11 • Policy Analysis and Evaluation Research **283**

Activities What is done in the project with these inputs (resources), for example, services

provided, staffing patterns, and use of materials and human and physical

resources (called "process" in many models)

Results *Specific *consequences of the project activities or the specific objectives of

the program, for example, amount of services provided, work completed,

production accomplished, or cases closed or cleared (called "output" or

"products" in many models)

Outcomes Accomplishment of broader-range societal goals; these are general consequences

of the specific accomplishments (outputs/results) of the program,

for example, better justice, health, safety, and education

Feedback Recycling of results/outcomes into the operation as additional (or modified)

inputs; profits may induce a corporation to reinvest in a particularly profitable

line, just as losses may lead it to eliminate a less profitable line (also

called "feedback loop")

Inputs and process represent specific organizational/program *efforts*, and outputs represent

specific organizational/program *results. *Outcomes represent impacts on general, external societal

activities. Note this *very *simple illustration:

Input Grant of $100,000 for a foot patrol program

Process Two officers assigned to foot patrol in Precinct A for one year

Results Fifty percent increase in arrests in Precinct A

Outcome Crime rate declines 10 percent and fear of crime declines 40 percent

Feedback Allocate $1,000,000 and twenty officers to expanded foot patrol program

To summarize Figure 11.1,

In this scheme, a criminal justice project is conceived of as a system consisting of

inputs (resources, guidelines, and operating procedures); *activities *(those things the

project and its personnel do); *results *(the initial consequences of the activities); and

outcomes (the long-range, socially relevant consequence of the project). The system

should contain a *feedback *loop through which the results and outcomes of a project

impact upon the operation of the project and act as additional inputs. (Schneider

et al., 1978, pp. 3-8)

TYPES OF EVALUATION RESEARCH

With the evolution and growth of evaluation research as a field has come a whole lexicon of

descriptive tags. Franklin and Thrasher (1976), for instance, mention a variety of research

approaches as they relate to evaluation: continuous-versus-one-shot evaluations, "hip pocket"-

versus-formal evaluations, policy research, applied research, decision-oriented research, social

audits, action research, operations research, discipline-related research, basic research, frontline

evaluations, utilization reviews, and continuous monitoring and quality control. Unfortunately,

many of these terms are used interchangeably by various writers, and there is no consistent

agreement on their meaning in the field. Even the terms *policy analysis *and *evaluation research*

are often used as synonyms.

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284 Chapter 11 • Policy Analysis and Evaluation Research

Monitoring

IMPACT EVALUATION

PROCESS EVALUATION

MONITORING

Inputs Activities Results

Inputs Activities

Inputs Activities

Results

Outcome

for Criminal Justice Evaluators. Washington, D.C.: U.S. Department of Justice, 1978, pp. 3-33.

Evaluation research is different from other types of applied research in that the data are used

to make a decision(s) regarding a specific program, rather than simply to represent findings of

theoretical interest. Although numerous types have been identified, there areevaluation research: process evaluation and impact evaluation. In most instances, it is the latter

term by which "evaluation research" is most often described in references. **Process evaluation**

establishes causal relationships between results (such as an increase in arrests) and project inputs

and activities (see Figure 11.2).

Impact evaluation establishes causal relationships between outcomes (such as crime

reduction) and inputs, activities, and results of programs.

Evaluation research is often confused with two related information-gathering activities:

assessment and monitoring. **Assessment **(sometimes called needs assessment) is the enumeration

of some activity or resource, for instance, the need for a particular service in some target area. "It is

a method of finding service delivery gaps and substantiating unmet needs in a community and is

used to establish priorities for addressing problems" (Office of Juvenile Justice, 1978, p. 2).

Monitoring is assessment of whether the plans for a project have in fact been realized: Are the

activities related to the inputs? Monitoring is similar to an audit, an assessment of program accountability:

Is the program doing what it is supposed to be doing (Waller et al., 1975)? A certain portion

of the operating budget of an organization might be set aside to fund such a monitoring task.

Evaluation research need not be restricted to solely an analysis of output; it can involve

any systematic assessment of various aspects of program review (Suchman, 1967). Effort,

efficiency, operation, effectiveness of performance, adequacy of performance, and the like can

all be subject to evaluation (Office of Juvenile Justice, 1978, p. 3).undertaken, it is important that it be decided whether an evaluation can and should be done.

crucial questions must be answered:

Will the findings be used?

Is the project evaluable?

Who can do this work?

Process

evaluation

Impact

evaluation

Assessment

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Chapter 11 • Policy Analysis and Evaluation Research **285**

Evaluability

assessment

Will the Findings Be Used?

of the agency or program to be evaluated. Levine, Musheno, and Palumbo (1980, p. 551) put

the matter succinctly: "The program administrator's desire to reaffirm his or her position with

favorable program evaluations may conflict with the social scientist's desire to acquire an

objective appraisal of a program's impact. The end result may be either a research design with

low scientific credibility and tainted results, or a credible study that never receives a public

hearing because the administrator does not like the results" (Levine, Musheno, and Palumbo,

1980, p. 551). Unless a sincere need for the research has been expressed by the agency administrators

and the effort is viewed as something other than a public relations plume, evaluation

research may become nothing more than a sham. In discussing problems with contract research,

in which the researcher is paid by the contractor, Punch (1986, p. 73) says, "Having paid the

piper they want copyright on the tune." This reflects concern that academic reliance on commercial

funds may damage academic freedom. Grinyer (1999) suggests that researchers should

think through potential questions before agreeing to contract research. These include:

- What happens if the client does not like the research findings?
- What ethical issues are raised by the client becoming the subject of the research?
- If the client objects to the findings, what are the implications for publication?

Is the Project Evaluable?

In asking *whether the project is capable of being evaluated*, the researcher is concerned with the

existing design, defined objectives, and other programmatic elements that enable the

measurement and assessment of specified criteria. For instance, if the purpose of the program is

simply defined as "to do good" and no objectives, records, or other evaluable materials are kept by

the organization, much grief can be saved by avoiding an evaluation of this particular organization.

The success of the entire evaluation process hinges on the motivation of the administrators

and organization in calling for an evaluation in the first place (Schulberg and Baker, 1977).

It should be possible to locate specific organizational objectives that are measurable. "The

key assumptions of the program must be stated in a form which can be tested objectively. That is,

not only must the outcome be definable, but also the process used to achieve it must be specifiable"

(Office of Juvenile Justice, 1978, p. 7). If proper data for evaluation are absent and clear

outcomes or criteria of organizational "success" are absent, then a proper evaluation cannot be

undertaken. Rutman (1977) refers to this process as "formative research," a reconnaissance

operation to determine program evaluability. Wholey (1977) suggests the following steps in

evaluability assessment (assessing whether the program is evaluable):

1. Bounding the problem or program or determining what the objectives of the program are

and where it fits in the service picture

2. Collecting program information that defines its activities, objectives, and assumptions

3. Modeling of the program and the interrelationships of program activities

4. Analyzing plans or determining whether the model and activities are measurable

5. Presenting to management (intended user) or reporting results of evaluation assessment

and determination of the next steps to be taken

Rabow (1964, p. 69), in speaking specifically to corrections research, suggests that before

any results are attributed to a particular treatment, the evaluation should address important

questions, as outlined in the three stages of Rabow's research model.

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Evaluability

assessment

Will the Findings Be Used?

of the agency or program to be evaluated. Levine, Musheno, and Palumbo (1980, p. 551) put

the matter succinctly: "The program administrator's desire to reaffirm his or her position with

favorable program evaluations may conflict with the social scientist's desire to acquire an

objective appraisal of a program's impact. The end result may be either a research design with

low scientific credibility and tainted results, or a credible study that never receives a public

hearing because the administrator does not like the results" (Levine, Musheno, and Palumbo,

1980, p. 551). Unless a sincere need for the research has been expressed by the agency administrators

and the effort is viewed as something other than a public relations plume, evaluation

research may become nothing more than a sham. In discussing problems with contract research,

in which the researcher is paid by the contractor, Punch (1986, p. 73) says, "Having paid the

piper they want copyright on the tune." This reflects concern that academic reliance on commercial

funds may damage academic freedom. Grinyer (1999) suggests that researchers should

think through potential questions before agreeing to contract research. These include:

- What happens if the client does not like the research findings?
- What ethical issues are raised by the client becoming the subject of the research?
- If the client objects to the findings, what are the implications for publication?

Is the Project Evaluable?

In asking *whether the project is capable of being evaluated*, the researcher is concerned with the

existing design, defined objectives, and other programmatic elements that enable the

measurement and assessment of specified criteria. For instance, if the purpose of the program is

simply defined as "to do good" and no objectives, records, or other evaluable materials are kept by

the organization, much grief can be saved by avoiding an evaluation of this particular organization.

The success of the entire evaluation process hinges on the motivation of the administrators

and organization in calling for an evaluation in the first place (Schulberg and Baker, 1977).

It should be possible to locate specific organizational objectives that are measurable. "The

key assumptions of the program must be stated in a form which can be tested objectively. That is,

not only must the outcome be definable, but also the process used to achieve it must be specifiable"

(Office of Juvenile Justice, 1978, p. 7). If proper data for evaluation are absent and clear

outcomes or criteria of organizational "success" are absent, then a proper evaluation cannot be

undertaken. Rutman (1977) refers to this process as "formative research," a reconnaissance

operation to determine program evaluability. Wholey (1977) suggests the following steps in

evaluability assessment (assessing whether the program is evaluable):

1. Bounding the problem or program or determining what the objectives of the program are

and where it fits in the service picture

2. Collecting program information that defines its activities, objectives, and assumptions

3. Modeling of the program and the interrelationships of program activities

4. Analyzing plans or determining whether the model and activities are measurable

5. Presenting to management (intended user) or reporting results of evaluation assessment

and determination of the next steps to be taken

Rabow (1964, p. 69), in speaking specifically to corrections research, suggests that before

any results are attributed to a particular treatment, the evaluation should address important

questions, as outlined in the three stages of Rabow's research model.

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286 Chapter 11 • Policy Analysis and Evaluation Research

Stage I is concerned with the population of offenders from which treatment and control

groups will be selected.

1. How is the population of offenders from which groups will be selected defined with

respect to age, record of offenses, geographical location, or any social or personality

characteristics thought to be important?

2. How is selection carried out in order to eliminate bias-by random means or some matching

process?

3. When and by whom is selection carried out? What are the mechanics?

4. What steps are taken to demonstrate the lack of bias in selection?

Stage II is concerned with the treatment process and the need to understand what is

involved in it.

1. What is the theory of causation upon which treatment is proceeding?

2. What is the intervention strategy utilized in the treatment by which the causation variables

will be modified?

3. Can a logical relationship between causation variables and intervention strategy be

demonstrated?

4. Can it be demonstrated that the treater is fulfilling role requirements specified by the

intervention strategy?

5. Assuming that treatment role requirements are being fulfilled, can it be demonstrated that

variables cited in the theory of causation are being modified?

6. How shall any change in the variables be measured?

Stage III involves actual comparisons of groups subsequent to treatment.

1. What are the goals of treatment, that is, how shall success be defined in terms of recidivism,

attitudinal change, new social relationships, and personality modification?

2. How is the measurement of these characteristics carried out?

3. Over what period of time are comparisons to continue?

4. How is the cooperation of subjects outlined?

Who Can Do This Work?

In asking "*Who can do this work?" *one must decide on internal or external evaluators. If the

evaluation is to be "in-house," that is, to be conducted by the internal staff of the agency to be

evaluated, then adequate time and manpower must be allocated to permit a careful and hopefully

objective evaluation. Outside evaluators may lend greater objectivity to the evaluation task but,

as we will discuss later, require orientation to, and cooperation of, the agency to address the

relevant objectives and goals from a policy perspective.

STEPS IN EVALUATION RESEARCH

The actual *steps in evaluation research *do not differ significantly from the basic steps in the

research process that were identified in Chapter 1:

Problem formulation

Design of instruments

Research design (evaluation model)

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Steps in

evaluation

planning

Data collection

Data analysis

Findings and conclusions

Utilization

Only in the last step does evaluation research differ significantly from other research processes.

There are, of course, a variety of ways of slicing a pie, but most alternative listings of steps one way

or another include the key elements we have identified above. For instance, Albright et al. (1973), in

Criminal Justice Research: Evaluation in Criminal Justice Programs: Guidelines and Examples, an

evaluator's manual prepared on behalf of the National Institute of Law Enforcement and Criminal

Justice (now NIJ), focus primarily on the data collection and analysis stages. They outline five essential

steps in evaluation planning (Albright et al., 1973, p. 5):

Quantify the objectives and goals

Determine a quantifiable objective/goal relationship

Develop evaluation measures

Develop data needs considering requirements, constraints, and reporting

Determine methods of analysis

These steps would be assumed or included in the design of instruments, research design,

data collection, and data analysis stages that we have discussed throughout this text.

Problem Formulation

Just as in the other types of research we have discussed, evaluation researchers are also often in a

hurry to get on with the task without thoroughly grounding the evaluation in the major theoretical

issues in the field. Glaser (1974) feels that evaluation research in criminal justice would be more

useful were it to differentiate offenses and offenders utilizing causal theory. Without this theoretical

grounding, familiarization with past and current literature, and valid operationalization of concepts,

many evaluation studies can easily deteriorate into glorious exercises in social accounting.

Glaser (1973) comments on how much of what is regarded as in-house evaluations in correctional

agencies has been co-opted and is little more than head counting or the production of

tables for annual reports.

The problem formulation stage, to reiterate a point that has been emphasized throughout

this text, is the most crucial stage of research.

Design of Instruments

On the basis of problem formulation, review of the relevant literature, and program reconnaissance,

a most important element in evaluation research is the identification and operationalization

of key components of the program to be analyzed. The National Advisory Committee on

Criminal Justice Standards and Goals (1976, p. 113) suggests that professional associations be

commissioned to establish standardized definitions based on the following:

A major problem in research on criminal justice organizations is the absence of

standardized definitions for such basic terms as dangerousness, recidivism, discretion,

disparity, equity, proportionality, uniformity, individualization, commitment sentence,

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probation, parole and length of follow-up. The confusion over definitions has not

only impeded communication among researchers and, more importantly, between

researchers and practitioners, but also has hindered comparisons and replications of

research studies. R&D-funding agencies, such as the National Institute of Law

Enforcement and Criminal Justice and the National Institute of Mental Health, should

be sensitive to the way in which the terminology is used in the research studies being

supported. Where appropriate, the use of common definitions can facilitate the direct

comparison of research findings and, hence, the aggregation of research knowledge.

For example, the development of standardized definitions has already occurred in the

use of some identically worded questions in victimization surveys.

The greater use of replication of instruments employed by others can contribute to more

confidence in the reality and validity of evaluation methodologies, as well as to more useful

cross-site comparisons.

Research Design

Ideally, researchers would prefer control over treatment and a classic experimental design, with

random assignment of cases to experimental and control groups. Seldom does the evaluation

researcher enjoy such a luxury in analyzing ongoing programs. Despite arguments to the contrary

(see Boruch, 1976), in many instances, it is very difficult to find organizations that would be

willing to undergo experimentation, particularly if it involves the denial of certain treatments

(control group) to some clients. Cook, Cook, and Mark (1977) describe somethe attempt to use randomized designs in field evaluations:

1. The program planners and staff may resist randomization as a means of allocating treatments,

arguing for assignment based on need or merit.

2. The design may not be correctly carried out, resulting in nonequivalent experimental and

control groups.

3. The design may break down as some people refuse to participate or drop out of different

treatment groups (experimental mortality).

4. Some feel that randomized designs create focused inequity because some groups receive

treatment others desire and thus can cause reactions that could be confused with treatments.

Strasser and Deniston (1978) distinguish between preplanned and postplanned evaluations.

Although the former may interfere with ongoing program functioning, the latter is less costly,

involves less interference in the organization, and is less threatening to the personnel being evaluated.

Much of the bemoaning concerning the inadequacy of research design in evaluation

methodology in criminal justice has arisen because of an overcommitment to experimental

designs and a deficient appreciation of the utility of post hoc controls by means of multivariate

statistical techniques (see, for instance, Cain, 1975; Posavec and Carey, 1992).

Logan (1980, p. 36) agrees with this point when he states:

It may be that more rapid progress can be made in the evaluation of preventive or correctional

programs if research designs are based on statistical rather than experimental

model. It was noted, above, that one major difficulty in evaluation research is in procuring

adequate control groups. Modern statistical techniques can provide a means of

resolving this problem by substituting statistical for experimental methods of control.

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Data Collection

One principal shortcoming of much evaluation research has been its overreliance on questionnaires

as the primary means of *data gathering. *The use of a triangulated strategy of data

collection employing multiple methodologies would assure greater confidence in the validity

of findings (see, for instance, Fry, 1973). Where possible, agencies' records as outcome

measures should be cross-checked against other data sources. Many of the issues discussed

previously in this text are, of course, also appropriate to evaluation research. All of the sources

of error, particularly in data collection, must be continually checked, to ensure that the findings

are true findings and not the result of measurement error. Schwarz (1980, p. 14) presents

the issue succinctly:

In practice, the cup seldom reaches the lip intact. Designs must be compromised.

There are mishaps in the field. Expecting both valid results and an impeccable

process is overly optimistic. The most that can be expected is that the findings will

be valid despite compromise and mishaps. Flaws cannot be avoided.

Although program supporters will jump on methodological or procedural problems in any

evaluation that comes to a "negative" conclusion, Schwarz echoes a theme that has been emphasized

throughout this text: There is no such thing as research without error. The only way to

avoid error is to do no research at all.

MacKenzie and McCarthy (1990, p. 8) indicate that criminal justice researchers should not

ignore secondary analysis, nor should they be afraid to reanalyze data previously collected by

someone else. Two particularly important sources for such data are the National Archive of

Criminal Justice Data (formerly the Criminal Justice Archive and Information Network

[CJAIN]) and the National Center for Juvenile Justice (NCJJ). National Archive of Criminal

Justice Data databases include many classic and well-known criminal justice studies, as well as

data from recent NIJ-sponsored studies. NCJJ archives data on juvenile justice system transactions

in about half of the states.

Data Analysis

The choice of appropriate statistical analysis must be based on whether the data meet the assumptions

necessary for each technique to be employed. An important additional consideration is

pointed out by Glaser (1976, p. 771):

Some research reports from correctional agencies are not suppressed, but might as

well be, for few officials-or even researchers-can understand them. Most

notable among such reports are those which describe the use of various types of

multiple correlation or multiple association statistical analysis of case data in

administrative records to find guides for correctional operations. These reports are

submitted to correctional officials who do not understand the statistical terminology

and who feel no urgency to learn to understand it since the researchers share

with the operations officials the impression that this statistical analysis has little or

no practical value at present. Thus these researchers operate in a separate world,

inadequately linked either with the university social system which seems to be their

reference group, or with the leaders of the correctional system, which they are

presumed to serve.

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What might be excellent choices of statistical analysis for professional or academic

purposes may not be appropriate in form for presentation to a lay audience. Recall in the first

chapter of this text the point that, unlike the chemist or physicist, the criminologists must

compete with "commonsensical" views and explanations and, unfortunately, must often pitch

their evidence toward the lowest common denominator. How, then, can the evaluation

researcher in criminal justice resolve this dilemma of treating data with the most appropriate

and rigorous statistical methodology they require, however esoteric, yet attempting to communicate

these findings so that even politicians would understand? A useful practice is to

perform the evaluation and write a report geared for a professional audience and then issue a

report for laypeople, in which the crucial findings are simplified, summarized, and understood

by nonresearch professionals. In writing such reports, the researcher may take license

in generalizing findings, but it is exactly this succinct presentation that is usually viewed as

most useful by the consumer. Instead of the results of stepwise multiple regressions and intercorrelation

matrices, the critical relationships or statistically significant findings could be

presented in simple bivariate tables, which are more easily understood by more people.

An interesting exercise is boiling down the entire evaluation report to a two-page summary,

the type that might be released as a press report. Although, of course, such a brief document

does not do justice to the complexity of the analysis, anyone desiring the details can consult

the full report.

Utilization

of evaluation findings.

In discussing the "politicization of evaluation research," Maida and Faucett (1978) point

out the increasing political nature of evaluations as they are increasingly used to decide the future

of programs. Adams describes the dilemma of the agency administrator who is to be evaluated:

Part of the administrator's concern about evaluative research comes from the dilemma

that research creates for him. The evaluation process casts him in contradictory roles.

On the one hand, he is the key person in the agency, and the success of its various

operations, including evaluation, depends on his knowledge and involvement. On the

other hand, evaluation carries the potentiality of discrediting an administratively

sponsored program or of undermining a position the administrator has taken. (Adams,

1975, p. 19)

Factors that limit the utilization of evaluation research findings in criminal justice are

much the same obstacles that prevent effective evaluation research.

WHAT WORKS IN CRIMINAL JUSTICE?

If we ran GE, GM, or GTE the way we sometimes run our criminal justice systems, they would

all be out of business. Ford would still be making Edsels. A revolution has taken place in criminal

justice at the dawn of the twenty-first century. Let us find out what works in criminal

justice, what is promising, and what does not work. About thirty years ago, XXXXX XXXXXson

(1974) rocked the correctional community after reviewing over a hundred programs and

concluding that "nothing works." It turns out that Martinson was wrong; some programs do

work, but how do we know?

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Chapter 11 • Policy Analysis and Evaluation Research **291**

In 1996, the U.S. Congress required the Attorney General to provide a "comprehensive

evaluation of the effectiveness" of over $3 billion annually in Department of Justice grants to assist

state and local law enforcement and communities in preventing crime. Congress required that the

research for the evaluation be "independent in nature" and "employ rigorous and scientifically

recognized standards and methodologies." The Assistant Attorney General for the Office of Justice

Programs asked the NIJ to commission an "independent review" of over 500 program impact

evaluations.

The congressionally mandated evaluation examined hundreds of different strategies used

in communities, families, schools, labor markets, places, and police and criminal justice settings

(Sherman et al., 1997). It found that very few operational crime prevention programs have been

evaluated using scientifically recognized standards and methodologies, including repeated tests

under similar and different social settings. Based on a review of more than 500 prevention

program evaluations meeting minimum scientific standards, the report (ibid.) concluded that

there is minimally adequate evidence to establish a provisional list of what works, what does not,

and what is promising. Exhibit 11.1 lists each of these.

EXHIBIT 11.1

Preventing Crime: What Works, What Doesn't, What's Promising

What Works?

**For infants**: Frequent home visits by nurses

and other professionals.

**For preschoolers**: Classes with weekly home

visits by preschool teachers.

**For delinquent and at-risk preadolescents**:

Family therapy and parent training.

**For schools**:

Organizational development for innovation.

Communication and reinforcement of clear,

consistent norms.

Teaching of social competency skills.

Coaching of high-risk youth in "thinking skills."

**For older male ex-offenders**: Vocational

training.

**For rental housing with drug dealing**:

Nuisance abatement action on landlords.

**For high- hot spots**: Extra police patrols.**For high-risk repeat offenders**: Monitoring

by specialized police units.

Incarceration.

**For domestic abusers who are**: On-scene

arrests.

**For convicted offenders**: Rehabilitation

with risk-focused treatments.

**For drug-using offenders in prison**:

Therapeutic treatment programs.

What Doesn't Work

- Gun "buyback" programs.
- Community mobilization against crime in

high-crime poverty areas.

- Police counseling visits to homes of couples

days after domestic violence incidents.

- Counseling and peer counseling of students

in schools.

- Drug Abuse Resistance (DARE).
- Drug prevention classes focused on fear

and other emotional appeals, including selfesteem.

- School-based leisure-time programs.
- Summer jobs or subsidized work for at-risk

youth.

- Short-term, nonresidential training programs

for at-risk youth.

- Diversion from court to job training as a condition

of dismissal.

- Neighborhood watch programs organized

with police.

- Arrests of juveniles for minor offenses.
- Arrests of unemployed suspects for domestic.
- Increased arrests or raids on drug market

locations.

- Storefront police offices.
- Police newsletters with local crime -formation.

(*continued*)

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Chapter 11 • Policy Analysis and Evaluation Research

- Correctional boot camps using traditional

basic training.

- "Scared Straight" programs whereby minor

juvenile visit adult prisons.

- Shock probation, shock parole, and split sentences

adding jail to probation or parole.

- Home detention with electronic monitoring.
- Intensive supervision on parole or probation

(ISP).

- Rehabilitation programs using vague, unstructured

counseling.

- Residential programs for juvenile offenders

using challenging experiences in rural settings.

What's Promising?

- Proactive drunk driving arrests with breath

testing (may reduce accident deaths).

- Community policing with meetings to set

priorities (may reduce perceptions of crime).

- Police showing greater respect to arrested

offenders (may reduce repeat offending).

- Police field interrogations of suspicious

persons (may reduce street crime).

- Mailing arrest warrants to domestic violence

suspects who leave the scene before arrive.

- Higher numbers of police officers in cities

(may reduce crime generally).

- Gang monitoring by community workers and

probation and police officers.

- Community-based mentoring by Big Brothers/

Big Sisters of America (may prevent abuse).

- Community-based afterschool recreation

programs (may reduce local juvenile crime).

- Battered women's shelters (may help some

women reduce repeat domestic violence).

- "Schools within schools" that group students

into smaller units (may pre-vent crime).

- Training or coaching in "thinking" skills for

high-risk youth (may prevent crime).

- Building school capacity through organizational

development (may prevent substance abuse).

- Improved classroom management and instructional

techniques (may reduce alcohol use).

- Job Corps residential training programs for

at-risk youth (may reduce felonies).

- Prison-based vocational educational programs

for adult inmates (in federal prisons).

- Moving urban public-housing residents to

suburban homes (may reduce risk factors for

crime).

- Enterprise zones (may reduce area unemployment,

a risk factor for crime).

- Two clerks in already-robbed convenience

stores (may reduce robbery).

- Redesigned layout of retail stores (may reduce

shoplifting).

- Improved training and management of bar

and tavern staff (may reduce violence, DUI).

- Metal detectors (may reduce skyjacking,

weapon carrying in schools).

- Street closures, barricades, and rerouting

(may reduce violence, burglary).

- "Target hardening" (may reduce vandalism of

parking meters and crime involving ).

- "Problem-solving" analysis unique to the

crime situation at each location.

- Proactive arrests for carrying concealed

weapons (may reduce gun crime).

- Drug courts (may reduce repeat offending).
- Drug treatment in jails followed by urine testing

in the community.

- Intensive supervision and aftercare of juvenile

offenders (both and serious).

- Fines for criminal acts.

What Works, What Doesn't, What's Promising.

Washington, D.C.: Office of Justice Programs, 1997,

NCJ 165366.

EXHIBIT 11.1 (Continued )

The clearinghouse for these evaluations had been contracted to the University of Maryland

by the NIJ. The reports were intended to be updated regularly (www.preventingcrime.org).

A major development has since taken place in attempting to identify "evidence-based" criminal

justice interventions (Sherman et al., 2002). These are ones that have been demonstrated to work

through replicable, controlled experiments. A strong movement has taken place domestically and

internationally to identify "best practice" programs and exemplary programs that might serve as

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Chapter 11 • Policy Analysis and Evaluation Research **293**

models in crime prevention. Similar lists of what works have been compiled for juvenile justice

programs (Waller and Welsh, 1998) and for international programs (International Center for the

Prevention of Crime in Montreal). The list of what works will grow more quickly if the nation

invests more resources in scientific evaluations to hold all crime prevention programs accountable

for their results.

None of these evaluations or placements as "working" or "not working" is final. Constant

replication and reevaluation is required, but a persistent, independent, scientific program of evaluation

will go a long way in replacing what we think works or what does not with what does

work. Perhaps the field of rehabilitation has overreacted to the previously discussed Martinson

report that concluded that "nothing works" in rehabilitation. Marlowe (2006) discusses the danger

to researchers who conclude that a program does not work of risking being branded with the

"Scarlet M" (for Martinson). The message to researchers is that if they question the value of

rehabilitation, they risk their professional reputations.

The Campbell Collaboration (C2)

The Campbell Collaboration is an international research organization founded in 2000 and

dedicated to preparing, maintaining, and publicizing systematic reviews of research on the

effects of social and educational programs and interventions. Modeled after the successful

Cochrane Collaboration in health care, the C2 program is named in honor of Donald

Campbell, an innovator in research and experimental designs. In examining "what works,"

the systematic reviews use scientific and explicit methods to identify, screen, and analyze

evaluation studies. The purpose of these reviews is to assist decision makers to better

understand the existing research and better inform their decisions using evidence-based

research. Various organizations have created a variety of Websites in a number of fields to

address evidence-based research. This includes Websites on the blueprints program

(Center for the Study and Prevention of Violence), child trends (programs to enhance child

development), the Cochrane Collaboration (health care), helping America's youth,

programs for justice-involved persons with mental illness, medical-clinical practice,

juvenile delinquency prevention, addiction, strengthening families, and alcohol abuse

(U.S. Department of HEW, 2008).

The nature of a C2 analysis can be illustrated by Brandon Welsh and David Farrington

(2002), who did a meta-analysis of the *Crime Prevention Effects of Closed Circuit Television*

(CCTV). An outline or summary of their procedure is instructive. They reviewed forty-six

relevant studies from both the United States and Britain on the effectiveness of CCTV

according to strict methodological criteria. CCTV had to be the main intervention, and the

outcome measure was crime. There had to be measures of crime levels both before and after

the intervention, and there had to be a comparable control area. Twenty-two of the forty-six

studies met these criteria and were included. They concluded that the best evidence suggested

the CCTV reduced crime to a small degree and was most effective with vehicle crime in car

parks but had least impact in public transportation and in the center city. The poorly controlled

(excluded) studies produced more desirable results than the better controlled (included)

studies (ibid.).

Another example of a comprehensive effort to evaluate successful program implementation

has been the Blueprints for Violence Prevention program at the University of Colorado

(OJJDP, 2004). Figure 11.3 describes the Blueprint Initiative as well as the model and

promising programs.

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294 Chapter 11 • Policy Analysis and Evaluation Research

ABOUT THE BLUEPRINTS INITIATIVE

Blueprints for Violence Prevention began at the Center for the Study and Prevention of Violence (CSPV) as an

initiative of the state of Colorado, with funding from the Colorado Division of Criminal Justice, the Centers

for Disease Control and Prevention, and the Pennsylvania Commission on Crime and Delinquency. The project

was originally conceived as an effort to identify model violence-prevention programs and implement them within

Colorado. Soon after the creation of Blueprints, the Office of Juvenile Justice and Delinquency Prevention (OJJDP)

became an active supporter of the project and provided funding to CSPV to sponsor program replications in sites

across the United States. As a result, Blueprints evolved into a large-scale prevention initiative.

The Blueprints for Violence Prevention initiative has two overarching goals:

- Identify effective, research-based programs.
- Replicate these effective programs through a national dissemination project sponsored by OJJDP

designed to

- Provide training and technical assistance (through the program designers) to transfer the requisite

knowledge and skills to implement these programs to sites nationwide.

- Monitor the implementation process to troubleshoot problems, provide feedback to sites, and

ensure that programs are implemented with fidelity to their original intent and design.

- Gather and disseminate information regarding factors that enhance the quality and fidelity of

implementation.

IDENTIFYING EFFECTIVE PROGRAMS

Identifying effective programs has been at the forefront of the national agenda on violence prevention for

the last decade. Federal funding agencies have increasingly emphasized the need to implement programs

that have been demonstrated effective. The focus on research-based practices has stimulated communities

to search for the best practices and to determine what types of programs would be most effective and

appropriate for their local problems and population.

In recent years, various governmental agencies, and some private organizations, have produced lists of

programs that demonstrate at least some evidence of positive effects on violence/aggression, delinquency,

substance abuse, and their related risk and protective factors. Taken as a whole, this work has resulted in a

large repertoire of research-based programs from which the practitioner community may choose. Although

these lists provide a valuable resource for communities, they can be confusing. Some lists are narrow in

focus-for example, limiting their descriptions to drug abuse, family strengthening, or school-based

programs only. In addition, and perhaps more importantly, the criteria for program inclusion vary

tremendously, with some agencies adopting a more rigorous set of criteria than others. In fact, one must be

diligent when examining the lists to ensure that at least a minimal scientific standard has been applied; for

example, programs should demonstrate effectiveness using a research design that includes a comparison

(i.e., control) group. Anything less rigorous than this approach cannot provide sufficient evidence to justify

disseminating and implementing programs on a wide scale.

The Blueprints initiative likely uses the most rigorous set of criteria in the field:

- Demonstration of significant deterrent effects on problem behavior (violence, aggression, delinquency,

and/or substance abuse) using a strong research design (experimental or quasi-experimental with

matched control group).

- Sustained effects at least one year beyond the intervention.
- Replication in at least one other site with demonstrated effects.

FIGURE 11.3 Successful Program Implementation: Lesson from Blueprints *Source*: Mihalic, Sharon, et al. "Blueprints

for Violence Prevention." *OJJDP Juvenile Justice Bulletin*, July 2001; Muller, Janine and Sharon Mihalic. "Blueprints:

A Violence Prevention Initiative." *OJJDP Fact Sheet*, #110, June 1999; and Mihalic, Sharon, et al. "Blueprints for

Violence Prevention Report." Office of Juvenile Justice and Delinquency Prevention, NCJ204274, July 2004.

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Chapter 11 • Policy Analysis and Evaluation Research **295**

This high standard is necessary if programs are to be widely disseminated because conducting an outcome

evaluation during every implementation effort will be costly, time consuming, and not always possible.

Therefore, it is important that programs demonstrate effectiveness, based on a rigorous evaluation, before their

widespread dissemination. Programs meeting all three of the criteria are classified as "model" programs,

whereas programs meeting at least the first criterion but not all three are considered "promising." To date,

Blueprints has identified eleven model programs and twenty-one promising programs.

THE BLUEPRINTS PROGRAMS

The Blueprints for Violence Prevention initiative has identified the following model and promising programs.

MODEL PROGRAMS

Big Brothers Big Sisters of America (BBBSA)

Bullying Prevention Program

Functional Family Therapy (FFT)

Incredible Years: Parent, Teacher, and Child Training Series

Life Skills Training (LST)

Midwestern Prevention Project

Multidimensional Treatment Foster Care (MTFC)

Multisystemic Therapy (MST)

Nurse-Family Partnership

Project Towards No Drug Abuse (Project TND)

Promoting Alternative Thinking Strategies (PATHS)

PROMISING PROGRAMS

Athletes Training and Learning to Avoid Steroids (ATLAS)

Brief Strategic Family Therapy (BSFT)

CASASTART

Fast Track

Good Behavior Game

Guiding Good Choices

High/Scope Perry Preschool

Houston Child Development Center

I Can Problem Solve

Intensive Protective Supervision

Linking the Interests of Families and Teachers

Preventive Intervention

Preventive Treatment Program

Project Northland

Promoting Action Through Holistic Education (PATHE)

School Transitional Environment Program (STEP)

Seattle Social Development Project

Strengthening Families Program: Parents and Children 10-14

Student Training Through Urban Strategies (STATUS)

Syracuse Family Development Program

Yale Child Welfare Project

Descriptions of these programs are available on the Blueprints Web site www.colorado.edu/cspv/

blueprints/index.html.

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Obstacles to

evaluation

research

OBSTACLES TO EVALUATION RESEARCH

In its first annual review volume of criminal justice evaluation, the National Criminal Justice

Reference Service (NCJRS, 1979) surveyed most of the authors whose works appeared in the

volume, members of the editorial board of the volume, as well as a companion volume,and Justice: An Annual Review of Research (Morris and Tonry, 1979). In the order of perceived

importance, the following dangerous pitfalls were identified by this group of evaluation experts (NCJRS, 1979, p. 370):

Poorly done evaluation design and methodology

Unsound and/or poorly done data analysis

Unethical evaluations

Naive and unprepared evaluation staff

Poor relationships between evaluation and program staff

Co-optation of evaluation staff and/or design

Poor quality data

Poorly done literature reviews of subject area

Focusing on the method not the process

Geller (1997, p. 4) describes impediments to police departments becoming learning

organizations:

Skepticism about research as ivory tower and impractical.

Resistance to cooperating with outside researchers because too often they have failed to

provide feedback soon enough to assist practitioners.

Distrust of evaluation research because of the blisters that linger from the last time the

department was burned by a poorly conducted study.

Skepticism that research findings developed in another jurisdiction have any application at

home.

The myth that encouraging critical thinking among the rank and file will undermine necessary

paramilitary discipline.

The belief that thinking inhibits doing.

An indoctrination process in most police departments that inhibits employees from contributing

meaningfully to organizational appraisal.

A police department that denigrates rank-and-file thinking about the organization's basic

business establishes a culture likely to ridicule or demean those who would take time from

routine activities (random preventive patrol, etc.), which police have taught themselves,

politicians, and the public as constituting real and tough police work.

Reluctance to have cherished views challenged.

Difficulty in engaging in organizational self-criticism while continuing to work with those

whose current efforts are criticized.

Insufficient time for employees to reflect on their work and a lack of time, authority,

resources, and skills for them to conduct research.

Fear of change.

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Chapter 11 • Policy Analysis and Evaluation Research **297**

Questions in

evaluation

research

RESEARCHERS AND HOST AGENCIES

The National Advisory Committee (1976, p. 133) suggests the following guidelines with respect

to relationships between those performing evaluation research and the *host agencies*:

R&D funding agencies that support studies of criminal justice organizations

should be sure that researchers who conduct such studies are sensitive to the needs

of the organizations that are part of the study. Such sensitivity will increase the

likelihood of completing the project to the satisfaction of the funding agency, the

organization that is part of the study (host agency), and the research team.

1. Before the research begins, clear agreements should be reached between the researcher and

the host agency on such issues as: the purpose of the research, duration of effort, data to be

collected, plans for protecting confidentiality of sensitive information, resources required

of the host agency, extent to which the host agency may be identified by name in publications,

form and timing of public disclosure of the results of the study, and any other topic

of mutual concern.

2. Funding agencies should assist researchers in establishing favorable relationships with

host agencies by:

a. Assuring that the research design does not necessarily interfere with the host agency's

normal operations.

b. Arranging for host agencies to receive timely feedback on research progress or results.

c. Considering the reimbursement of expense incurred by the host agency in cooperating

with the research project.

3. Existing educational programs for researchers could be broadened to include relevant

courses, on-site projects conducted in cooperation with an operating agency, internships,

and exchange programs to make researchers more cognizant of procedures that may

improve their relations with criminal justice organizations. These programs should stress

the necessity of developing a viable partnership with the host agency during the planning,

conduct, and follow-up of a research study.

Summary

Policy analysis is the study of government behavior.

It includes proposals, programs, decisions, and

effects. The policy process involves identification,

formulation, legitimation, implementation, and evaluation.

Policy experiments are applied field

experiments with immediate practical policy implications.

Evaluation research is an applied branch of

social science that evaluates policies and programs

to determine whether and how well they work. The

NIJ's research program emphasizes policy-oriented

programs and attempts to link researchers with practitioners.

A *systems model *of evaluation research

consists of inputs, activities, results, outcomes, and

feedback.

Before an evaluation is undertaken, three crucial

questions must be answered: Will the findings

be used? Is the project evaluable? Who can do this

work? Formative research, or an evaluability assessment,

addresses these questions before an evaluation

is agreed to be undertaken.

The *steps in evaluation research *are problem

formulation, design of instruments, research design

(evaluation model), data collection, data analysis,

findings and conclusions, and utilization.obstacles or pitfalls in evaluation research are poor

evaluation design and methodology, poor data analysis,

unethical evaluations, naive or unprepared evaluation

staff, poor relationships between evaluation

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298 Chapter 11 • Policy Analysis and Evaluation Research

and program staff, co-optation of evaluation staff

and/or design, poor-quality data, poor literature

reviews, and focus on method rather than process.

Much evaluation research exemplifies some of these

problems, particularly the politics of evaluation.

Of particular importance in effective evaluation

is the need for effective relationships between the

researcher and the host agency (site to be evaluated).

The National Advisory Committee on Criminal

Justice Standards and Goals (1976) suggests clear

agreements beforehand, assistance from funding

agencies in bringing the two parties to suitable agreements,

and training programs to acquaint researchers

with agency problems and needs.

Key Concepts

Policy analysis *277*

Evaluation research *278*

Policy experiments *280*

Systems model *282*

Process evaluation *284*

Impact evaluation *284*

Assessment *284*

Monitoring *284*

Evaluability assessment *285*

Steps in evaluation

planning *287*

Obstacles to evaluation

researchReview Questions

1. How does evaluation research fit into the general

scheme of policy analysis? Using the NIJ program,

what role can research have in public policy debates

in criminal justice?

2. Describe the "systems model" of evaluation research.

In what way can such a model inform public policy in

criminal justice?

3. Evaluation research seldom takes place as planned.

Using the discussions in the chapter, elaborate on

obstacles to evaluation research in criminal justice.

Useful Web Sites

American Evaluation Association *www.eval.org*

net/proposal

net/dissthes/

Successful Program Implementation: Lessons from

Blueprints *www.ncjrs.org/pdffiles1/ojjdp/204273.pdf*

icaap.org/methods/

pubs/reports/jj_needs_assessment.htm

org/jjec/

Blueprints: Successful Program Implementation

www.ojp.usdoj.gov

program/progeval/Ref-PGprogeval.htm

library/evaluatn/fnl_eval.htm

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**THIS IS THE END OF CHAPTER 11**

C H A P T E R

12 Data Management

Coding, Tabulation, and Simple Data

Presentation

Variables List

Computers

Data Management

Editing

Coding

Coder Monitoring

Keyboard Entry

Data Verification

Simple Data Presentation

Rates

Proportions

Percentages

Ratios

The Frequency Distribution

Graphic Presentations

Pie Charts

Bar Graphs

Frequency Polygons (Line Charts)

Using SPSS for Graphs

Crime Clocks

Table Reading

Why Bother with Tables?

What to Look for in a Table

Steps in Reading a Table

Summary of Table 12.3

How to Construct Tables

Presentation of Complex Data

General Rules For Percentaging a Table

Improper Percentaging

Elaboration

Lying With Statistics

Summary

Key Concepts

Review Questions

Useful Web Sites

It is hoped that earlier decisions in the research process have paved the way for the researcher

in data analysis, data summarization, and presentation. Novice researchers, however, are

seldom prepared for the massive challenge of efficient data management. Months of

painstaking effort in problem formulation, research design, and data gathering can be wasted by

inefficient and poorly thought-out data analysis and presentation.

Data analysis should be planned at the beginning of a project rather than at the end.

Recall, for instance, our description of the use of dummy tables as an exercise to check for

the inclusion of necessary items for analysis. For very small studies that involve fewer

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300 Chapter 12 • Data Management

than 100 subjects and only a few variables, it is possible to simply page through and tally data

directly from the questionnaire. Most studies, however, are simply too large to permit such

simple analysis; and even though deliberate planning for later analysis may at times appear to

be a ritualistic obstacle in the project, it is absolutely essential.

VARIABLES LIST

A **variables list **keyed to questionnaire items enables the identification and examination of

questionnaire content to ensure proper coverage, balance, and nonduplication of items. Such a

variables list of questionnaire items justifies the inclusion of questions in the study. Figure 12.1

illustrates a typical variables list; each variable is identified and keyed to a hypothetical question

number. On the basis of construction and review of a variables list, the researcher may

discard or add items.

To construct a variables list, the researcher simply goes through the questionnaire that has

been constructed and identifies the concept or variable that each question was designed to measure.

For example, Figure 12.1 Section 2, deals with professional-paraprofessional roles, with questions

17 and 22 addressing paraprofessional roles, item 23 measuring appropriate activities, items 24 and

25 dealing with professionalism, and so forth. By means of such a list, the researcher is able to

check, before the fact, for omission of important items, duplication of items, and similar content

problems to ensure that the instrument is addressing all of the issues necessary for later analysis.

Variables list

1. *Demographic Variables*

Sex-34a, Race-34b, Age-34c, Marital

Status-34d,

Dependents-34e

Education-34f, Training-34g (Type)-34h,

Hometown-34j, Job History-35,

Parents' Background-36a-d,

Spouse's Background-36e, f,

Experience with Disability-8

Professional Roles-

Appropriate Activities-*23*

Rating of Profession-*26, ProfessionalizationAttitude*

3. *Recruitment to Rehabilitation Work*

Individual Recruitment-2, 3

Career Choice-5a, b, 6

Agency Recruitment Policies-20, 21

FIGURE 12.1 Variables List.

4. *Utilization*

Present Employment-1a, Type

of Agency-1b

Supervisory Responsibility 4a, b,

Job Satisfaction-7a, b

Duties-9, 10, 11

Suggested Changes-12

Training since Employed-13

Desired Occupational Mobility-14, 15

Job Satisfaction-16

Promotion-18

Characteristics of Work-29

Important Tasks-31, 32

Agency Climate-33

5. *Additional Areas of Investigation*

Agency Change-19, 39

Client Preference-30

Agency Mission-37

Severely Disabled-38

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COMPUTERS

For much of this discussion, possession of basic computer literacy is assumed, because the

computer is now used for all but the most simple data analysis. Those who are computer illiterate

are at a disadvantage in today's information society. Computers are handy tools for

research that offer numerous possibilities of analysis once the data have been properly

entered. Before data are input into a computer for storage, analysis, and retrieval, they must

first be coded so that they can be read by the computer. An orientation tour of your local

computer center will acquaint you with the available equipment, which may vary from

terminals connected to a large mainframe computer to self-sustained minicomputers and

microcomputers (similar to personal computers).

No extensive knowledge of computers or computer programming is required in most

instances, as a number of user-friendly, canned statistical packages (software), which calculate

most statistics, are available. The most widely used computer packages in the social

sciences are SPSS and SAS. Our presentation will focus on SPSS, which is the most common,

although the others contain some features that have advantages over SPSS. SPSS stands

for Statistical Package for the Social Sciences. The PC version of SPSS is able to perform

personal computer analyses that at one time could be performed only on a mainframe

computer. The current version as of this writing is SPSS 10.1. Although this discussion will

concentrate on the statistical capabilities of computer software, these programs also have

many other data management capabilities, which are invaluable to the criminal justice

researcher. These programs manage data files (sorting, merging, and saving files), manage

data (sampling, selecting, and recording), and produce graphics and reports (pie charts, bar

graphs, and tables). The microcomputer (PC or personal computer) has become very powerful

and, in addition to statistical and data management functions, can perform functions such

as client record management, business applications, word processing, desktop publishing,

and decision support systems such as evaluation research (Monette, Sullivan, and DeJong,

1994, pp. 357-360).

DATA MANAGEMENT

Data management, in the context of this chapter, is concerned with the process by which the

raw data gathered by some instrument or measurement are converted into numbers for analysis

purposes. Figure 12.2 outlines the *steps in the data management process: *collecting the information

with the *data-gathering instrument *and, using a *codebook*, transferring this information onto

a *codesheet. *The numerical data on the codesheet are used to create a *data file. *This data file may

be created by *data entry *using a *computer keyboard. Data files *should also be cleaned

(edited/verified) to ensure the accuracy of the data.

Data

management

Data-Gathering

Instrument

e.g., Questionnaire Codes/Instructions

for Coding

Transfer

Sheet

Keyboard Entry

Keypunch

Cleaning Data Disks/Tape/

Computer Memory

or Data Decks

Codebook Codesheet Data Entry Data

Verification

Data File

FIGURE 12.2 Steps in the Data Management Process.

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302 Chapter 12 • Data Management

Editing

Prior to the actual coding, the questionnaires must be *edited. *Members of the research staff

should check each questionnaire to be certain that the field interviewer or respondent completed

each item accurately. Although most questions, particularly closed or structured questions, were

probably precoded, codes may have to be developed for the open-ended items on the basis of a

sampling of the initial returns.

In Chapter 5, we mentioned that researchers must decide whether to ask open-ended or

closed questions. Although open-ended questions give respondents the opportunity to provide

responses not limited to response categories, such questions raise greater difficulties

with respect to coding. A useful *procedure in developing codes for open-ended items *is to

read through a sufficient number of responses and create a preliminary code on the basis of

these responses. Such a code, as any preliminary code, may require revision once the remaining

responses are coded. According to a rule of thumb, a code may require revision when

10 percent or more of the responses are classified as "other," or as not fitting any of the categories.

It is thus useful to keep "other" sheets on which coders record the case number, the

variable number, and a shortened version of the actual response recorded as "other." Patterns

of "other" responses are thereby quickly noted and the recoding process is hastened.

Generally, if more than 10 percent of the responses fall into "other," the code needs to be

revised in order to include many of these responses.

Coding errors can be a major source of errors in surveys. The bulk of survey research work,

particularly in large research organizations, is conducted by those who have the least training and

often the least commitment to the scientific goals of research. Sussman and Haug (1967) speak of

the perils of "hired hand research" and discovered that mechanical errors in such procedures as

coding account for a significant level of error in survey research.

Coding

Coding is the assignment of numerical values to responses (information) gathered by a research

instrument. As soon as or even before the data are gathered, the researcher can begin to construct

a code for each item to be measured. Such codes are compiled into a *codebook*, which guides the

numerical classification of questions to be coded. Figure 12.3 lists some typical questionnaire

items. Figure 12.4 is a sample codebook for these same questions. The responses of a hypothetical

respondent have been added for illustrative purposes.

Coding

Background Information

Please circle or fill in the correct information about yourself.

1. Sex: (circle one) Male Female

Black White Other

(specify)

2. Race: (circle one)

3. Religious background in your home: (circle one)

Catholic

Married Single, never married Separated or divorced Widowed

Jewish Protestant Other

4. Present marital status: (circle one)

5. When were you born?

(month)

6 42

(year)

(specify)

FIGURE 12.3 Sample Survey Instrument.

Editing

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Chapter 12 • Data Management **303**

The general purpose of the conversion of questionnaire information into numerical data is

that once this process is completed, the researcher can basically store the questionnaires and

work from the summarized information-numbers. This can be particularly appreciated when a

large number of cases and a large number of questions are asked. It becomes unmanageable to

attempt to work directly from the original instrument.

To summarize, coding is development of a code for each question in the questionnaire. The

combination of each code is called a **codebook**. All relevant questions are coded using the codebook

as a guide, and these numbers are assigned to appropriate cells or columns on a codesheet

or spreadsheet (Figure 12.5).

Throughout this process, the code or codebook is used as a guide in reading the numerical

information. The codebook may require revision during the course of the coding procedure, particularly

for open-ended items that may call for considerable judgment on the part of the coder.

Each column in our codebook (Figure 12.4) represents a box or cell on the **codesheet**

(or transfer sheet) (Figure 12.5). Coding may be handled in a variety of ways, depending on the

nature of the data-gathering instrument and the resources available. In addition to use of a separate

codesheet, researchers may employ self-coding (similar to the pencil-in answer sheets used

in machine-scored tests) or edge coding (in which the margins of the questionnaire itself are used

for coding, thus eliminating the need for separate coding sheets). Self-coding instruments can be

entered automatically by an optical scanning sensor device, whereas edge-coded questionnaires

Codebook

Codesheet

Question Item Column Code

- Study Number 1 As assigned

- Case Number XXXXX As assigned

- Coder Identification 5-6 As assigned

1. Sex 7 1. Male

2. Female

9. Not ascertained

2. Race 8 1. Black

2. White

3. Other

9. Not ascertained

3. Religious Background 9 0. None

1. Catholic

2. Jewish

3. Protestant

4. Other

9. Not ascertained

4. Present Marital Status 10 1. Married

2. Single, never married

3. Separated or divorced

4. Widowed

5. Not ascertained

5. Age 11-12 Code last two digits of year

respondent was born. Not

ascertained

FIGURE 12.4 Sample Codebook.

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Customer reply replied 9 years ago

304 Chapter 12 • Data Management

C:\SPSSSV\EMPLOYEE.SAV

Id Gender Race Genrace Age Educ Jobcat Salary Salbegin

1 1 0 0 1 41 15 5 57000 27000

2 2 0 0 1 36 16 1 40200 18750

3 3 1 0 3 65 12 1 21450 12000

4 4 1 0 3 46 8 1 21900 13200

5 5 0 0 1 39 15 1 45000 21000

6 6 0 0 1 35 15 1 36000 13500

7 7 0 0 1 37 15 1 36000 18750

8 8 1 0 3 27 12 1NNN-NN-NNNN/p>

9 9 1 0 3 48 15 1 27900 12750

10 10 1 0 3 47 12 1 24000 13500

1

1

2

0

3

1

4

6

5

1

6

4

7

2

8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

41 42 43 44 45 46 47 48 49 50

61 62 63 64 65 66 67 68 69 70

31 32 33 34 35 36 37 38 39 40

51 52 53 54 55 56 57 58 59 60

71 72 73 74 75 76 77 78 79 80

2

FIGURE 12.5 Sample Codesheet. Codes Assigned to Cells 1-8 Refer to the Coding of

the Survey Instrument (Figure 12.3) Using the Codebook (Figure 12.4).

can be designed so that they are precoded and can be directly keyboarded. Such instruments are

usually limited to closed or structured response questions. Figure 12.6a illustrates this same data

input into an SPSS spreadsheet, while Figure 12.6b shows ten cases on an SPSS spreadsheet

from a file called "employee."

Let us illustrate the coding procedure by means of the hypothetical responses in the sample

survey instrument (Figure 12.3) and our sample codebook (Figure 12.4). According to the

codebook we must first assign a "study number" to this project. This item does not refer to any

question number in the instrument and is assigned by the researcher. Because this is our first

FIGURE 12.6A Example of Data Entry Using a Spreadsheet.

FIGURE 12.6B Examples of a Spreadsheet Data File.

Study Case Coder Sex Race Religion

1 1 16 14 2 2 1

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Chapter 12 • Data Management **305**

hypothetical study, we will call it study 1. Code 1 is assigned to cell 1 on the codesheet. If only

one study is being analyzed, creation of a computer file name may eliminate the necessity for a

study number for each case. The next item in the codebook is the "case number" that is assigned

to the respondent. Assume that the top of the questionnaire indicated that this was case 16.

Because cells 2, 3, and 4 have been reserved to record respondent case numbers, it appears that

more than 100 and fewer than 999 subjects were expected to participate in the study. Recording

case number XXXXX in cells 2 and 3 would result in its being read as 16*X *(*X *being 0 to 9). Instead, 016

should be coded in cells 2, 3, and 4, respectively. The next item in the code is the "coder identification."

In larger studies, each coder is given a coder number beforehand. Our hypothetical coder

is number 14; therefore, we enter 14 in columns 5 and 6.

Finally, we begin coding actual substantive items in the sample survey instrument with

question 1-sex. The respondent indicated that she was female, which, using our code, is a 2.

This is entered in column 7 on the codesheet. Question 2-race-finds the response is "white,"

which is also a 2 in the code and is entered in column 8. Proceeding in similar fashion,

1-"Catholic"-is entered in column 9, and 3 for "separated or divorced" is marked in column

10. Finally, a two-digit code was necessary to accommodate the last two digits in year of birth.

In this case, the numbers 4 and 2 were coded in columns 11 and 12, respectively. Although our

sample codebook was a simple one for illustrative purposes, the same basic procedure is

followed for all relevant items in longer instruments.

Figure 12.7 illustrates the process involved in downloading a study from the National

Archive of Criminal Justice Data (NACJD). Care must be taken that one understands the codebooks

and other idiosyncrasies with respect to the data. Research staff at NACJD and other similar

sites are usually more than willing to assist in clarifying issues and answering questions.

Coder Monitoring

Coder monitoring involves checking the work of coders for accuracy. Coder monitoring is

reconciliation procedures as essential quality-control checks on mechanical error. Each questionnaire

is double-coded; that is, two different coders independently code the same questionnaire.

Next, disagreements are identified. Reconciliation involves the coders coming to an agreement on

the proper code. Such a procedure not only eliminates outright errors in coding, but also results in

greater uniformity and consistency. Such a process can also be supplemented with computer edit

programs, which identify by column the incorrect values (those not defined by the codebook as

proper values). Unfortunately, unchecked mechanical errors may be the true rival causal factor

in many pieces of reported research. Thus, the results of a survey may not be due to accurate

measurement; rather, they may simply be due to miscoding, data entry, and other human and

mechanical mistakes. In some instances, precision and care in earlier stages of a project are disregarded

once the "boring" routine of "number crunching" is begun.

Keyboard Entry

The **keyboard entry **technique is the most widely used means of inputting data. The data typed

on the keyboard are displayed on a video terminal. The terminal displays case 1, variable name 1,

and prompts (asks for information) for case 1. Once these data are entered, the screen prompts for

the data for case 2; eventually, all of the data are entered. The computer can save the data (as a file

in its memory) or output the data onto some medium, for example, paper (printout), magnetic

tape, or diskettes, for later use. The printout is produced by a printer, which is similar to a

typewriter. Data stored in memory or on tape or a disk are referred to as a completed *data file.*

Coder

monitoring

Keyboard

entry

ISBN 0-558-58864-6

FIGURE 12.7 Download-National Archive of Criminal Justice Data. *Source: *www.icpsr.umich.edu/cgi-bin/

archive.prl?path=NACJD;format=tb;study=6542&emai . . .

Data

verification

Data Verification

Data verification or *cleaning *involves double-checking the data file in search of errors, many of

which are inevitable despite the conscientiousness of workers. Code entries can be checked by

computer programs themselves, as well as by checking data columns for inaccuracies. A simple

frequency distribution run for each variable will identify unauthorized values, for example:

Sex *N*

1. Male 48

2. Female 47

5. 2

6. 1

9. Unknown 2

100

Chapter 12 • Data Management **307**

Marginal run

In this example, values 5 and 6 were not authorized in our code and are errors. Software

packages generally further assist by identifying the case numbers of these unauthorized values,

which can then be checked by examining whether the data were incorrectly entered (e.g., a column

skipped). One can check the coding by going back to the original questionnaire. Some computer

programs identify all unauthorized (not identified in codebook) values before doing any analysis.

Ultimately, despite painstaking efforts, some errors are likely to remain; if a reasonable effort is

made to clean the data, these errors should be minor. Once the data file has been cleaned to the

satisfaction of the researcher, it is ready for analysis.

SIMPLE DATA PRESENTATION

Simple data presentation involves summarizing and using univariate statistics. The initial step in data

analysis is a **marginal run**. It is called "running the marginals" because it consists of single variable

tabulations of the type of data that appear in the margins of tables to be constructed later. Table 12.1

depicts a standard marginal run that reports both the number and the percentage of cases. Such information

is usually reported in the descriptive parts of a write-up. For inexperienced researchers, little

thought is given to going beyond such tallying, although in reality the work has just begun. Such

information as number of people victimized, number of people afraid of crime, or age, sex, and race

characteristics of the population surveyed may be useful; but researchers are generally also

interested in how victimization or fear might be affected by the age, sex, or race of respondents.

We have all been victims of the folly of asking a person about their summer vacation and

then listening to a chronology of minute details. Although slides, postcards, and other graphic

portrayals of the account sometimes make it more interesting or more tolerable, most people are

simply interested in the highlights-noteworthy incidents or unexpected developments.

Although a scientific report does not have entertainment as its major purpose, it also need not be

a cure for insomnia. Such reports must contain sufficient detail to enable the reader to assess the

logic and validity of the procedures used; however, they certainly should not burden the reader

with huge amounts of raw data or routine information.tables, graphic displays, frequency distributions, and other summarizing procedures, it should

be possible to communicate the significant findings in an understandable and painless fashion.

Rates

Rates, proportions, percentages, and ratios are meaningful ways of standardizing data so that

useful comparisons can be made between unequal populations. A rate expresses the number of

cases of the criterion variable per unit of population, for example, per 1,000. These measures

also summarize raw data in a form that is easier to read and understand. Suppose City A with a

population of 1,500,000 had 400 serious index crimes in a given year, and City B with a population

of 900,000 had 250. Which city had the worse crime problem is not readily apparent.

City A City B

Crimes 400 250

Population 1,500,000 900,000

Crime rate The **crime rate **could be calculated using the following formula:

Crime rate =

Number of crimes

Population * 100,000

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308 Chapter 12 • Data Management

TABLE 12.1 Comparison of Demographic Characteristics of Men and Women in

National Violence Against Women Survey (NVAWS) and U.S. Population

Men (%)a Women (%)a

Demographic

Characteristics NVAWS

U.S.

Populationb NVAWS

U.S.

Populationb

Age (*N *= 7,920) (*N *= 92,748,000) (*N *= 7,856) (*N *= 100,679,000)

18-24 11.4 13.0 9.8 11.9

25-29 10.4 10.2 9.6 9.4

30-39 25.4 23.8 24.6 21.9

40-49 24.0 20.0 22.5 18.9

50-59 13.5 13.0 14.4 12.9

60-69 8.8 10.1 9.9 10.7

70-79 5.2 7.0 6.8 8.9

80+ 1.5 2.9 2.5 5.5

Race/Ethnicity (*N *= 7,353) (*N *= 93,282,000) (*N *= 7,453) (*N *= 101,117,000)

White 87.4 84.8 86.6 83.7

African-American 9.0 10.9 10.5 12.0

American Indian/

Alaska Native

1.4 0.7 1.2 0.7

Asian/Pacific Islander 2.2 3.5 1.8 3.6

Hispanic Originc (*N *= 7,916) (*N *= 93,282,000) (*N *= 7,945) (*N *= 101,117,000)

Hispanic 7.3 9.4 7.9 8.5

Non-Hispanic 92.7 90.6 92.1 91.5

Marital Status (*N *= 7,928) (*N *= 92,007,000) (*N *= 7,921) (*N *= 99,588,000)

Never married 21.2 26.8 15.5 19.4

Currently married 66.8 62.7 62.7 59.2

Divorced, separated 10.2 8.3 13.3 10.3

Widowed 1.9 2.5 8.6 11.1

Educationd (*N *= 7,010) (*N *= 79,463,000) (*N *= 7,068) (*N *= 86,975,000)

Less than high school 9.4 18.3 10.7 18.4

High school and equivalent 29.3 31.9 34.6 35.7

Any college 48.3 40.4 45.7 39.7

Advanced degree 13.0 9.4 9.0 6.2

aPercentages may not total 100 due to rounding.

bBased on U.S. Bureau of the Census estimates, Current Population Survey, 1995.

cPersons of Hispanic origin may be of any race.

dFor persons aged 25 years and older.

Source: Tjaden, Patricia, and Nancy Thoennes. "Stalking in America: Findings from the National Violence Against

Women Survey." *Research in Brief *(National Institute of Justice and Centers for Disease Control and Prevention),

April 1998, p. 15.

ISBN 0-558-58864-6

Chapter 12 • Data Management **309**

For our data we would calculate

A more meaningful standardized comparison can now be made. Although City A has

more crime, this is in part expected because it also has a larger population than City B. If the

crime rate is expressed per 100,000 population, City A actually has a slightly smaller crime

rate (26.7) than City B (27.7). This same information can be expressed using other summary

devices.

Proportions

Proportions express the number of cases of the criterion variable as part of the total

population:

In our example of two cities we calculate

Proportions are obviously less useful in examples such as ours in which the criterion variable

is a relatively rare event. In such cases, rate is a far more useful summary statistic.

Percentages

Percentages are calculated by dividing a frequency by the total *N *and multiplying the result by

100. Percentages can be calculated quite easily from proportions:

For our example, the calculations would be:

In both cities, less than 1 percent of the citizens were victimized.

(City B) percentage = (100)

250

900,000 = .027

(City A) percentage = (100)

400

1,500,000 = .026

Percentage = 100

Frequency

N

(City B) proportion =

250

900,000 = .00027

(City A) proportion =

400

1,500,000 = .00026

Proportion =

Frequency of criterion variable

N

(City B) crime rate =

250

900,000 * 100,000 = 27.7

(City A) crime rate =

400

1,500,000 * 100,000 = 26.7

310 Chapter 12 • Data Management

16 12 22

5 30 18

19 28 27

4 13 4

2 17 5

8 6 12

10 16 20

12 1 4

1 9 8

4 12 2

Ratios

To illustrate the calculation of a ratio, we use a new example that provides more useful data for

the purposes of this statistic. A **ratio **simply compares the number of cases in one category with

the number in another. For example, suppose that in a given city 200 crimes were recorded, 40 of

which were committed by females. The ratio of male to female criminals could be obtained using

the following formula:

The ratio of male to female criminals is 4 to 1.

Often, in expressing ratios of criminals by sex, a demographic calculation called the sex

ratio is made

In our example

A sex ratio of 400 indicates that for every 100 female criminals there are 400 male criminals.

THE FREQUENCY DISTRIBUTION

In addition to the calculation of summary statistics such as those just discussed, it is standard

procedure for researchers to summarize and group data into a form that is more easily interpreted

by the reader. Suppose, for example, we had the followingAmerican cities:

Sex ratio =

160

40 * 100 = 400

Sex ratio =

Frequency males

Frequency females * 100

Ratio ( males to females ) =

160

40 =

4

1

or 4:1

Ratio =

Frequency 1

Frequency 2

Simple scrutiny of the data does not provide a very neat picture of the relative distribution

of crime in these cities. A **frequency distribution **is a procedure in which the data are arranged

in a more meaningful summary table.

There are a number of unwritten rules regarding the construction of a frequency distribution.

First, the analyst must decide on the number of categories (classes) into which the data will be

Frequency

distribution

ISBN 0-558-58864-6

TABLE 12.2 Frequency Distribution for Victimization

Rates in Thirty Cities (Hypothetical)

Victimization Rate* *N *Percentage

0-5 8 26.7

6-10 5 16.7

11-15 7 23.3

16-20 5 16.7

21-25 2 6.7

26-30 3 10.0

Total 30 100.1

*Per 100,000 population.

grouped. Generally, selection of too few (less than five) or too many (say fifteen or so) groups defeats

the purpose of categorizing-the former because it fails to distinguish the data and the latter because

it is unwieldy and hard to read. Second, the groupings should be mutually exclusive; that is, it should

be possible to assign each case to one and only one group. Finally, the groups should cover the entire

distribution, with the within-group intervals as equal in size as possible. The major exception to the

last rule would be the use of *over *or *under *categories for extreme cases. For example, the age group

ninety and over would include the rare person who is 127 years old. Given unordered victimization

rates for thirty cities, Table 12.2 illustrates a typical frequency distribution for such data.

The data were organized into six equal categories with both the frequency and percentage

reported. Note that the percentages do not total to 100. This was due to rounding error,

which will be discussed in greater detail later in this chapter in the presentation on table

construction.

Despite the report writer's time-consuming attempts to make sense out of data and present them

in a most appropriate and simple manner, many readers are quite frankly bored by statistical presentations.

SPSS has a simple format for calculating frequencies. The user selects "ANALYZE" from the

menu bar, then "Descriptive Statistics" and then "Frequencies." In addition, a "Statistics coach" function,

which is available by clicking "HELP" on the menu bar and then selecting "Statistics Coach"

prompts the user with questions and explains the types of data required for particular procedures.

GRAPHIC PRESENTATIONS

Graphs or pictorial presentations of data are an attractive means of capturing the reader's attention

as well as of summarizing data, particularly information from frequency distributions. Software

such as SPSS, Harvard Graphics, or Microsoft Excel do a marvelous job of creating graphic

displays. For instance, in order to create graphs using SPSS, the user begins by choosing

"GRAPHS" from the menu bar and then selecting the icon for the type of chart that he or she wants.

Because "a picture is worth a thousand words," pictorials may similarly provide a useful way of

presenting complex data. Among graphic presentation techniques are:

Pie charts

Bar graphs

Frequency polygons

Graphs

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312 Chapter 12 • Data Management

Pie charts

Bar graphs

Murder

0.1%

Violent and property crimes

per 100,000 inhabitants Forcible rape

0.7%

Robbery

3.5%

Aggravated assault

7.5%

Motor vehicle theft

10.5%

Burglary

18.1%

Larceny-theft

59.4%

Crime in the United States, 2002. Washington, D.C.: U.S. Government Printing Office. 2003, p. 5.

In addition to these, there are other devices used, particularly in criminal justice, such as

crime clocks. SPSS graphs perform all of these and more.

Pie Charts

Pie charts are simply circles (pies) whose pieces represent proportions of some phenomenon

and total 100 percent. Figure 12.8 presents a typical pie chart. With crime index offenses from

the Uniform Crime Reports (UCR), the relative percentages of each index offense are presented

as pieces of a pie. The appeal of pie charts is their obvious simplicity of interpretation. In this

instance, it is easy to note that larcency-theft made up more than half of the index offenses, and

together with burglary, it accounted for more than three-fourths of index crimes.

Bar Graphs

Bar graphs consist of rectangles. The width often represents the class intervals (not depicted

here), and the height represents quantity or amount (Figure 12.9). There are a number of rules for

constructing and reading bar graphs and frequency polygons:

Score values are usually arranged along the horizontal dimension (across) and amounts

such as frequencies and percentages are plotted vertically (upward or downward).

Chapter 12 • Data Management **313**

Frequency

polygons

Percent

Age

Pittsburgh Males

0

5

10 11 12 13 14 15 16 17 18 19

10

15

20

25

FIGURE 12.9 Prevalence of Serious Violence by Age in Pittsburgh. *Source*: XXXXX, XXXXX Tatem,

et al. "Epidemiology of Serious Violence." *Juvenile Justice Bulletin*, June 1997, p. 5.

Appropriate labels should be used so that the graph is self-explanatory. The horizontal line,

for example, could include name of city, type of crime, and so forth; for the vertical line,

some calibration of amounts, percentages, or *N*s should appear.

Zero points should begin at the far left, and ascending values upward and to the right.

Figure 12.9 shows the percent variation of serious adolescent violence by age among

Pittsburgh males.

Frequency Polygons (Line Charts)

In **frequency polygons **(or line charts), the frequency or percentages of the midpoint of each

score value are plotted and connected by a straight line that begins and ends at the baseline.

Figure 12.10 presents some typical frequency polygons, in this case, from the UCR. The horizontal

axis contains the years 1995 to 1999, and the vertical axis contains percentage changes

over the base year of 1995, which is recorded as zero. Note the dip below zero representing the

decline in reported crime. Similarly, the actual horizontal axis is raised above the base to permit

delineation of negative percentages that fall below the base zero line. In discussing the importance

of graphic displays, Tracy (1990, p. 76) notes:

Tables are effective when more than one statistical measure is being reported or when

sets of exact scores should be given. On the other hand, figures, such as histograms

and bar charts, are very effective for displaying descriptive measures when the

interest is in highlighting particular relationships, especially comparative differences

across groups. Line charts are essential in depicting data trends over time.

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314 Chapter 12 • Data Management

1995

3

0

-3

-6

-9

-12

-15.6

-22.1

-24.9

-18.0

-8.0

-5.3

-6.2

-9.7

-15

-18

-21

-24

-27

1996 1997 1998 1999

Number of Offenses

Rate per 100,000

FIGURE 12.10Crime in the United States, 1999. Washington, D.C.: U.S. Government Printing Office, 2000, p. 52.

The easy availability of sophisticated statistical software packages has encouraged the use of

statistical analysis, which is well and good. However, this has led some report writers to ignore the

use of tables and figures in describing their data. "The most simple analyses, effectively displayed,

are often the most convincing and communicative to the reader" (ibid). The same software packages

can generate terrific graphic displays.

Figure 12.11 is a comparative frequency polygon in which two different distributions are

plotted on the same grid. Note how the frequency polygon better captures the similarity between

the two groups, representing one group by a solid line and the other by a dashed (broken) line. A

variety of other means of graphically depicting data exist. For more detailed information, see

Zeisel (1957).

Using SPSS for Graphs

Software programs such as SPSS 11.5 (Statistical Package for the Social Sciences) aid considerably

in the process of selecting and constructing highly useful graphic displays.

Tutorials that are featured with the software guide users in making their selections. To create

a chart, one chooses "Graphs" from the menu bar and then chooses the icon for the type of

ISBN 0-558-58864-6

Research Methods in Criminal Justice and Criminology, Eighth Edition, by Frank E. Hagan. Published by Prentice Hall. Copyright © 2010 by Pearson Education, Inc:

Chapter 12 • Data Management **315**

Relative Professionalism Level of Rehabilitation Counseling

As Perceived by Student Panels

Professionalism of

Rehabilitation Counseling

to

N

to

high-marginal

low-marginal

low -0

123

-4

-5

7

-8

5.7

5.1

18.2

28.0

27.4

7.6

2.2

2.5

99.9

314

high

Total %

1965

%

1972

%

5.8

8.6

16.1

27.9

28.7

5.9

.7

1.3

99.9

707

%

0 1 2 3 4 5

5

10

15

20

30

25

6 7 8

Typical Professions for Comparison

Welfare agency

social worker

Clinical

psychologist

Physician

Lowest rating of

rehabilitation

counselor

Highest rating of

rehabilitation

counselor

FIGURE 12.11 Relative Professionalism Level of Rehabilitation Counseling as Perceived by Student

Panels. The Graph Comprises Plotted Distribution of the Data in the Table: -, 1965 cohort; -, 1972

cohort. As Suggested by the Spread of Ranks, Differences Between the Two Groups Are Not

Statistically Significant: Kolmogorov-Smirnov *D *= 0.358, *p *> .05. *Source*: Hagan, Frank E., Marie R.

1965 and 1972. 2nd series, Working Paper No. 5. Cleveland: Case Western Reserve University,

Institute on the Family and the Bureaucratic Society, 1975, pp. 50-51.

ISBN 0-558-58864-6

316 Chapter 12 • Data Management

chart desired. In SPSS, clicking on "Graphs" and then "Gallery" yields a pull-down menu

that features a variety of choices:

- Graphs
- Gallery
- Bar
- Line
- Area
- Pie
- High-Low
- Pareto
- Scatter
- Histogram
- Normal P-P
- Normal Q-Q
- Sequence
- Autocorrelations

The Graphs Gallery gives a main chart gallery with icons. The latter makes it possible to

envision the type of graphic display one may desire.

Crime Clocks

Despite its words of caution to the public (see description in Figure 12.12), the FBI publishes

figures called **crime clocks **as part of the annual UCRs. Figure 12.12 shows "Crime Clock,

2002," which indicates that one crime index offense occurred every three seconds and that one

violent crime occurred every twenty-two seconds.

In such circumstances, we could have the same proportion or even a relative decline in crime

relative to population growth, but the crime clock would misleadingly show a consistent increase.

A simple example may illustrate this point. Suppose that in 1980 a given city had 356 serious

crimes for its population of one million. Ten years later, the city had 712 serious crimes, but now a

population of two million. The crime clock approach would suggest that crime doubled during the

second period, whereas by controlling for population we find that the crime rate is actually the

same.

The misleading feature of the crime clock is that it fails to control for population growth

and uses a constant, fixed unit of comparison time. Although the FBI acknowledges this feature

as misleading, it continues to publish the clock year after year.

If you have learned anything at all about crime clocks, please do this writer and many

others in the criminology/criminal justice field a favor, and ten years from now, when you are

the director of some agency and asked to give a speech on crime to some civic club, do not

begin your speech with a trite recitation of crime clock statistics, as so many unfamiliar with

the inadequacy of such graphic displays are fond of doing. Better yet, if you hear such a

speech, ask the speaker how the crime rate compares with these statistics over the past few

years.

The sometimes tedious prospect of constructing figures has been in part alleviated by the

fact that most computer packages will provide graphic displays of data suitable for presentation

in a report or professional article. The reading and construction of graphic figures requires, at a

simpler level, many of the same skills that are necessary in interpreting or building tables.

Crime clocks

ISBN 0-558-58864-6

Chapter 12 • Data Management **317**

One

Aggravated Assault

every 35 seconds

The Crime Clock should be viewed with care. Being the most aggregate representation of

UCR data, it is designed to convey the annual reported crime experience by showing the

relative frequency of occurrence of the Index Offenses. This mode of display should not be

taken to imply a regularity in the commission of the Part 1 Offenses; rather, it represents

the annual ratio of crime to fixed time intervals.

One

Murder

every 32 minutes

One

Violent Crime

every 22 seconds

One

Forcible Rape

every 6 minutes

One

Robbery

every minute

One

Property Crime

every 3 seconds

One

Burglary

every 15 seconds

One

Larceny-Theft

every 5 seconds

One

Motor Vehicle Theft

every 25 seconds

One

Crime Index Offense

every 3 seconds

Reports: Crime in the United States, 2002. Washington, D.C.: Government Printing Office,

2003, p. 4.

ISBN 0-558-58864-6

318 Chapter 12 • Data Management

TABLE READING

Tables are presentations of quantitative data in a summary or uniform fashion. Many standardized

tests such as civil service exams, the Graduate Record Exam (GRE), and professional tests feature a

section on table reading. Individuals who are bored or panicked by such tables under normal

conditions are very likely to do poorly in such testing situations. This is unfortunate because the

mastery of some rather elementary procedures is likely to improve one's scores considerably. Table

reading and construction in this presentation involve at least a 2 × 2 table in which percentaging and

standard statistical procedures, to be discussed in detail later in Chapter 13, are performed.

A cross tabulation (or contingency table) examines one variable in terms of another (or other)

variable(s). A 2 × 2 table is a cross tabulation that looks at two values of the first variable and two

values of the second variable at the same time. For example, in tabulating or counting responses we

would tally four (2 × 2) categories, let us say Male and Female and Criminals and Noncriminals.

This procedure will be explained in more detail in the section on "Presentation of Complex Data."

Why Bother with Tables?

Many people find tables boring and skip them when reading journal articles or reports; at the

same time, they may spend an hour reading verbal reports of what the author claims a table

shows. The mastery of table reading can result in a great economy of effort, tantamount to speedreading.

Readers may find themselves skipping the written portions of reports and reading the

tables, gaining much of the needed information in much less time. In addition to being a useful

skill, table reading and construction are valuable scientific and administrative tools, essential for

summarizing and analyzing figures.

What to Look for in a Table

Table 12.3 is a typical table one might find in criminal justice or criminology. Let us ransack this

table and systematically draw out some major points one should examine in a table.

There are a number of essential characteristics of most tables that a patient and systematic

reader can look for which can be overlooked by a less methodical approach (Cole, 1972,

pp. 28-37; Wallis and Roberts, 1956).

STEPS IN READING A TABLE

The first step in systematically reading a table is to *carefully read the title. *A good title will inform

the reader of exactly what is being presented. Table 12.3, for instance, tells us that we are examining

personal crimes as opposed to crimes committed against commercial establishments. A properly

constructed title will also usually list the dependent variable first and then the independent

variable(s). In Table 12.3, for instance, victimization rates are the dependent variable; race and age

are the independent variables.independent variable(s) (age and race). In addition, the title of Table 12.3 indicates that the data

are for persons age 12 and over and that the data presented will be broken down by the type of

crime. The title also indicates that the data are for the year 1992.

Next, the *headnote*-section appearing in parentheses below the title-should be examined.

This explains exactly what the numbers we are looking at represent. In this case, we are reading

the rate per 1,000 persons in each age group. This is important to note because sometimes readers

Table reading

ISBN 0-558-58864-6

Rates for Persons Age 12 and Over, by Race and Age of Victims

and Type of Crime

Rate per 1,000 Persons in Each Age Group

Robbery Assault

Race and Age

Total

Population

Crimes of

Violence

Completed

Violent

Crimes

Attempted

Violent

Crimes Rape Total

With

Injury

Without

Injury Total Aggravated Simple

White

12-15 11,304,360 75.0 28.8 46.2 1.1* 10.8 2.3* 8.5 63.1 17.4 45.7

16-19 10,896,950 70.5 22.9 47.6 2.0* 10.2 4.2 6.1 58.3 20.2 38.0

20-24 15,131,160 67.5 23.9 43.7 2.6* 7.8 3.6 4.2 57.1 16.8 40.3

25-34 34,815,850 35.7 13.3 22.3 0.3* 6.4 2.2 4.2 28.9 9.0 19.9

35-49 40,013,130 21.0 7.0 14.0 0.3* 3.3 0.9 2.4 17.4 6.3 11.1

50-64 28,847,500 9.4 2.2 7.2 0.1* 2.2 0.9* 1.3* 7.1 2.1 5.0

65 and over 27,605,090 4.3 1.2* 3.0 0.3* 0.9* 0.0* 0.9* 3.1 1.3* 1.8

Black

12-15 2,219,000 83.3 23.9 59.4 1.5* 5.3* 4.1* 1.3* 76.5 35.7 40.7

16-19 2,039,150 125.5 59.4 66.1 0.0* 46.7 11.1* 35.6 78.8 59.0 19.8

20-24 2,446,270 102.4 40.5 61.9 3.7* 34.5 6.0* 28.5 64.2 30.1 34.2

25-34 5,259,930 51.5 22.7 28.8 1.7* 17.3 10.9 6.4* 32.6 12.3 20.2

35-49 6,144,400 25.8 11.7 14.1 1.4* 7.2 3.4* 3.8* 17.1 13.1 4.1*

50-64 3,258,690 17.0 10.5* 6.5* 0.0* 8.2* 4.0* 4.2* 8.8* 4.8* 4.0*

65 and over 2,504,830 10.7* 5.3* 5.3* 0.0* 7.6* 4.0* 3.6* 3.0* 1.4* 1.6*

Note: Detail may not add to total shown because of rounding.

*Estimate is based on about ten or fewer sample cases.

Source: U.S. Department of Justice. *Criminal Victimization in the United States, 1992: A National Crime Victimization Survey Report*. Washington, D.C.: Bureau of

Justice Statistics, March 1994, p. 28.

ISBN 0-558-58864-6

320 Chapter 12 • Data Management

are not sure whether they are interpreting raw numbers, percentages, or other types of data. Be

sure to note *what units *are being used in a table.

Another very important item for the reader to note is *the source *from which the data in the

table were drawn. In this case, the original source was the U.S. Department of Justice National

Crime Victimization Survey, which was conducted in 1992. Those familiar with this survey from our

previous discussion are aware that it is conducted by the U.S. Bureau of Census on behalf of the U.S.

Bureau of Justice Statistics and is a model of its kind. The data are based on a stratified multistage

cluster sample that is representative of households in the United States. Of course, the statistics

reported are claimed victimizations of the survey sample rather than official police records. One reason

for noting the source is to obtain a relative evaluation of the reliability of the data. In this case,

given known limitations, this source is generally regarded as one of the very best of its type.

Footnotes contain additional information that may be of importance in judging the data

presented in the tables. In this case, the footnote mentions that the detail (data breakdowns) may

not sum to the total shown in parentheses because of rounding. The numbers in the second column

refer to the total national population in that group. The latter is important because it indicates that

the sample data have been inferred to the national population and we are reading national statistics

as if everyone in the United States had been surveyed. Finally, the footnote asterisk which refers

to a few of the figures in the table states that these estimates may be unreliable because they are

based on roughly ten or fewer sample cases. Thus, for instance, statistics on the rape rate are based

on too few cases to be reliable.

Read the subheads, or stubs, as a guide to the information in the columns and rows. Similar

to columns in a building, table columns run vertically while rows run horizontally. The subhead for

rows appears in the far upper left-hand corner, and each subcategory runs down the left-hand side

of the table. In this case, the rows refer to different age groups and races. The column subheads

identify various types of crimes. Because the race-specific age groups are of unequal size, the only

fair comparison would be to percentage or establish rates within each independent variable

(age-race cohorts). As will be explained later, we wish to knowvariable (race-specific age cohorts) is a category of the dependent (have been victimized). Thus,

proper percentaging or rate calculations are read across or within each category of the independent

variable(s). Reading the first cell, 75 per 1,000 whites who were 12 to 15 years of age

(*N *= 11,304,360) were victimized.

Another useful statistic to *look for *is the general *overall average and range *(variation from high

to low) in the data. In this case, Table 12.3 fails to provide any figures on overall rates for total, whites,

blacks, or all ages. We can, however, obtain a picture of the general variation in the data. Although

unreliable because of small sample *N*s, the lowest victimizations, estimated at zero, were for rape

among blacks ages 16 to 19 and 50 or over and among whites ages 25 and over. By contrast, the highest

rates, 125.5 per 1,000, were for blacks ages 16 to 19 who were victims of crimes of violence. The

highest specific victimization rate, 59 per 1,000, was for aggravated assault for blacks ages 16 to 19.

Next, one should *examine the fluctuation of this range and/or average *within each category

of the dependent variable (type of victimization). For crimes of violence, which include adjacent

subcategories of rape, robbery, and assault, the most victimized group was blacks ages 16 to 19

(125.5 per 1,000); by contrast, the least victimized group was whites age 65 or over (only 4.3 per

1,000). In other words, blacks in their late teens were about 31 times more likely to be victimized

than whites over the age of 65.

Examination of marginals or column and row totals is useful in obtaining a general

overview of effects. Unfortunately, this table does not possess such figures, and this will be

illustrated with a later example. *For each independent variable, examine the overall effects.*

ISBN 0-558-58864-6

Customer reply replied 9 years ago

Chapter 12 • Data Management **321**

With a total variation of 4.3 to 125.5 for crimes of violence, how do these rates vary by

age and race? With only some exceptions for particular crimes, in general, the older the age

cohort, the less likely the respondents indicated having been victimized. Also, blacks were

more likely to be victimized by crime than whites.

Finally, those reading tables should examine each cell and look for inconsistent elements.

Are there any countertrends or rates that go against the grain? In this table, there did not appear

to be any noteworthy anomalies.

Summary of Table 12.3

A summary of Table 12.3 would, of course, be much more brief than our detailed account. It

would read that among victims of personal crimes ages 12 and over in the United States in 1992:

Violent victimization ranged from a high of 125.5 per 1,000 among blacks ages 16 to 19 to

a low of 4.3 among elderly whites ages 65 and over.

Although there was considerable variation within each age-race category for most crimes,

there was a decrease in victimization by age.

If the race of the victim were considered, blacks were more likely to be victims of crime in

almost all age cohorts for assault, rape, and robbery.

Much of the procedure for reading tables is, of course, also applicable to the reading of figures

and other graphic presentations discussed earlier in this chapter. Careful reading of the title, units,

source, headnotes, footnotes, and the like will assist in mastery of the data. Of course, researchers

should attempt to make explicit all of these elements in tables and figures they are developing.

To illustrate the usefulness of reading marginal totals of a table, a feature that was missing in

our previous example, Table 12.4 is presented. Ignoring for the time the footnote that describes statistical

procedures, which will be analyzed in Chapter 13, the marginal totals are values below and to the

side of the cells and serve as benchmarks with which to compare the intercellular values. For instance,

the total marginals for rows (across the side) would indicate that 64 percent of all defendants were

jailed. Comparing this with each category, we discover that 79 percent of the "unattractive," compared

with 54 percent of the "attractive," were incarcerated-a significant difference. Given knowledge of

the marginals, proportion of total incarcerated gives us some basis on which to examine differences

within categories of the independent variable, in this case, attractiveness or unattractiveness.

TABLE 12.4 Incarceration by Attractiveness

(All Figures Are Percentages)*

Attractiveness

Incarcerated Below Average Above Average Total *N *Percent

Yes 79 54 45 (64)

No 20 46 25 (36)

Total *N *29 41 70 (100)

*All figures are percentages. *X*2 4.87, 1 *df, p < *.05.

Source: Adapted from XXXXX, XXXXX E. "Defendant's Attractiveness as a Factor in the Outcome

of Criminal Trials: An Observational Study." Paper presented at the Southeastern Psychological

Association Convention, New Orleans, Louisiana, 1979. Reproduced by permission of the

author.

ISBN 0-558-58864-6

322 Chapter 12 • Data Management

TABLE 12.5 One Variable Tables

N Percent

Defendant Disposition in Criminal Trials

Incarcerated 45 64

Not incarcerated 25 36

Total 70 100

Rated Attractiveness of Defendants in Criminal Trials

Attractive 41 59

Unattractive 29 41

Total 70 100

Source: Adapted from XXXXX, XXXXX E. "Defendant's Attractiveness As a Factor in

the Outcome of Criminal Trials: An Observational Study." Paper presented at the

Southeastern Psychological Association Convention, New Orleans, Louisiana,

1979. Reproduced by permission of the author.

HOW TO CONSTRUCT TABLES

Table 12.4 was the simplest type of table, the one-variable (univariate) table, which reports the

type of data that ordinarily appear as marginal totals of more complex tables. For example,

tabular presentation of the data from Stewart's study (1979) of incarceration by attractiveness

of defendant would result in Table 12.5.

PRESENTATION OF COMPLEX DATA

One-variable tables are only the first and simplest step in reporting research findings. The next

step is more analytical and attempts to discover which independent variables are most predictive

of the outcome of the dependent variable(s). This may take the form of bivariate tables, to be

presented in this chapter, or multivariate analysis to be discussed in Chapter 13 on statistical

procedures. Because of the emergence of canned statistical programs (computer software) that

perform sophisticated analysis more quickly and efficiently, some feel that tabular analysis may

be outmoded-an antique. Hirschi and Selvin (1973, pp. 171-172) point out, however, that

despite its obvious limitations, tabular analysis is still an excellent means of reporting the final

results of a more complicated analysis in a form that is more easily understood by both

professionals and the lay reader. A thorough grounding in tabular analysis also assists in better

understanding the basic logic of more complex statistical procedures.

Bivariate tables, or those in which there is a two-variable cross tabulation, examine how

one variable influences the other. Consider an adapted example from Cole (1972, p. 29): It would

be as if we had a room full of defendants in a criminal trial and were to ask all those who are not

to be incarcerated to move to the front of the room and all those who are to be incarcerated to the

back. Next, we would ask all those who are not attractive (ugly) to move to the left and all those

who are attractive to move to the right. The room would now look like this:

(BACK)

Ugly incarcerateds (23) Attractive incarcerateds (22)

Ugly nonincarcerateds (6) Attractive nonincarcerateds (19)

TABLE 12.5 One Variable Tables

N Percent

Defendant Disposition in Criminal Trials

Incarcerated 45 64

Not incarcerated 25 36

Total 70 100

Rated Attractiveness of Defendants in Criminal Trials

Attractive 41 59

Unattractive 29 41

Total 70 100

Source: Adapted from XXXXX, XXXXX E. "Defendant's Attractiveness As a Factor in

the Outcome of Criminal Trials: An Observational Study." Paper presented at the

Southeastern Psychological Association Convention, New Orleans, Louisiana,

1979. Reproduced by permission of the author.

HOW TO CONSTRUCT TABLES

Table 12.4 was the simplest type of table, the one-variable (univariate) table, which reports the

type of data that ordinarily appear as marginal totals of more complex tables. For example,

tabular presentation of the data from Stewart's study (1979) of incarceration by attractiveness

of defendant would result in Table 12.5.

PRESENTATION OF COMPLEX DATA

One-variable tables are only the first and simplest step in reporting research findings. The next

step is more analytical and attempts to discover which independent variables are most predictive

of the outcome of the dependent variable(s). This may take the form of bivariate tables, to be

presented in this chapter, or multivariate analysis to be discussed in Chapter 13 on statistical

procedures. Because of the emergence of canned statistical programs (computer software) that

perform sophisticated analysis more quickly and efficiently, some feel that tabular analysis may

be outmoded-an antique. Hirschi and Selvin (1973, pp. 171-172) point out, however, that

despite its obvious limitations, tabular analysis is still an excellent means of reporting the final

results of a more complicated analysis in a form that is more easily understood by both

professionals and the lay reader. A thorough grounding in tabular analysis also assists in better

understanding the basic logic of more complex statistical procedures.

Bivariate tables, or those in which there is a two-variable cross tabulation, examine how

one variable influences the other. Consider an adapted example from Cole (1972, p. 29): It would

be as if we had a room full of defendants in a criminal trial and were to ask all those who are not

to be incarcerated to move to the front of the room and all those who are to be incarcerated to the

back. Next, we would ask all those who are not attractive (ugly) to move to the left and all those

who are attractive to move to the right. The room would now look like this:

(BACK)

Ugly incarcerateds (23) Attractive incarcerateds (22)

Ugly nonincarcerateds (6) Attractive nonincarcerateds (19)

(FRONT)

TABLE 12.5 One Variable Tables

N Percent

Defendant Disposition in Criminal Trials

Incarcerated 45 64

Not incarcerated 25 36

Total 70 100

Rated Attractiveness of Defendants in Criminal Trials

Attractive 41 59

Unattractive 29 41

Total 70 100

Source: Adapted from XXXXX, XXXXX E. "Defendant's Attractiveness As a Factor in

the Outcome of Criminal Trials: An Observational Study." Paper presented at the

Southeastern Psychological Association Convention, New Orleans, Louisiana,

1979. Reproduced by permission of the author

Chapter 12 • Data Management **323**

Statistically, this is exactly what Stewart (1979) did with his data in Table 12.5. This is presented

in a two-variable table of these data in Table 12.6.

Usually, a two-variable table such as Table 12.6 is not very useful in its raw or original

form. Such tables are usually percentaged, and it is here that many errors in analysis as well as

interpretation are made.

GENERAL RULES FOR PERCENTAGING A TABLE

Although this presentation may be overly simplistic, there is often a virtue in simplicity that, if

ignored, may lead to error. Many readers of this text may possess an intuitive logic that enables

them without blundering to percentage tables correctly. If any doubt exists, utilization of the

following rules may be of assistance:

1. *Choose a title for the table *on the basis of knowledge of the dependent variable (denoted

by *Y*) and independent variable(s) (denoted by *X*). Recall that the dependent variable is the

outcome the researcher wishes to predict, whereas the independent variable(s) is the predictor.

The title should read: *Dependent Variable by Independent Variable(s) *(*Y *by *X*).

Although not pertinent to our concern with percentaging, the table should also contain as

much additional information as is necessary to enable the reader to understand the source

of data, units being measured, and the like.

2. Keep in mind the need for fair comparisons if uneven-size groups are to be contrasted.

The larger group is likely to exhibit the greatest amount of any condition and the smallest

group the least amount, unless the comparison is made within rather than between

groups.

3. Always percentage within the independent variable rather than the dependent variable.

This controls for problems created by comparing unequal-size groups.

4. When doubt exists regarding the direction of proper percentaging, filling in the appropriate

variables in the following question may be of assistance: What percentage of the independent

variable ______ is a category of the dependent variable ______? (Cole, 1972, p. 30)

Zeisel (1957) says simply to percentage in the causal and representative direction.

Whether the independent or dependent variable should be listed at the top of the table or the

side and whether tables should be percentaged across or down are questions more of style.

The emerging preference is to list the independent variable on top and the dependent on the

side. One then *percentages down *and *reads the table across. *The important thing to remember

is to always percentage within categories of the independent variable; then, if you

percentage down, read across, or, if you percentage across, read down (Babbie, 1992, p. 399).

Unknowns should be eliminated from the base total in percentaging a table, and this should

TABLE 12.6 General Rules for Percentaging a Table

Attractiveness

Number

Incarcerated

Below

Average

Above

Average

Yes 23 22

No 6 19

Total 29 41

Statistically, this is exactly what Stewart (1979) did with his data in Table 12.5. This is presented

in a two-variable table of these data in Table 12.6.

Usually, a two-variable table such as Table 12.6 is not very useful in its raw or original

form. Such tables are usually percentaged, and it is here that many errors in analysis as well as

interpretation are made.

GENERAL RULES FOR PERCENTAGING A TABLE

Although this presentation may be overly simplistic, there is often a virtue in simplicity that, if

ignored, may lead to error. Many readers of this text may possess an intuitive logic that enables

them without blundering to percentage tables correctly. If any doubt exists, utilization of the

following rules may be of assistance:

1. *Choose a title for the table *on the basis of knowledge of the dependent variable (denoted

by *Y*) and independent variable(s) (denoted by *X*). Recall that the dependent variable is the

outcome the researcher wishes to predict, whereas the independent variable(s) is the predictor.

The title should read: *Dependent Variable by Independent Variable(s) *(*Y *by *X*).

Although not pertinent to our concern with percentaging, the table should also contain as

much additional information as is necessary to enable the reader to understand the source

of data, units being measured, and the like.

2. Keep in mind the need for fair comparisons if uneven-size groups are to be contrasted.

The larger group is likely to exhibit the greatest amount of any condition and the smallest

group the least amount, unless the comparison is made within rather than between

groups.

3. Always percentage within the independent variable rather than the dependent variable.

This controls for problems created by comparing unequal-size groups.

4. When doubt exists regarding the direction of proper percentaging, filling in the appropriate

variables in the following question may be of assistance: What percentage of the independent

variable ______ is a category of the dependent variable ______? (Cole, 1972, p. 30)

Zeisel (1957) says simply to percentage in the causal and representative direction.

Whether the independent or dependent variable should be listed at the top of the table or the

side and whether tables should be percentaged across or down are questions more of style.

The emerging preference is to list the independent variable on top and the dependent on the

side. One then *percentages down *and *reads the table across. *The important thing to remember

is to always percentage within categories of the independent variable; then, if you

percentage down, read across, or, if you percentage across, read down (Babbie, 1992, p. 399).

Unknowns should be eliminated from the base total in percentaging a table, and this should

TABLE 12.6 General Rules for Percentaging a Table

Attractiveness

Number

Incarcerated

Below

Average

Above

Average

Yes 23 22

No 6 19

Total 29 41

Rules for

percentaging a

table

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324 Chapter 12 • Data Management

Given: A bivariate table which looks at the relationship between

Sex of Respondent and Crime Commission

Crime is the dependent variable since it is more logical to

assume that a person's sex might influence crime commission

rather than crime commission influencing a person's sex.

Dependent

Variable

Crime

Commission (*Y *)

(*Y *)

1. Choose a Title: Dependent Variable by Independent Variable

Y (Crime) by *X *(Sex)

2. Independent Variable

Sex (*X*)

Male Female

Sex (*X*)

3.

5. Read Across Dependent Variable

6. Answer the Question: What percentage of the independent

variable (in this case of males or females) is a category of

the dependent variable (committed crime)?

4. Percentage Within or Down Independent Variable

FIGURE 12.13 How to Percentage a Table.

be stated in a footnote. It is generally good form to indicate in this same footnote the original

N, prior to elimination of the unknowns. Also note if, because of rounding, percentages do

not sum to 100. Figure 12.13, "How to Percentage a Table," schematically depicts one means

of doing so.

Prior to exploring the utility of these rules in examining and constructing tables, a very

brief refresher example on percentaging may prove useful. To obtain a percentage as in "What

percentage of 200 is 40?" one divides 40 by 200 and obtains 20 percent. If the question is "What

is 20 percent of 200?" simply multiply 200 by .20 to get 40. Percentages are usually rounded to

the nearest whole number; for example, 70.7 is rounded to 71. If the percentage is .5, always

round to the nearest whole number.

ISBN 0-558-58864-6

Chapter 12 • Data Management **325**

Now, using this information, our discussion returns to the raw data in Table 12.6. Seldom

are such data presented in such a form in reports. In most cases, the data would be displayed in

percentage form. Table 12.7 presents the same data in the properly percentaged form. Note that

the percentaging took place within each category of the independent variable, attractive/unattractive,

and was intended to address the question "What percentage of the independent variable

(of 41 attractive and 29 unattractive defendants) was a category of the dependent, incarcerated

or not (23 of 29 79 percent and 22 of 41 54 percent)?"

In many research reports, these data are usually presented in summary form as in

Table 12.8. Thus, 79 percent of unattractive defendants were incarcerated, whereas only

54 percent of the attractive ones were jailed. In reading summary tables, the number in parentheses

always refers to the total number of cases of the independent variable on which

calculation of the percentage was based. In other words, 79 percent (29) does not mean that

79 percent equals an *N *of 29 but that 79 percent of 29 cases, or 23 cases, were unattractive and

incarcerated. The negative condition, not incarcerated, can easily be obtained by subtracting the

percentage from 100 percent.

Improper Percentaging

It is not unusual to find errors in the presentation of data caused by the improper percentaging of

raw information. Table 12.9, for instance, is an example of improper percentaging of the

information in Table 12.6. The percentaging in Table 12.9 fails to address the correct research

TABLE 12.7

Attractive

Percent Incarcerated No Yes Total *N*

Yes 79 54 45

No 21 46 25

Total *N *29 41 70

TABLE 12.8

Attractive Percent Incarcerated

No 79 (29)*

Yes 54 (41)

*Total number of cases is given in parentheses.

Now, using this information, our discussion returns to the raw data in Table 12.6. Seldom

are such data presented in such a form in reports. In most cases, the data would be displayed in

percentage form. Table 12.7 presents the same data in the properly percentaged form. Note that

the percentaging took place within each category of the independent variable, attractive/unattractive,

and was intended to address the question "What percentage of the independent variable

(of 41 attractive and 29 unattractive defendants) was a category of the dependent, incarcerated

or not (23 of 29 79 percent and 22 of 41 54 percent)?"

In many research reports, these data are usually presented in summary form as in

Table 12.8. Thus, 79 percent of unattractive defendants were incarcerated, whereas only

54 percent of the attractive ones were jailed. In reading summary tables, the number in parentheses

always refers to the total number of cases of the independent variable on which

calculation of the percentage was based. In other words, 79 percent (29) does not mean that

79 percent equals an *N *of 29 but that 79 percent of 29 cases, or 23 cases, were unattractive and

incarcerated. The negative condition, not incarcerated, can easily be obtained by subtracting the

percentage from 100 percent.

Improper Percentaging

It is not unusual to find errors in the presentation of data caused by the improper percentaging of

raw information. Table 12.9, for instance, is an example of improper percentaging of the

information in Table 12.6. The percentaging in Table 12.9 fails to address the correct research

TABLE 12.7

Attractive

Percent Incarcerated No Yes Total *N*

Yes 79 54 45

No 21 46 25

Total *N *29 41 70

TABLE 12.8

Attractive Percent Incarcerated

No 79 (29)*

Yes 54 (41)

*Total number of cases is given in parentheses.

TABLE 12.9

Attractive Percent Incarcerated

No 76 (25)*

Yes 49 (45)

*Total number of cases is given in parentheses.

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326 Chapter 12 • Data Management

Elaboration

Replication

Specification

Explanation

question. It answers the question "Does incarceration affect attractiveness?" rather than the more

logical concern "Does attractiveness influence incarceration?" In short, it makes attractiveness

rather than incarceration the dependent variable. Recall that the condition we are attempting to

predict is always the dependent variable, whereas the independent variable is usually something

like age, sex, race, or in this case appearance, which is uninfluenced, given, or precedes in time

the outcome variable.

ELABORATION

Elaboration refers to the process of introducing or controlling for third variables (control or test

factors) by subclassifying original tables. In discussing the resolution of the causality problem in

Chapter 3, we described three steps:

1. Demonstrate a relationship between the variables

2. Specify the time order (which is *X *[independent variable] and which is *Y *[dependent

variable])

3. Control for or exclude rival causal factors

One way of controlling for such other factors is before-the-fact-that is, through research design.

Another way is statistically through the subclassification of tables (elaboration) and through various

statistical procedures such as partial correlation and multiple correlation and regression (to be discussed

in Chapter 13). Elaboration enables us to introduce statistical or tabular controls after-the-fact. Here we

will be discussing five basic results of elaboration, which are depicted in Figure 12.14.

Replication takes place when the partial tables replicate or reproduce the relationship in the

original table. In controlling for a rival causal factor (*Z*), for example, the original relationship

between *X *and *Y *should hold. Hypothetically, let us say that a researcher examined the relationship

between sex (*X*) and delinquency (*Y*) and found a strong relationship-that is, that males are more

delinquent than females. In this case, controlling for social class (*Z*) did not alter this relationship.

Tracy (1990) gives another hypothetical example: An individual's level of education might be used

to predict prejudice even when controlling for age, race, or religion.

Specification specifies the conditions under which the original relationship holds. The

elaboration or subclassification of tables might produce very different partial tables-for

example, one with weaker and one with stronger relationships than in the original table. The

third variable (*Z*), for example, could be antecedent or intervening. Consider another

hypothetical example examining the relationship between sex (*X*) and delinquency (*Y*). Does

a positive relationship exist between these two variables? Not in a case that controls for social

class (*Z*). Such a case could show (specify) that although there is a strong relationship

between sex and delinquency among the lower-class adolescents, there is no such relationship

among middle- and upper-class groups.

Explanation occurs when the relationship observed in the original bivariate table weakens

or disappears in the partial tables. If this third variable (*Z*) is antecedent and logically precedes the

independent variable (*X*), then this is called *explanation. *If it logically occurs as an intervening

variable, then it is an example of **interpretation**. Thus, although in *interpretation *the partial table

relationships also weaken or disappear, the control variable is an intervening one or occurs

between *X *and *Y.*

As an example of explanation, consider the case of a researcher who claimed to have made

the astounding discovery that there is a positive relationship between foot size (*X*) and intelligence

(*Y*). But it turns out that upon controlling for a third "antecedent" variable-age (*Z*)-the original

Interpretaion

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Chapter 12 • Data Management **327**

Replication -

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The partial tables replicate (reproduce) the original table; the

control variable (*Z*) has no effect upon original relationship

between *X *and *Y*.

Specification - The partial tables do not replicate the original table or relationship;

for example, one partial table shows a stronger relationship and the

other no relationship. The control variable specifies the conditions

under which the relationship holds.

Explanation - Interpretation - The relationship that existed in the original table

disappears (is shown to be spurious) in the partial tables. If the

time order of *Z *is before *X *(antecedent), this is called explanation.

If the time order of *Z *is after *X*, it is called an intervening variable

and the process is called interpretation.

Suppression - Although there is little or no relationship in the original table,

relationships appear in the partial tables when the control variable

is introduced.

FIGURE 12.14 Types of Elaboration (All Figures Represent Percentages).

relationship disappears. That is, the third variable is the critical factor: Adults are bigger than

children and are smarter. Controlling for age-that is, among adults or among children-causes

the relationship to disappear.

Interpretation can be illustrated by the following hypothetical example. A researcher

suspects that a hypothetically strong relationship exists between broken homes (*X*) and

delinquency (*Y*). In controlling for social class (*Z*), however, he or she finds that the relationship

disappears-that is, among both lower-class and upper-class individuals, there are no differences

by family type in delinquency. Lower-class groups do tend to have higher delinquency rates

overall, but this rate does not vary by family type.

Suppression takes place when relationships occur in the partial tables even though there

is no original bivariate relationship. Suppose the original table shows no relationship between

broken homes (*X*) and delinquency (*Y*); however, when we control for social class (*Z*), lowerclass

broken homes are found to produce higher delinquency rates than non-lower-class

broken homes.

Suppression

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328 Chapter 12 • Data Management

The elaboration model could be used to control for rival causal factors by dividing our original

bivariate table into subtables based upon control variables, but doing this could be an interminable

process. This task is aided by computer software that can perform crosstabs (crossbreaks) very

quickly. Although much multivariate analysis relies upon more sophisticated statistical procedures,

the elaboration model gives one a thorough grounding in what Rosenberg calledAnalysis (1968), and such tabular analysis is also far more readily understandable to the lay reader of

quantitative reports. Readers are referred to Lazarsfeld, Pasanella, and Rosenberg (1972), Rosenberg

(1968), Hirschi and Selvin (1973), and Zeisel (1957) for more details regarding elaboration.

LYING WITH STATISTICS

Zeisel (1957) describes *How to Lie with Statistics *and particularly illustrates the misuse of

graphic displays that exaggerate or underplay statistical findings by drawing figures out of scale

or using calibrations of the horizontal or vertical axes that are misleading. He advises readers on

"how to talk back to statistics" and, by addressing the following issues, to avoid "learning a

remarkable lot that isn't so" Zeisel (1957):

Who Says So?

Look for bias such as "the laboratory with something to prove for the sake of a theory, a

reputation, or a fee; the newspaper whose aim is a good story; labor or management with a

wage level at stake."

How Does He or She Know?

Is the sample large enough to permit any reliable conclusion? You won't always be told

how many cases. If percentages are given, make sure the raw figures are also present.

Did Somebody Change the Subject?

It is all reminiscent of the way that Lincoln Steffens and Jacob A. Riis (in the early 1900s),

as New York newspapermen, once created a crime wave. Crime cases in the papers reached

such proportions, both in numbers and in space and big type given to them, that the public

demanded action. Theodore Roosevelt, as president of the reform Police Board, was

seriously embarrassed. He put an end to the crime wave by simply asking Steffens and Riis

to lay off. It had all come about simply because the reporters, led by those two, had got into

competition as to who could dig up the most burglaries and whatnot. The official police

record showed no increase at all Zeisel (1957).

Is It a Real Conclusion?

Beware of a switch somewhere between the raw figures and the conclusion, in which one

thing is reported as another. For example, more reported cases is not the same thing as

actual cases, just as a voter's poll is not the same thing as voter turnout.

Does It Make Sense?

Many statistics defy our best judgment, but manage to get by "only because the magic of numbers

brings about a suspension of common sense." Beware of impressively precise figures:

$40.13 sounds more precise than "about $40." Beware of long-term trend predictions, as

seldom are "all other things equal" (that is, other variables that are not taken into account).

Lying with

statistics

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Summary

In this chapter, we have attempted to explore some

of the major decisions and approaches involved in

the initial analysis of data. Many important decisions

related to this stage are made prior to the collection

of data. A *variables list *keyed to questionnaire items

is quite useful in ensuring that the instrument covers

the elements that the researcher wishes to investigate.

Coding is the assignment of numerical values

to questionnaire items. A code is developed for each

question and entered in a *codebook. *Each question is

coded in the appropriate cell on a codesheet. The

codesheet information is keyboard entered into a

computer, with each cell corresponding to a column

on the card. These data are then edited, and analysis

begins.

Simple data presentation begins with the

reporting of one-variable frequencies, tallies, or

marginals. Various summarizing devices are available

for reporting this information in an attractive

and succinct format. These include the calculation

of rates, ratios, proportions, and percentages, as

well as the use of frequency distributions, graphic

displays, and tables. Calculation of statistics, such

as crime rates, is a useful way of standardizing

information to fairly compare unequal-size

groups. Frequency distributions serve to order,

group, and percentage data into tables that are

easier to read and understand. *Graphic *or

pictorial presen-tations include pie charts, bar

graphs, and *frequency polygons. *Often, readers

who are bored by frequency distributions and

tables are attracted by the pictorial appeal of

graphic displays. Among other types of graphics,

crime clocks were described as a misleading

manner of comparing changes in crime over time,

because they fail to control for population growth,

while using time as the constant base for comparison.

The same care must be taken in constructing

graphs that is taken in preparing tables:

Categories must be similar in size and mutually

exclusive, and appropriate labels must be supplied

to make the figure self-explanatory. Another form

of data presentation is the bivariate or multivariate

table. Guidelines on both the reading and the construction

of tables were given. Following carefully

the presentation on things to look for in tables will

help individuals in constructing their own tables.

Note some *general rules for percentaging a table*:

1. Give the table a proper title, generally "dependent

by independent variable(s)."

2. Keep in mind fair comparisons.

3. Always percentage within categories of the

independent variable.

4. When in doubt, ask, "What percentage of the

independent variable is a category of the

dependent variable?"

Three-variable tables involve the introduction

of a third (control) variable to assess its

impact (elaborate) on the original relationship.

Such statistical controls instituted after the fact,

through the subclassification of tables, constitute

an alternative to precontrols developed during

research design.

Elaboration refers to the process of introducing

or controlling for third variables by subclassifying

tables (creating partial tables). The

major types of elaboration are: replication, specification,

explanation, interpretation, and

suppression. In *replication*, the partial tables

replicate (reproduce) the original table; for example,

the relationship holds when controlling for a

third variable. In *specification*, the relationship is

specified and may or may not remain when the

original table is subclassified. One partial table

may show a stronger or weaker relationship than

the original table. Suppose the original relationship

disappears (was spurious). This is called

explanation; if *Z *(the control variable) occurs

before *X*; if after *X*, it is called an intervening

variable and *interpretation. Suppression *occurs

when little or no relationship in the original table

produces a relationship in the partial tables.

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330 Chapter 12 • Data Management

Key Concepts

Variables list *300*

Data management *301*

Editing *301*

Coding *302*

Codebook *303*

Codesheet *303*

Coder monitoring *305*

Keyboard entry *305*

Data verification *306*

Marginal run *307*

Crime rate *308*

Proportions *309*

Percentages *309*

Ratio *310*

Frequency distribution *310*

Graphs *311*

Pie charts *312*

Bar graphs *312*

Frequency polygons *313*

Crime clocks *316*

Steps in reading a table *318*

General rules for percentaging

a table *323*

Elaboration *323*

Replication *326*

Specification *326*

Explanation *326*

Interpretation *326*

Suppression *327*

Review Questions

1. Describe the "steps in the data management process."

How does each step build on the others in producing

valid data for analysis?

2. Graphic displays have sometimes been employed to

"lie with statistics." How is this done, and how might

readers avoid being misled by such displays?

3. What are some useful hints in reading a table?

Although it is certainly not exciting, why is table

reading an important subject? How was this illustrated

by Wilbanks' examination of interracial crime in the

NCS?

4. What does the process of elaboration involve? How

does such a process enable one to take into account

(or control for) rival causal factors?

Useful Web Sites

johnp71/javastat.htm/#descriptives

Pitfalls of Data Analysis (Or How to Avoid Lies and

Damned Lies)pitfalls/

interactivate/lessons/sm3.html

section3/scatterp.htm

data/scatter.htm

graph.html

labwrite/res/gt/graphtut-home.html

Create a Graph *http://nces.ed.gov/nceskids/graphing/*

ISBN 0-558-58864-6

THIS IS THE END OF CHAPTHER 12

Customer reply replied 9 years ago

C H A P T E R

13 Data Analysis

A User's Guide to Statistics

Why Study Statistics?

Using SPSS for Statistics

Types of Statistics

Measures of Central Tendency For

a Simple Distribution

Mode

Median

Mean

Measures of Dispersion

Range

Standard Deviation (σ)

Standard Deviation Units (*Z *Scores)

Chi-Square (χ**2)**

Calculation of Chi-Square

Cautions

Chi-Square-Based Measures of Association

Phi Coefficient () and Phi-Square (2)

Contingency Coefficient (*C*)

Nature and Types of Statistics

Nonparametric Statistics

Null Hypothesis

Tests of Significance

The *t *Test (Difference of Means Test)

Types of *t *Tests

Anova (Analysis of Variance)

Calculation of ANOVA

Other Measures of Relationship

The Concept of Relationship

Correlation Coefficient (Pearson's *r*)

Interpretation of Pearson's *r*

Calculation of Pearson's *r*

Regression

Ordinal-Level Measures of Relationship

Spearman's Rho (*r*s)

Interpretation of Rho

Gamma

Multivariate Analysis

Partial Correlation

Multiple Correlation and Regression

Statistical Software

Caveat Emptor

The Ecological Fallacy

Summary

Key Concepts

Review Questions

Useful Web Sites

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332 Chapter 13 • Data Analysis

Mention the word *statistics *and many people, particularly those in nonmathematical

fields such as criminal justice and other social sciences, "turn off." These same

individuals, however, may have at one point in their lives been able to rattle off batting

averages, league standings, engine r.p.m.'s, or other such statistics that they found important. For

most nonstatisticians, statistics are not interesting in themselves but become so when they are

relevant to an issue of substantive concern.

The purpose of this chapter is to provide a succinct computational and interpretive orientation

to the typical statistics criminal justice professionals may expect to find in the literature in

their field. This presentation will provide the reader with an overview of the various methods and

also a reference to the most commonly used statistical devices. Statistics are essentially tools or

summarizing devices. One need not have extensive statistical training to acquire a basic knowledge

of how to interpret reported statistical findings. Although this chapter consists primarily of

illustrations, computational examples, and "how to" interpretation suggestions for the most commonly

used statistics, it should not be used as a crutch and is not intended as a substitute for solid

statistics courses for the more serious student. Even for the serious student, however, it serves as a

handy refresher or quick reference guide to other sources of "need-to-know" information.

Statistical software such as SPSS 11.6 provides a relatively simple, Windows-based means of

analyzing data, complete with a statistics "coach" and tutorial functions.

WHY STUDY STATISTICS?

Although many people view studies that use many esoteric statistical techniques as an attempt by

the writers to intimidate, impress, or intellectually bully readers, there are many very good reasons

for becoming familiar with statistics. It is almost impossible to read most published literature in

criminal justice and the social sciences without some familiarity with statistics. Most research

published today is quantitative in nature, and such data require statistical analysis. Electronic

calculators and minicomputers are the toys of the next generation, making access to statistical

thinking more widespread in developed societies. Furthermore, a survey of 172 criminal justice

programs in the United States by Robertson, Zeller, and Fields (1986) indicated that the majority

of four-year undergraduate programs required a statistics course.

Statistics summarize data. Once a few symbols are mastered, a mountain of data can be

succinctly presented, as well as read and understood. Statistics enable us to discover patterns in

data, design useful research, simply describe large amounts of information, and infer to larger

populations. The study of statistics provides us with a standard universal language with which to

communicate research findings. Statistics should not be used to impress, confuse, or sanctify

hollow data. Statesman Benjamin Disraeli is reported to have cynically remarked that there are

"lies, damn lies, and statistics." And although statistics are neutral, they can be misused-to "lie

with statistics" (Huff, 1966); however, individuals who have a basic familiarity with statistics are

in a much better position to avoid being duped. Even though "figures don't lie, liars can figure."

Readers of research reports or journal articles are very likely to run across information

similar to the following:

z = 3.01, *p *< .01

X = 3.6 σ = 1.2

Gamma = .32, n.s.

r = .71, *p *< .01

x2 = 4.67, 1 *df*, *p *< .05

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Chapter 13 • Data Analysis **333**

Descriptive

statistics

Inferential

statistics

Many readers skip such statistical accounts and rely on the author(s) to describe what these

things mean. If one cannot speak the language, one is obviously at the mercy of the judgment,

honesty, and analytical skill of others.

If you recall, in the first chapter of this book we asked the question "Sprechen Sie

Researchese?" ("Do you speak the language of research?") Although one's response to some of

the above figures might be "It's Greek to me!" (which in fact it is, as some of the mathematical

symbols used in statistics are Greek letters), without a simple understanding of statistics, the

researcher is at a critical disadvantage when exposed to these simple research findings. The simple

object of this chapter is to enable the reader to be able to interpret and understand the meaning

of these statistics. For a more thorough understanding of these and other statistics, the reader

will be continuously referred to more detailed presentations in standard statistics textbooks.

USING SPSS FOR STATISTICS

SPSS 11.6 (Statistical Package for the Social Sciences) contains user-friendly tutorials for selecting

and interpreting various statistical procedures. In searching a statistical procedure from the

menu bar, choosing "analyze" produces a drop-down chart:

- Analyze
- Reports
- Descriptive statistics
- Corporate means
- General lineal model
- Mixed models
- Correlate
- Regression
- Loglinear
- Classify
- Data reduction
- Scale
- Nonparametric tests
- Survival
- Multiple response

Many of these choices, of course, have further subcategories of choices, all with tutorials, to

further direct you.

TYPES OF STATISTICS

Generally, statistics can be classified into two types: descriptive statistics and inferential statistics.

Descriptive statistics are intended to summarize or describe data or show relationships between

variables. Correlational measures actually do more than describe data but are included under

descriptive statistics for simplicity of presentation. We begin by discussing the simplest descriptive

statistics-measures of central tendency and dispersion. **Inferential statistics **enable generalization

or inference of sample findings to larger populations or assessment of the probability of certain findings.

We briefly discuss some of the more common inferential statistics such as chi-square, *t*, *z*, and

F tests. Rather than burden you with too much information all at once, we will discuss the nature and

types of statistics later in the chapter. First, let us become acquainted with a few statistics.

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334 Chapter 13 • Data Analysis

Measures of

central

tendency

Mode

Median

MEASURES OF CENTRAL TENDENCY FOR A SIMPLE DISTRIBUTION

Measures of central tendency are summary statistics that describe the "typical," "middle," or "average"

of a distribution of scores. The three most commonly used **measures of central tendency **are:

Mode

Median

Mean

Mode

The **mode **is the simplest measure of central tendency and is simply the most frequently occurring

score. Although the mode can be used with any of the levels of data discussed earlier (nominal,

ordinal, interval, or ratio), it is the only one that is appropriate for nominal-level data.

In most instances, with a simple distribution, the mode can be obtained simply by looking

at the data for the following distribution:

1 3 4 5 3 4 4 2 6

Without even ordering or grouping the data it is simple to obtain the mode of 4. What about

the following distribution?

1 3 4 5 3 1 4 5 4 2 2 3

We now have what is called a bimodal distribution, or a distribution with two modes,

scores 3 and 4. When plotted, a bimodal distribution of scores would show two peaks rather than

just one. Those familiar with criminological theory will recall Reckless' (1967) theory regarding

the bimodal distribution of crime commission in the United States wherein crime is highest

among the lower and upper classes.

Median

The **median **(or midpoint) is a measure of central tendency that is applicable to ordinal (ranked)

data. It is the score that divides the distribution in half, so that 50 percent of the scores are above

the median and 50 percent below. The median is calculated as follows:

1. Arrange all scores into an ordered array, that is, from highest to lowest or vice versa.

2. Calculate the median position by means of the formula

where *N *equals the number of cases.

3. Now locate the median by counting up or down the distribution until the score that is in the

median position is located.

Calculate the median for the following scores.

1 3 4 5 7 9 10

The median position is obtained (7 1)/2, or the case in the fourth position or the score

4. Again calculate the median for the following scores:

6 1 2 9 7 8 3 4

The data must first be reordered in an array: 1, 2, 3, 4, 6, 7, 8, 9. Calculating the median

position, (8 1)/2 4.5th position, or the score midway between 4 and 6, or the median 5.

position of median =

(N + 1)

2

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Chapter 13 • Data Analysis **335**

Mean

Example A

Simple Distribution

Example B

Grouped Frequency Distribution

Score Score *F*

2 76-100 4

2 51-75 8

5 26-50 16

6 1-25 10

10

Mean

The **mean **(average) is the most familiar measure of central tendency and simply involves dividing

the total score by the total number of cases *N. *It is most appropriate for interval- or ratio-level

data. For simple distributions, it is calculated by means of the formula

where

Using data from our last example in discussing the median (6, 1, 2, 9, 7, 8, 3, 4),

The mean, expressed as (pronounced "*X *bar") is simply the sum of the scores

divided by the number of scores. A variation of this formula for data that have been put into

a simple frequency distribution is where *f *equals the frequency of a score, for

example:

Score Frequency *FX*

1 2 2

2 1 2

3 3 9

4 2 8

N8 *fX*21

These measures of central tendency were calculated for a simple distribution as in

Example A. If, however, the data are grouped, as in Example B, different calculations must be

performed. Calculations and explanations of the measures of central tendency for grouped frequency

distributions are presented in Appendix C.

X = ©*fX/N *= 21/8 = 2.6

X = ©f*X / *N

X

X = 40/8 = 5

N = total number of cases

X = raw scores

© = sum of (letter is capital Sigma)

X = mean

X = ©*X / *N

If you can answer the following questions correctly, you have enough of an understanding

of what we have covered to proceed.

ISBN 0-558-58864-6

Pop Quiz 13.11

For example A, calculate the following:

1. Mode _____

2. Median _____

3. _____

MEASURES OF DISPERSION

In addition to measuring the central tendency of a distribution, it is also standard to report the

dispersion variability, or spread of a distribution. The simple reporting of the average score does

not tell us whether this average was representative of the particular scores. Figure 13.1 illustrates

three different curved frequency distributions, all of which have the same average. Note that for

each group the average score was the same; however, the distribution of scores was not. In

Example A, we have a bimodal distribution of scores with most of the cases scoring around 50

and 90. In Example C, we have great variability, with the mean, median, and mode at 70 but the

scores ranging from 0 to 100. Although there are three major measures of dispersion-range,

average deviation, and standard deviation-we concentrate on the range and standard deviation

because these are the most useful and the most commonly used.

Range

The **range **is the simplest measure of dispersion and represents either the highest and lowest

scores or the distance between the highest and lowest scores in a distribution. The range is calculated

by subtracting the true upper limits of a distribution from the true lower limits. For example,

to find the range of scores in the interval 1-10, we calculate

Had we, as some suggest, merely subtracted the highest from the lowest score 10 - 1, we would

have identified only nine units from 1 to 10, whereas there really are ten (1, 2, 3, 4, 5, 6, 7, 8, 9, 10).

The range is not a very useful calculation because it is based on extreme scores. It

ignores other information regarding distribution. A far more useful statistic is the standard

deviation.

Standard Deviation (σ)

The **standard deviation (σ) **and the related statistic variance (σ2) are far more useful than the

range. They make use of information regarding each score and are of greater utility in later statistical

analysis. In fact, knowledge of these measures is essential in order to understand the basis

of many more advanced statistical techniques. The use of standard deviation assumes that we

have internal or ratio-level variables. To calculate the standard deviation, obtain the square root

of the sum of the squared deviations from the mean divided by the number of cases:

range = 10.5 - 0.5 = 10

range = true upper limit - true lower limit

Had we, as some suggest, merely subtracted the highest from the lowest score 10 - 1, we would

have identified only nine units from 1 to 10, whereas there really are ten (1, 2, 3, 4, 5, 6, 7, 8, 9, 10).

The range is not a very useful calculation because it is based on extreme scores. It

ignores other information regarding distribution. A far more useful statistic is the standard

deviation.

Standard Deviation (σ)

The **standard deviation (σ) **and the related statistic variance (σ2) are far more useful than the

range. They make use of information regarding each score and are of greater utility in later statistical

analysis. In fact, knowledge of these measures is essential in order to understand the basis

of many more advanced statistical techniques. The use of standard deviation assumes that we

have internal or ratio-level variables. To calculate the standard deviation, obtain the square root

of the sum of the squared deviations from the mean divided by the number of cases:

range = 10.5 - 0.5 = 10

range = true upper limit - true lower limit

X

336 Chapter 13 • Data Analysis

1Answer to Pop Quizzes are given in Appendix D.

ISBN 0-558-58864-6

Example A:

Frequency

Score

Example B:

Frequency

Score

Example C:

Frequency

Score

0 100

X = 70

Range = 0-100 or 100

0 100

X = 70

Range = 55-85 or 30

0 100

X = 70

Range = 0-100 (100)

FIGURE 13.1 Hypothetical Scores on Police

Promotion Tests.

Deviation Score Formula

where

σ the standard deviation (this is sometimes represented as small *s *to indicate that

one is dealing with sample data). If calculating *s*, the denominator is *N *- 1.

*x*2 the sum of the squared deviations from the mean obtained by taking each score

(*X*) and subtracting from (X) score and squaring each result and summing them.

N total number of cases.

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The basic steps in calculating the standard deviation for a simple distribution using the

deviation score formula are

1. Calculate the mean, .

2. For each score, calculate the deviation score (*x*), where ; that is, the mean is

subtracted from each raw score.

3. Square each deviation score (*x*2).

4. Sum the squared deviation scores, divide by *N*, and obtain the square root.

It is much easier using a calculator to employ the raw score formula for obtaining the standard

deviation:

Raw Score Formula

For our data in Tables 13.1a and 13.1b:

σ = 41©X2/N2 - X2

x = X - X

X = ©*X / N*

TABLE 13.1A Standard Deviation Using the Deviation

Score Formula for a Simple Distribution

X x x2

9 3.6 12.96

8 2.6 6.76

7 1.6 2.56

6 .6 .36

5 .4 .16

2 3.4 11.56

1 4.4 19.36

Σ*X * 38 Σ*X*2 53.72

N 7

X 5.4

σ = 253.72/7 = 27.7 = 2.8

TABLE 13.1B Calculation of Standard Deviation

Using the Raw Score Formula for

a Simple Distribution

X X2

9 81

8 64

7 49

6 36

5 25

2 4

1 1

N 7 Σ*X*2 260

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Chapter 13 • Data Analysis **339**

In addition to the formulas that we have presented, there are others that are appropriate for

group frequency distributions. Space, however, does not permit detailed coverage of each of

these, and the reader can find further treatment of standard deviation for a grouped frequency

distribution in Appendix C.

Interpreting Standard Deviation. The standard deviation has a great many uses beyond

simply measuring dispersion of scores about the mean. The standard deviation squared is a measure

of variance, a statistic whose importance will become apparent particularly in our later discussion of

analysis of variance. To explain the meaning and interpretation of a standard deviation score, it is

necessary to introduce a basic notion in statistics, the **normal distribution**. According to Gauss'

law, most scores bunch around the mean; the remainder decline gradually as they reach the extremes

of the distribution. If these scores are plotted, they form a bell-shaped curve-the normal distribution.

Scientists have discovered that, when plotted, a variety of naturally occurring phenomena, such

as height, IQ, and standardized test scores, fall into this distribution. Figure 13.2 illustrates standard

deviation units and the areas of the normal curve each covers.

One standard deviation unit, plus and minus, covers approximately 68 percent of the area of

the normal curve. If the mean score on a test were 75 and the standard deviation were 5, then we

would know that roughly 68 percent of those taking the test scored between 70 and 80. About

95 percent of a distribution is covered by plus and minus two standard deviation units, or, in our

example, around 95 percent of the cases would have scored between 65 and 85. Finally, nearly all

cases (99.78 percent) would fall within plus and minus three standard deviation units or, in our

example, scores of 60 to 90.

Suppose we knew that an individual scored 80 on this exam. What percentage of cases did

this individual beat? This can be computed quite easily by examining Figure 13.2. As half of the

distribution is below the mean of 75, we already know that half of the distribution lies below this

score, plus an additional 34 percent. Thus, roughly 84 percent of the scores fell below 80.

= 2.8

= 27.98

= 237.14 - 29.16

σ = 21260/72 - 15.422

.11% .11%

2.16% 13.6% 34.13% 34.13% 13.6% 2.16%

-3 -2 -1 X +1 +2 +3

FIGURE 13.2 Standard Deviation Units and Areas of the Normal Curve.

ISBN 0-558-58864-6

Many readers may regard the standard deviation as an illustration of statistical legerdemain,

wondering why, for instance, one standard deviation unit (plus and minus) always covers

68 percent of the area2 or why scores distribute as a normal curve. It is best simply accepted on

faith similar to π (pi) in geometry, which always equals 3.1416. Many of us accept the operations

of the internal combustion engine without any idea of how it works.

Pop Quiz 13.2

1. If for an examination, 68 percent of the students scored between _____

and _____.

2. If then 68 percent of the students scored between _____ and _____.

3. Using either the raw score or deviation score formula, calculate the *X*, median, mode, and σ.

X = 72 and σ = 6,

X = 75 and σ = 5

340 Chapter 13 • Data Analysis

STANDARD DEVIATION UNITS (*Z *SCORES)

Returning to our test example, it is possible, given knowledge of the mean, the standard deviation,

and the areas of the normal curve, to calculate the position of any score in a series of scores, provided

they are normally distributed. **Standard deviation units**, or ** Z scores**, measure the deviation

from the mean relative to the standard deviation. Each score is converted into a *Z *score, or standard

deviation unit. In other words, the *Z *score measures the distance of a raw score from the mean and

expresses this in standard deviation units. The formula for obtaining a *Z *score is

where or the score minus the mean of the distribution. In Figure 13.2, it was pointed

out that one standard deviation, plus and minus, covers roughly 68 percent of the curve.

Similarly, one *Z *score, plus and minus, covers 68 percent. A *Z *score of 1.96 covers about

95 percent of the curve, whereas a *Z *of 2.58 covers 99 percent.

Using a table of *Z *values from Appendix E and our previous example of tests with a mean

of 75 and standard deviation of 5, let us calculate the *Z *scores for each and obtain the percentile

(proportion) of the distribution a given score is higher than:

Score *Z *Score Percentile

80 1.0 84.13

75 0.0 50.00

70 1.0 15.87

87 2.4 99.18

x = X - X

Z =

x

σ

2 Mathematically, it is the point where the slope of the curve changes from convex to concave, or where it changes its sign.

X

1

1 X _____

3 Median _____

5 Mode _____

5 σ _____

Chapter 13 • Data Analysis **341**

Assume, for example, that you received an 80 percent on an examination where the class

average was 75 and the standard deviation was 5. Your *Z *score would equal *X*(80)

Appendix E reports that the area between *X *and a *Z *of 1.0 is 0.3413,

or roughly 34 percent of the area above the mean. Because 50 percent of the normal curve is

below the mean of 75, your percentile score would be approximately 50 percent 34 percent

84 percent. Only 16 percent performed better than you on the test. Similarly, a score of 75

yields a *Z *score of 0 (exactly at the mean), which beats 50 percent of the scores below the mean.

Note that Appendix E reports proportions for only half of the curve (a *Z *score of 4.0 covering

nearly .50 or 50 percent). Calculation of percentile calls for some logic on the student's part.

One must picture a normal curve as in Figure 13.2, and if the *Z *score is positive, the area proportion

is added to .50 (the other part of the curve), and if *Z *is negative, the area proportion is

subtracted from .50.

Illustrating the procedure by means of our last score of 87,

Using the standard *Z *table in Appendix E we find that a *Z *score of 2.4 covers 49.18 percent

of the positive half of the curve, as well as automatically 50 percent of the negative portion of the

curve, or 99.18 percent. In addition to being useful for calculating percentile areas, *Z *scores are also

very important in assessing probability levels, as we will see later in this discussion.

So far, we have examined only descriptive statistics, those that simply summarize or

describe information. We will now look at an inferential statistic, which attempts to generalize

or infer to a larger population, or to assess whether the findings are due to chance or sampling

error.

Pop Quiz 13.3

Given and σ 3, calculate *Z *scores for the following scores and identify the percentile

such a score occupies on a normal curve:

X Score *Z *Score Percentile

1. 13 ___ ___

2. 7 ___ ___

3. 8 ___ ___

4. 12 ___ ___

CHI-SQUARE (χ2)

Chi-square (symbolized by the Greek letter chi, squared, χ2) is a test of the independence of the

relationship between nominal or categorical variables. It asks whether the two variables are independent,

exhibit no relationship or an association due to chance, or are dependent where the

relationship is real and would seldom occur due to chance alone. Table 13.2 illustrates the notion

of independence/dependence.

Inspection of Table 13.2 (*a*) shows that there is no relationship between sex and fear of crime;

that is, 30 percent of both sexes are afraid. Fear of crime can be said to be independent of the sex of

the individual. In Table 13.2 (*b*), however, there appears to be some relationship between fear of

crime and sex because 40 percent of the males and only 10 percent of the females are afraid of crime.

X = 10

Z =

(87 - 75)

5

=

12

5

= 2.4

X(75) , s(5) = +1.0Z

Chi-square (symbolized by the Greek letter chi, squared, χ2) is a test of the independence of the

relationship between nominal or categorical variables. It asks whether the two variables are independent,

exhibit no relationship or an association due to chance, or are dependent where the

relationship is real and would seldom occur due to chance alone. Table 13.2 illustrates the notion

of independence/dependence.

Inspection of Table 13.2 (*a*) shows that there is no relationship between sex and fear of crime;

that is, 30 percent of both sexes are afraid. Fear of crime can be said to be independent of the sex of

the individual. In Table 13.2 (*b*), however, there appears to be some relationship between fear of

crime and sex because 40 percent of the males and only 10 percent of the females are afraid of crime.

TABLE 13.2 Fear of Crime by Sex

Afraid Male Female

(a) Yes 30 30 60

No 70 70 140

100 100 200

(b) Yes 40 10 50

No 60 90 150

100 100 200

Chi-square does not measure the degree of association, although we will discuss measurements

based upon chi-square later; it measures the significance of a relationship if one exists.

Calculation of Chi-Square

Basically, the chi-square statistic compares observed cell frequencies with expected cell frequencies

(or values that could be expected by chance, given table marginals); then, use of the chi-square

formula assesses the probability of obtaining such a value by chance using a table of expected

chi-square values from any statistical textbook. A formula for calculating chi-square is

where

f0 frequency observed (the actual cell values)

fe frequency expected (values that would be expected by chance based on cell values)

Σ "the sum of" (in this case for each cell value)

Utilizing the data in Table 13.2 (*b*), the following procedure will result in the calculations

presented in Table 13.3. Follow these steps to calculate chi-square:

1. Cross-tabulate the data into a table with observed cells and marginals.

2. To obtain the *f*e (expected frequencies) for each cell use the formula

For example, for the *top left cell *of Table 13.2 (*b*)

fe =

(50)(100)

200 = 25

fe =

(row total)(column total)

total N

x2 = ©[( *f*0 - *fe*)2/*fe*]

TABLE 13.3 Fear of Crime by Sex (Hypothetical)

Afraid Male Female

Yes 40(25)* 10(25) 50

No 60(75) 90(75) 150

100 100 200

*Values in parentheses are expected values.

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Chapter 13 • Data Analysis **343**

Degrees of

freedom

For the3. Now, applying the formula for each cell, calculate the chi-square statistic.

4. Assess the significance of chi-square by consulting Appendix F, a table of expected chisquare

values. The calculated value must be the same as or larger than the table value to be

significant at a particular chosen level. This notion of "statistical significance" is described

in detail in the next section.

5. Calculate the appropriate degrees of freedom (*df *)

where

R rows

C columns

Degrees of freedom refer to the number of cells that are free to vary; that is, once the value

of certain cells are fixed, the others are no longer free to vary. In our example, if one cell

was set at 20, the other cell values are determined by subtracting from the marginals.

In our example, the degrees of freedom equal (2 - 1)(2 - 1) or 1. For a 3 × 2 table, *df * 2, and

for a 3 × 3 table, *df*4, and so forth. For our example, χ224, 1 *df*, and is greater than the expected

table value (statistically significant) at both the .05 level (3.8) and the .01 level (6.6). The latter means

that only one time in 100 could such a relationship between sex and fear of crime be caused by sampling

error (chance variation). Had this example been reported in a journal article, the author would

have written: χ224, 1 *df*, *p* .01; that is, a chi-square of 24, with one degree of freedom, is "statistically

significant" at the .01 level of probability. Only one time in 100 could such a result have been

obtained solely because of sampling error. Had the calculated value not exceeded the expected value,

it would have been described as "n.s." (not significant at the .05 level).

Cautions

Chi-square can accommodate any number of cells, although with a large number of cells the likelihood

increases that there may be few values in some cells, a situation that distorts the chi-square

statistic. In such cases, it is recommended that the number of cells be collapsed or combined. Chisquare

is also unstable in the 2 × 2 case and especially if any of the expected cell frequencies are less

than 10. In such circumstances, one should employ the Yates correction in which .5 is deducted from

the observed-minus-expected frequencies in each cell. Space does not permit an explanation, but

readers should be alert to this limitation and consult more detailed coverage in any standard statistics

test when its use appears warranted. Similarly, if any of the expected cell frequencies are less than 5,

readers should apply Fisher's exact test (Siegel, 1956).

df = (*R *- 1)(*C *- 1)

= 24

=

225

25

+

225

25

+

225

75

+

225

75

x2 =

(40 - 25)2

25 +

(10 - 25)2

25 +

(60 - 75)2

75 +

(90 - 75)2

75

fe =

(50)(100)

200 = 75

ISBN 0-558-58864-6

Pop Quiz 13.4

1. What do the following mean?

a. χ2 1.6, 1 *df*, n.s.

b. χ2 6.4, 2 *df*, *p * .05

2. What are the appropriate degrees of freedom for the following size tables?

a. 2 × 2

b. 4 × 3

c. 5 × 4

3. Do the following chi-square values exceed or not exceed the expected table values at the

.05 probability level?

a. χ2 4.8, 1 *df *______

b. χ2 4.2, 2 *df *______

c. χ2 2.6, 1 *df *______

CHI-SQUARE-BASED MEASURES OF ASSOCIATION

The concept of relationship (or association) of variables is explored in detail later in the chapter.

At this point, it is sufficient to know that if variables are related, it means that they vary together

(as one increases, so does the other). This may be a positive relationship where as one increases in

value, so does the other; for example, years of education and lifetime income are positively related.

There may be no relationship between variables, such as height and musical ability, or there may be

a negative (inverse) relationship, where as one variable increases in value (e.g., education) the other

decreases in value (e.g., prejudice).

As indicated previously, chi-square is not a measure of relationship. There are, however, a

number of nominal measures of association based on the chi-square statistic. Despite certain limitations

with respect to interpretation, they are appealing in that, once the chi-square statistic is

obtained, only relatively simple modification of this statistic is required to calculate chi-squarebased

measures of association.

Phi Coefficient (φ) and Phi-Square (φ2)

For 2 × 2 tables, the **phi coefficient **or **phi-square **can be utilized. They are calculated in the

following manner:

Using the chi-square value from our previous example of fear of crime by sex, phi-square

can be calculated:

The phi coefficient takes on values between zero (no relationship) and one (perfect relationship),

although positive or negative signs are meaningless. Its chief limitation is that it cannot be applied to

tables larger than 2 × 2. A phi coefficient of .34 indicates only a very negligible relationship.

φ = 224/200 = 2.12 = .34

φ2 = 24/200 = .12

φ2 =

x2

n

φ = 2x2 / *N*

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Chapter 13 • Data Analysis **345**

Parametric

statistics

Nonparametric

statistics

Phi-square is a very useful statistic in that it contains a highly preferred feature. It is a(proportional reduction in error) measure that has a direct operational interpretation; given

knowledge of one variable, for example, sex, we can reduce the error in predicting or explaining

a given proportion of the other variable, fear of crime. In our example, only about 12 percent of

the variance in fear of crime is explained by a respondent's sex.

Contingency Coefficient (*C *)

The **contingency coefficient ( C) **is calculated in the following manner:

This is a less useful chi-square-based measure of association in that a *C *of zero is interpreted

as no relationship, but the upper limit is less than 1.00, and its value depends on the number of rows

or columns.

Cramer's *V*

Cramer's *V *is useful for contingency tables that are larger than 2 × 2. The formula for calculating

V is

where *K *is the smaller of either rows or columns. *V *is more useful than *C *in that its upper value is

not determined by the size of the table. It varies between 0 and 1.0, from no relationship to perfect

relationship.

Pop Quiz 13.5

1. χ2 5.0 and *N * 10; calculate phi-square (φ2):_______

2. What does this value indicate?

NATURE AND TYPES OF STATISTICS

Rather than expose you to too many statistical distinctions at the beginning of the chapter, you

have been shown a few statistics (measures of central tendency, dispersion, chi-square, and chisquare-

based measures) to "get your feet wet." Hopefully, you have gained a little confidence as

well. Before we continue, some important further distinctions regarding statistics must be made.

Nonparametric Statistics

We have already discussed the difference between *descriptive statistics *(which summarize data

or describe relationships) and *inferential statistics *(which generalize data to larger populations).

Another important distinction that can be made between types of statistics is that between

parametric and **nonparametric statistics**. Generally, parametric statistics assume some interval

level measurement and that the sample was representatively drawn from a normal or bell-shaped

population distribution. *Nonparametric measures *(see Siegel, 1956) are appropriate for ordinal

and nominal data and are often referred to as "distribution-free statistics"; that is, statistics in

which few assumptions need to be made regarding the normality of the distribution. In this

V = 2x2>[*N*(*K *- 1)]

C = 2x2>(*N *+ x2)

Contingency

coefficient

Cramer's *V*

ISBN 0-558-58864-6

346 Chapter 13 • Data Analysis

Null

hypothesis

chapter, we assume the prevailing conservative view of basic assumptions that are necessary to

use various statistical tests. Many of these statistics are, however, quite robust (versatile). Binder

(1984) maintains that in a majority of cases in the social sciences, and particularly in criminal

justice and criminology, researchers may use statistics without so rigorous a concern or anxiety

regarding assumptions about scale (nominal, ordinal, interval, etc.) properties. Table 13.4 depicts

various statistics we have discussed or will discuss in terms of these qualities.

Thus, gamma and Spearman's rho (*rs*), which, as we will see, are appropriate for ordinal

data, are nonparametric alternatives to Pearson's *r*, and chi-square is used for nominal data

instead of *Z*, *t*, or *F *tests, which require higher level assumptions regarding the nature of the data.

SPSS 11.6 contains an online "Statistics Coach" feature in its help menu, which helps you select

the correct statistical procedure or graph for your data.

Null Hypothesis

In conducting inferential studies, or studies in which the objective is generalization to larger

populations, researchers generally employ

The null hypothesis

The research hypothesis

The **null hypothesis**, symbolized by *H*0, generally states that there is no difference between

the groups being compared, or that there is no relationship in the general population, or that any

observed differences are due to random error. The *research hypothesis *is the relationship or finding

that the researcher is attempting to demonstrate, for example, that some independent variable

or treatment had an impact on the dependent variable. In our earlier example, the null hypothesis

would state that there are no differences between the sexes with respect to crime. The alternative

or research hypothesis could be nondirective (there are differences between the sexes) or directive

(males are more afraid). Researchers approach this issue in what might appear as a roundabout

manner. Generally, one tests the null hypothesis and either rejects or fails to reject it. If the null

hypothesis is rejected, one can then assume that the research hypothesis is probably correct.

TABLE 13.4 Types of Statistics*

Descriptive Inferential

Parametric X t

σ *Z*

Median

Mode

Phi

Nonparametric C Chi-square

V

Gamma

rs

*This is an abbreviated table classifying statistics by function. For a more detailed classification, including level of

measurement, see any standard statistics text.

ISBN 0-558-58864-6

Chapter 13 • Data Analysis **347**

Tests of

significance

Tests of Significance

Similar to the procedure we followed in assessing the significance of a calculated chi-square,

investigators utilize **tests of significance **to assess whether the differences observed could be

due to chance (sampling error) or whether it is highly improbable that they have been due to

sampling error and thus are considered statistically significant at a given probability level.

Suppose, as in our previous chi-square analysis of fear of crime by sex, that there are actually

no differences in the population. Using even random sampling methods, it is possible by chance

to obtain an unusual number of fearful males and fearless females such that the samples (due to

atypical samples or sampling error) show a relationship that does not in fact exist in the population.

Rather than prove his or her hypothesis, the researcher estimates the likelihood of the

assumption being correct, given a certain probability of error. Further theoretical detail on

hypothesis testing is beyond the scope of our presentation. One final point, however, is required

before continuing with our overview of selected statistical measures.

The *level of statistical significance *is set by the investigator in terms of the amount of risk or

willingness to be in error in rejecting the null hypothesis (assuming a significant relationship).

Statisticians speak of Type I error (mistakenly rejecting a true null hypothesis) or Type II error

(mistakenly accepting a false null hypothesis). Customarily, researchers use the .05 probability level

(*p * .05; sometimes also symbolized as α [alpha]) as the minimum acceptance level for statistical

significance. This means that we are 95 percent confident that the relationship is a real one; however,

we are willing to accept being in error 5 times out of 100. That is, 5 in 100 times the results may be

due to sampling error rather than real differences in the population. A .01 probability level *(p * .01)

indicates that only 1 time in 100 could the results have occurred by chance. The reader is once again

referred to any good standard statistics text for a more detailed discussion (see, for instance,

Bachman and Paternoster, 1997). Most statistical measures of association have corresponding tests

of significance that involve comparing a calculated statistic with an appropriate table of probabilities.

Most statistics textbooks provide needed detail on how to use such tables.

THE *t *TEST (DIFFERENCE OF MEANS TEST)

A test of significance that often appears in the criminal justice literature is the ** t test **(Student's

Many people assume that the name "Student" is associated with the *t *test because it was developed for

the benefit of students. The actual origin is far more interesting as well as illustrative of the usefulness

of the *t *statistic. "Student's" *t*, which could be regarded as "the beer drinker's statistic," was the pen

name of a W. S. Gosset, who at one time worked for a brewery. In planning each formula for brewing,

he had the problem of having to adjust for different quality of grains. He developed statistics that

would enable him, with given degrees of error, to predict the most useful mixtures. One product of this

investigation was the development of the *t *test and, incidentally, some excellent beer.

The *t *test is generally used to compare the sample means of two groups. If they are sufficiently

different, the *t *test will be significant, thus enabling the researcher to reject the null

hypothesis of no difference (or that the samples are from the same population). Failure to obtain

a *t *statistic sufficiently high enough to exceed expected table values of *t *(see any standard statistics

text) means that any differences could have been caused by sampling error alone. To use the

t test and the *Z *score, which was discussed earlier but can also be used as a test of significance as

we will see, certain assumptions must be met:

1. Although the assumption can be violated for some data with little apparent harm (see Binder,

1984), generally, interval level measurement of data is required. Thus, the use of such tests

t test

ISBN 0-558-58864-6

348 Chapter 13 • Data Analysis

with ordinal data is questionable. For nominal data, it is impossible, because means cannot be

calculated. For example, what is the mean of the following data?

A mean cannot be calculated with nominal data.

2. Some type of random or probability sampling is assumed.

3. The variables being sampled come from populations that are normally distributed.

Types of *t *Tests

A full explication of *t *tests requires at least a full chapter in a standard statistics text and will not

be attempted here. We examine the most common types and refer you to statistics texts for detail

on the others. There are *three types of t tests*:

1. *t test for large samples *(*N * 30 for both samples). In this case, *t *is the same as *Z*

(standard deviation scores previously discussed).

GROUP 1 GROUP 2

N1 50 *N*2 40

X1 = 10 *X*2 = 12

N

a. Homicides 20

b. Rapes 16

c. Burglaries 42

σ1 3.6 σ2 4.2

2. *t test for small samples *(if either group is less than 30). An adjusted formula is required.

GROUP 1 GROUP 2

N1 10 *N*2 20

X1 = 110 *X*2 = 105

σ1 10 σ2 12

3. *t test for correlated samples *(pre- and posttests of same group).

BEFORE AFTER

N 6

The *t test for large samples *can be calculated using our example from type 1 and the formula

=

-2

2.2592 + .441

=

-2

2A12.96/50B + A17.64/40B

=

10 - 12

2A(3.6)2/50)B + A(4.2)2/40B

t =

X1 - *X*2

2Aσ21/*n*1 B + Aσ22

/*n*2 B

X1 = 110 *X*2 = 82

ISBN 0-558-58864-6

Customer reply replied 9 years ago

Chapter 13 • Data Analysis **349**

For samples containing 30 or more, the calculation of *t *is the same as that of *Z.*

There are alternate formulas that must be used for *t *if sample sizes are below 30, are of

unequal size, or if matched samples (before-after) are being compared. Detailed treatment of

these are beyond the purposes of this presentation but are obtainable in any standard statistics text.

Our primary interest is in providing the reader with a general ability to interpret and understand

reports using such tests.

Interpretation of Z and t tests of significance is dependent first on a full understanding of

figures such as the following:

Z 1.86, one-tailed, *p * .05

Z 2.48, two-tailed, .01 *p * .05

t 2.60, two-tailed, *p * .01

Using appropriate tables of probability (*t *or *Z*), the calculated values exceeded the

expected values at the given levels. A one-tailed test makes use of only one half of the probability

curve (shown in Figure 13.2) and reflects a directional hypothesis, comparable to predicting

males will be more afraid of crime than females. A two-tailed test is a nondirectional

hypothesis and simply states that there will be differences by sex in fear of crime. Our first

example says that *Z *predicting direction was significant at the 5 percent level. Our second

nondirectional *Z *was significant at the .05 but not the .01 level, while our *t *was nondirectional

and significant at the .01 level.

In our example calculation, *t * -2.39 is significant (two-tailed at the .05 level requires a

value of at least 1.96). Thus a difference in sample means of between 10 and 12 is sufficiently

large to permit us to assume that differences exist in the population from which the samples were

drawn.

Pop Quiz 13.6

For the following data, calculate *t *and test its significance at the .05 probability level, two-tailed

(table value with significance 1.96).

X1 = 10 *X*2 = 5

t = -2.39

=

-2

.8368

=

-2

2.7002

σ1 2 σ2 2

n1 30 *n*2 40

t _____

ANOVA (ANALYSIS OF VARIANCE)

In our discussion of *t *and *Z*, we examined statistics that measured the statistical significance

between two means. But often researchers are confronted with comparing three or more groups.

They could simply compute *t *tests for each combination which would require three *t *tests for

three groups, six *t *tests for four groups, and ten *t *tests for five groups. Such computations would

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350 Chapter 13 • Data Analysis

TABLE 13.5 Professionalism in Three Police Departments*

High Medium Low

10 9 5

9 7 3

8 5 3

7 3 3

6 1 1

X 8 5 3

*1 low professionalism, 10 high professionalism.

become unmanageable and with a large number of such tests, a given proportion, for example, 5

in 100, are bound to be significant by chance, in this case at the .05 level.(ANOVA) is used in comparing three or more sample means. One-way ANOVA (the type we

will briefly discuss) involves three or more categories of an independent variable, such as a comparison

of three different income groups with respect to some fear of crime scale score. There is

such a thing as two-way ANOVA in which two independent predictors are examined. For a

detailed presentation on the latter, see any more advanced statistical text.

The basic logic of ANOVA is that in comparing groups, types, or categories, there should be

much greater variation between groups than within groups. If, for example, we were comparing three

departments with respect to professionalism of the officers, where a score of 1 equals low professionalism

and 10 equals high professionalism, then the high professionalism department should have

more professional members than the medium or low departments. Table 13.5 illustrates this notion.

In Table 13.5, a sample of five officers from the three departments suggests that although lower

professionalism departments have some officers with higher professionalism ratings than some higher

professionalism departments, in general it appears that the characterizations are useful types. ANOVA

goes beyond such a judgmental approach and examines this question statistically, particularly because

we are asking whether the differences that do exist do so by chance (sampling error).

Calculation of ANOVA

The basic idea of ANOVA is to have large variance between groups and small variance within

groups. ANOVA uses the *F *statistic (which, similar to *t *and *Z*, has a table of probabilities with

which the calculated statistic is compared). ANOVA is a fairly complex process and is summarized

below simply to acquaint the reader with how the *F *statistic is obtained. It is not expected

from this brief presentation that the student be able to perform ANOVA.

ANOVA can be viewed as a series of steps that lead to completion of the following chart:

Source

Sum

of Squares

Degrees

of Freedom Variance (*S*2)

Between (2) (4) *K *- 1

(5)

(2)

(4)

*F*

Within (3) (4) *N *- *K*

(5)

(3)

(4)

Total (1) (4) *N *- 1

ANOVA

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1. Calculate the sum of squares for the total (*SS*total). This is given in our example but is

detailed in Appendix C. *SS*T 121.33.

2. Calculate the sum of squares for between groups (*SS*between). This is also given in our

example and detailed in Appendix C. *SS*B 63.33.

3. Calculate the sum of squares for within groups (*SS*within).

SSwithin *SS*total - *SS*between

121.33 - 63.33

58

4. Calculate the degrees of freedom (*df*).

dfbetween *K *- 1

where *K *is the number of groups or categories being compared.

dfbetween 3 - 1

2

dfwithin *N*total - *K*

15 - 3

12

dftotal *N*total - 1

15 - 1

14

5. Calculate the variance between groups (*S*2

B) and within groups (*S*2

W).

S2

B *SS*between/*df*between

63.33/2

31.67

S2

W *SS*within/*df*within

58/12

4.83

6. Calculate the *F *ratio (test of significance).

F *S*2

between/*S*2

within

31.67/4.83

6.56.

7. Compare it with the *F *table of probabilities at appropriate degrees of freedom [reading first

dfbetween (*K *- 1) and second *df*within (*N *- *K*)].

F 6.56, 2, 12 *df *Table value significant at .05 level (3.88) but not

.01 level (6.93). Reject null hypothesis.

Table 13.6 plugs the values we have calculated into the chart.

A table of *F *distributions is available in any statistics text. On the basis of our analysis,

our initial judgment is borne out. There was, in fact, sufficient similarity within groups and

difference between groups to enable us to conclude that there are real differences between the

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352 Chapter 13 • Data Analysis

three police departments with respect to professionalism. Five in 100 times, however, this could

be caused by sampling error, although a 95 percent chance of being correct seems a reasonable

risk of being wrong.

As with other statistics, certain assumptions regarding the nature of the data must be

reached before justifying their usage. The assumptions required for using ANOVA are:

Interval data

Random sampling

Sample drawn from a normal distribution.

Pop Quiz 13.7

What is indicated by the following values?

F 7.61, 12, 4 *df*, *p * .05

OTHER MEASURES OF RELATIONSHIP

The Concept of Relationship

Previously, we explored chi-square-based measures of relationship for nominal level data.

Discussion will now focus on measures of association appropriate for higher level data such as

ordinal and interval scale information.

The notion of relationship or association is central to scientific investigation and was identified

in Chapter 3 as the first essential step in resolution of the causality problem. The idea of

relationship assumes that, if one variable enables prediction of the values of a second variable, the

variables are related. Perhaps a simple illustration will serve to explain this idea (Table 13.7).

TABLE 13.6 ANOVA Calculations

Source

Sum

of squares

Degrees

of Freedom Variance (*S*2)

Between 63.33 2 31.67/4.83 *F*

Within 58 12

Total 121.33 14

TABLE 13.7 *Examples of Relationships

Case A Case B Case C

X Y X Y X Y

1 1 1 4 1 1

2 2 2 3 2 1

3 3 3 2 3 1

4 4 4 1 4 1

Positive relationship Negative relationship No relationship

*1 low, 4 high.

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Chapter 13 • Data Analysis **353**

Positive

relationship

Negative

relationship

Case A (Table 13.7) illustrates a perfect **positive relationship. **As variable *X *increases in

value, so does variable *Y*; or, given knowledge of the value of variable *X*, the value of variable *Y *can

be predicted exactly. Case B (Table 13.7) demonstrates a perfect **negative **(or inverse)

relationship. As values of *X *increase, values of *Y *decrease proportionately. In Case C (Table 13.7),

there is no relationship between *X *and *Y. *Changes in the value of *X *have no impact on *Y*, which

maintains the same constant score.

CORRELATION COEFFICIENT (PEARSON'S *r*)

The Pearson product moment correlation coefficient (**Pearson's r**) is an interval level measure of

relationship. To employ Pearson's *r*, three assumptions must be met with respect to the data:

1. They must be of interval level measurement.

2. If the joint frequency distribution were to be plotted, the relationship would be linear or resemble

a straight line. If the relationship is nonlinear, such as curvilinear, then other statistical

measures must be used.

3. The deviations of points from this line must be relatively uniform (homoscedastic) or

demonstrate equal variance.

Interpretation of Pearson's *r*

Values of the correlation coefficient (*r*) range from 0 (no relationship) to or - 1.00 (a perfect

relationship). A negative relationship is indicated by a minus sign and a positive relationship by

a plus sign. In interpreting a correlation coefficient, the closer to zero it is, the weaker or lower

the relationship, and the closer to 1.0 it is, the higher or stronger correlation is closer to 1.0. As a

general rule of thumb, the following scale of correlation coefficients can be used:

Of particular importance is the fact that *r*2 (Pearson's *r*, squared) is a PRE measure (a proportional

reduction in error measure) and can be interpreted as variance explained. For example,

if the relationship between education and income is *r * .50, *r*2 (.50)(.50) or .25, or 25 percent

of the variation in income is explained by education.

Calculation of Pearson's *r*

Our discussion would be enhanced at this point by illustrating the computation of Pearson's *r *for

a simple distribution. Two alternate formulas can be used to calculate the correlation coefficient;

one uses raw data and the other makes use of deviation scores. The formula for calculating

Pearson's *r *using raw scores for a simple distribution is

Table 13.8 is actually two tables. The first table (*a*) contains the original data, and the

second table (*b*) contains the calculation required to use the raw score formula.

Using the data in Table 13.8 (*b*), the steps in calculating Pearson's *r *using the raw data

formula are

1. Obtain the Σ*X *(sum of *X*) and Σ*Y *(sum of *Y*). Simply add down each column. In our example,

Σ*X * 15 and Σ*Y * 30.

r =

N©*XY *- ©*X*©*Y*

4C*N*©*X*2 - (©*X*)2 D C*N*©*Y *- (©*Y*)2 D

Pearson's *r*

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354 Chapter 13 • Data Analysis

2. Calculate *X*2 (*X *square) and *Y*2 (*Y *square) for each score and sum these to obtain Σ*X*2 (the

sum of *X *square) and Σ*Y*2 (the sum of *Y *square). In our example, Σ*X*2 65 and Σ*Y*2 190.

3. Calculate the cross-product or *XY *for each case. The Σ*XY *(sum of *X *times *Y*) equals 104

for our example.

4. Plug these values into the raw score formula:

Statistical Significance of Pearson's *r*

In general, in line with our earlier suggested interpretations of the meaning of correlation

coefficients, low *r*'s are not likely to be significant. If the *r *is above .7, it is almost always statistically

significant. Similar to other statistical tests we have discussed, expected values of *r*

have been calculated given specific sample sizes. These tables are available in any standard

= .99

=

70

70.71

=

70

25000

=

520 - 450

2[325 - 225][950 - 900]

r =

5(104) - (15)(30)

2[5(65) - (15)2][5(190) - (30)2]

TABLE 13.8 Scores of Five Correctional Officer Recruits on Mathematical

(*X*) and Verbal (*Y*) Ability

(a)

X Y

0 4

2 5

3 6

4 7

6 8

Total 15 30

(b)

X Y X2 *Y*2 *XY*

0 4 0 16 0

2 5 4 25 10

3 6 9 36 18

4 7 16 49 28

6 8 36 64 48

Total 15 30 65 190 104

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Chapter 13 • Data Analysis **355**

Regression

equation

Y ¿ = 3.9 + .7*X*

Using this formula, if a new recruit had a score of 8 in verbal ability, we would predict a

score of 9.5 on the math portion [*X * 3.9 .7(8) 9.5]. In criminal justice, such prediction

formulas would serve many needs in estimating future outcomes from known data. This is particularly

the case with multiple correlation and regression techniques, which we will discuss later in

statistical text. For our computed *r *of .99, the expected table value of .88 for an *N *of 5 is

exceeded (*a * .01, two-tailed); therefore, we are able to reject the null hypothesis and conclude

that math scores (*X*) are very much related to verbal scores (*Y*). Previously, we indicated

that *r*2 (variance explained) is a very meaningful statistic. For our example, .992 equals .98, or

98 percent of the variance in verbal scores is explained given knowledge of the mathematical

score.

Pop Quiz 13.8

1. What do the following values mean and what percent of the variance is explained?

r .70, *p * .05

2. For the following data, calculate Pearson's *r*:

X Y

1 3

3 3

5 6

REGRESSION

The correlation coefficient not only tells us the strength of a relationship but also provides us

with the raw data, enabling calculation of a **regression equation**. With the regression equation,

we are able to predict, on the basis of the value of one variable, a person's score on a second variable.

The formula for calculating a regression line is

Y' *a **b*X

(predicted *Y*) (*Y *intercept) (slope *X*)

where

Y' refers to a predicted score of *Y *(in our case, verbal scores)

a the *Y *intercept or place where the regression line crosses the *Y *axis (see Figure 13.3)

b the slope of the line (slope coefficient)

The formulas for calculating the regression equation for the raw data in Table 13.8 are

presented in Appendix C.

Figure 13.3 plots the values of *X *and *Y *for the five correctional officers we have been

examining, and by using the same calculations from our correlation example, we are able to

obtain a formula for a regression line that predicts values of *Y *if we are given values of *X.*

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356 Chapter 13 • Data Analysis

Spearman's rho

this chapter. But first, because many of the data we work with in criminal justice are of an ordinal

rather than interval nature, let us examine some ordinal-level measures of relationship.

Pop Quiz 13.9

1. What does the following equation mean?

2. With the formula for predicting correctional officer recruits, calculate the predicted values

of *Y *(verbal ability) for new recruits with the following math scores (*X*):

a. 10 _____

b. 5 _____

ORDINAL-LEVEL MEASURES OF RELATIONSHIP

There are a number of useful ordinal-level measures of relationship. We will restrict our coverage

to only two of these: Spearman's rho and gamma.

Spearman's Rho (*r*s)

Spearman's rho (symbolized by *r *sub s), or Spearman's rank order correlation coefficient, is an

appropriate measure of relationship for ordinal-level data. In previous discussion of ordinal data,

it was indicated that ordinal-level measurement supplies only information regarding rank or

Y oe= *a *+ *bX*

10

9

8

7

6

5

4

3

2

1

0 1 2 3 4 5

X

Y

6 7 8 9 10

FIGURE 13.3 Regression Line for Scores of Five Correctional Officer Recruits on Mathematical (*X*)

and Verbal (*Y*) Ability.

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Chapter 13 • Data Analysis **357**

higher or lower properties, and the actual scores do not contain any meaningful interval units

between scores. Suppose, for instance, we wanted, similar to police assessment exercises, to

measure the relationship between a sample of scores received at the police academy (*X*) and

subsequent supervisor ratings of officer effectiveness (*Y*). Table 13.9 presents such fictitious

data. Using the data in Table 13.9, we will illustrate the steps in calculating Spearman's rho:

1. Assign ranks to each score. Begin with the lowest score in column *X*, and assign it the

lowest rank of 1; then rank the next lowest and so forth to the highest score, which is

assigned the highest rank. (In case of tied ranks, assign the average of the ranks that would

have been assigned.) If scores were tied for third and fourth place, they would each be

assigned the rank of 3.5. The ranking of scores could be reversed, assigning the lower

ranks to higher scores, as long as each variable is ranked similarly.

2. Follow this same procedure for converting *Y *scores into *Y *rank scores.

3. Calculate *D *(difference in rank scores) by subtracting for each case the *Y *rank score from

the *X *rank score.

4. Obtain *D*2 by squaring each *D *value and calculate the Σ*D*2.

5. Plug these values into the formula for Spearman's rho (*r*s):

Table 13.10 contains the calculations for *r*s using the data from our example.

= +.95

= 1 - .04

= 1 -

48

990

rs = 1 -

6(8)

10(100 - 1)

rs = 1 -

6©*D*2

NC(*N*)2 - 1D

TABLE 13.9 A Sample of Ten Officer Effectiveness Scores (*Y*)

and Police Academy Scores (*X*)*

Officer *X Y*

A 71 20

B 78 31

C 79 32

D 80 28

E 83 42

F 85 81

G 89 72

H 90 84

I 92 96

J 98 99

*Academy scores ranged from 70 (pass) to 100 (excellent). Officer scores ranged

from 1 (ineffective) to 100 (most effective).

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Gamma

Interpretation of Rho

Similar to Pearson's *r*, rho requires assumptions regarding linearity (a straight-line relationship if

plotted) and random sampling from the population. Unlike *r*, *r*s is appropriate for ordinal data.

Spearman's rho can be interpreted in the same manner as Pearson's *r*, with a 0.0 indicative of no

relationship and a 1.0 or -1.0 indicating a perfect, either positive or negative relationship. Our

example of a .95 is indicative of a very high positive relationship.

Similar to other statistics that we have discussed, tables of expected probabilities for *r*s

exist in standard statistical texts in which the statistical significance of *r*s values can be assessed.

Our calculated value of .95 for an *N *of 10 exceeds the value at the .05 probability level (.65)

as well as the .01 level (.79) for two-tailed tests. Thus in only one in 100 samples could such a

result have taken place by chance or sampling error.

Of even greater significance is the fact that (rho squared) is areduction in error) measure or a measurement of the proportion of variance explained. In our

example, (.95)2 equals .90, or 90 percent of the performance ratings of officers can be predicted

on the basis of academy scores.

Gamma

Goodman and Kruskal's **gamma **(G) is another measure of relationship for ordinal data that requires

the same assumptions as Spearman's rho: linearity, random samples, and ordinal data. The values of

gamma also vary between 0.0 (no relationship-or no reduction in error in predicting the dependent

variable, given knowledge of the independent variable) to 1.0 or -1.0 (perfect relationship-total

predictability). Gamma is a PRE measure and the calculated statistic can be interpreted directly as

variance explained. Yule's *Q *is a special case of gamma applicable to 2 × 2 tables only and can be

interpreted in the same manner as gamma. We explore the calculation of gamma using data that have

been placed in a contingency table (Table 13.11).

The formula for calculating gamma is

G =

(A - D)

(A + D)

r s

2

TABLE 13.10 Data for Spearman's Rho

Officer *X *Rank *X Y *Rank *Y D D*2

A 71 1 20 1 0 0

B 78 2 31 3 -1 1

C 79 3 32 4 -1 1

D 80 4 28 2 2 4

E 83 5 42 5 0 0

F 85 6 81 7 -1 1

G 89 7 72 6 1 1

H 90 8 84 8 0 0

I 92 9 96 9 0 0

J 98 10 99 10 0 0

Σ*D*2 8

PRE measure

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Chapter 13 • Data Analysis **359**

where

A agreements or cases in predicted direction

D disagreements or cases not in predicted direction

Agreements and disagreements can be best explained by illustration. The steps in calculating

gamma are

1. First, arrange the data from high to low (as in our example in Table 13.11). Both values of

each variable should decrease in value as they move from the upper left cell.

2. Obtain the agreements by multiplying each value, beginning with the upper left cell, and

by the sum of all cells below and to the right. Total the resulting values.

A 58(3 5 1 17 2) 77(5 1 17 2) 25(1 17 2)

9(17 2) 24(2)

A 4,268

3. Now calculate the disagreements (*D*) beginning with the upper right one by multiplying

each cell value by the sum of all values below and to the left.

4. Plug these values into our calculating formula to obtain gamma.

G .76

A gamma of .76 is indicative of a relatively high relationship between membership in professional

associations and remaining in one's field of training. Similar to other statistical techniques,

there is a test of significance for gamma. In this case, a formula (see Appendix C) is used

G =

4,268 - 579

5,268 + 579

= 579

+ 19(5 + 3 +1) + 25(3 +1) + 77(1)

D = 3(17 + 1 + 5 +3 +1) + 24(1 + 5 + 3 + 1)

TABLE 13.11 Attrition Among Professionals in Rehabilitation by Membership

in Professional Associations*

Attrition

Membership IN Out *N*

In 58 77 25 9 24 3 196

Out 1 3 5 1 17 2 29

225

*Attrition refers to the act of leaving the occupation for which one was trained. Measurement was by means

of a fairly complex two-level judgmental scale which is described in detail in the original source.

Variation from *N *of 243 is due to the elimination of unknowns. There is a positive relationship between

membership in organizations in or related to the field of training and retention, gamma .76, *p *.001.

The Impact of Rehabilitation Services Administration Support in Nine Occupations. Cleveland: Institute on the

Family and the Bureaucratic Society, Case Western Reserve University, 1975, p. 64.

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Customer reply replied 9 years ago

360 Chapter 13 • Data Analysis

to convert gamma into a *Z *score that is compared with a table of expected *Z *scores. Our gamma

was equivalent to a *Z *of 4.75, *p * .001.

Pop Quiz 13.10

1. Calculate gamma for the following data:

Income

Education High Low

High 10 5 10

Low 5 5 10

X Y

1 3

2 2

4 1

3 2

In most cases the criminal justice researcher does not calculate most of the statistical

procedures that we have discussed by hand but rather uses "canned" (prewritten) computer packages

such as **SPSS **(Statistical Package for the Social Sciences). With these packages, the researcher's primary

concerns are employing the proper statistics with respect to the nature of and assumptions

regarding the data to be analyzed and interpreting the meaning of the calculations performed by the

computer. The purpose of our more detailed presentation of specific statistics is to acquaint the reader

with some general methods. These are intended to provide a general overview or introduction so that

the reader could then consult more in-depth treatment in statistical texts once the appropriate or

required measure for their purposes is chosen. General familiarity with these statistics assists in

understanding the description and discussion of other statistics.

In Chapter 3, we discussed the three steps essential to resolution of the causality problem:

demonstration that a relationship exists, specification of the time order of this relationship, and

exclusion of or control for other variables that may be the actual cause of the relationship. We have

examined the demonstration of two-variable relationships such as chi-square-based measures,

gamma, and the correlation coefficient. Specification of the time order or direction of causality

took place with our identification of the independent (predictor) variable and dependent (outcome)

variable. Also in Chapter 3, we discussed how researchers can attempt to control for rival

causal factors through research design. We also indicated that often research topics do not lend

themselves to such prior controls and that investigators can accomplish much the same thing

through statistical controls, after the fact. Multivariate statistical analysis enables the statistical

control of rival causal factors.

MULTIVARIATE ANALYSIS

A variety of statistical techniques attempt to control for other variables. Subclassification of

tables, partial correlation, two-way analysis of variance, multiple correlation and regression, and

other procedures enable the investigator to statistically control for the effects of other variables.

SPSS

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Chapter 13 • Data Analysis **361**

Partial

correlation

Multiple

correlation

Multiple

regression

Detailed coverage of each of these is beyond the intended scope of what is essentially a research

methods text; however, brief exposure to partial correlation and multiple correlation and regression

will serve to illustrate multivariate techniques.

Partial Correlation

correlation looks at the relationship between two variables while controlling for (taking into

account) the effects of one or more other variables. In reporting correlation coefficients, it is

standard procedure to list subscripts, as in *rxy. *This indicates that we are looking at the relationship

between variables *X *and *Y. *Such a simple correlation does not have any controls for other

variables and is referred to as a zero-order correlation coefficient. A dot after the first two

subscripted variables indicates that the partial correlation coefficient has controlled for other

variables. If one variable follows the dot, then this is called a first-order partial correlation

coefficient. If two variables follow the dot, then we have a second-order partial correlation

coefficient. Examine the following partial correlations:

rXY

rXX.ZAB

rXY.1

Our first example is of a zero-order correlation coefficient (no controls). The second case

shows a third-order partial *r *with the relationship between *X *and *Y *controlled for (or taking into

account the effects of variables *Z, A*, and *B*). Finally, our third correlation is a first-order partial *r*

controlling for only one variable labeled 1. Multiple correlation and regression are generally

regarded as more useful than partial correlations because they can simultaneously examine and

control for multiple intercorrelations.

The reader is once again referred to statistics texts for detailed treatment of partial *r*, our

purposes being met in providing a familiarity with the technique.

Multiple Correlation and Regression

An understanding of multiple correlation and regression is an extension of what we have discussed

so far with respect to simple correlation and regression. Correlation measures the strength

of the relationship and a regression line provides an equation with which to predict values of the

dependent variable.regression, which involves predicting *Y *(the dependent variable) on the basis of multiple predictors.

Multiple regression has the general formula

where

a the *Y *intercept (or point where the regression line crosses the *Y *axis)

b partial slope coefficient

e a residual error term (this is usually ignored once the predictive equation is calculated)

Yoe = *a *+ *b*1

X1 + *b*2*X*2 +

. . . bk Xk + *e*

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362 Chapter 13 • Data Analysis

Subscript 1 stands for variable 1, subscript 2 for variable 2, to subscript *K *for the total

number of additional variables.

The interpretation of both multiple correlation and regression is analogous to our previous

discussion of simple correlation and regression. Thus, *R*2 equals variance explained and

the regression equation enables us to predict *Y *given knowledge of multiple predictors. For

example, in our multiple regression formula, *Y *could represent likely parole outcome, and *X*1

previous record, *X*2 length of incarceration, and so forth. The necessary computations for

multiple *R *and regression are most ordinarily performed by computer and are far too involved

for our purposes.

Final Quiz

For the final quiz, describe what the statistical terms with which we began this chapter mean.

1. χ2 4.67, 1 *df, p * .05

2. *r * .71, *p * .01

3. Gamma .32, n.s.

4. 3.6, α 1.2

5. *Z * 3.01, *p * .01

There are a large number of statistical techniques. Some feel that the field of criminal justice,

because of the ready availability of funding beginning in the seventies, has been under an avalanche

of such esoteric techniques. Given a basic knowledge of some of the techniques we have discussed,

it is hoped that the reader will have the confidence to realize that, if one runs across an unknown

technique, it is often a variation of one of those we have discussed and that it can be looked up and

generally understood without the need for detailed mathematical explanations.

It is hoped that our discussion of the presentation of statistical findings will assist the reader

in developing a healthy, confident disrespect in approaching such data. Rather than intimidation, a

brief exposure to the interpretive approach we have discussed should inspire some confidence.

Throughout this chapter the reader has frequently been referred to standard statistics textbooks for

more detailed analysis. Some to consult are Bachman and Paternoster (1997), Kanji (1993), Levin

and Fox (1999), Vito and Latessa (1989), and Vogt (1993).

STATISTICAL SOFTWARE

The role of computers in research made its earliest impact in creating data files, managing these

data, and particularly in the analysis of data by means of sophisticated software programs such as

SPSS, SAS, BMDP, MICROCASE, and MINITAB. The advent of such computerized statistical

analysis has eliminated much of the drudgery from "numbers crunching" by hand or calculator,

but still requires that the researcher have a good basic knowledge of statistics, assumptions

regarding their usage, appropriate levels of measurement, and the interpretation of statistics. The

ability of computer programs to quickly perform sophisticated analysis does not prevent the

inappropriate use and interpretation of such statistics.

The emergence of "expert systems" and "artificial intelligence" such as Statistical Navigator

Professional (Malcolm, 1992) can assist in such statistical decision making. Similar to a "help"

menu common in many computer programs, Statistical Navigator Professional contains a menu

and series of questions that enable the user to narrow down his or her choices of appropriate statistics

from 200 statistical procedures. The program also identifies appropriate statistical software and

X

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Chapter 13 • Data Analysis **363**

Ecological

fallacy

provides a brief tutorial on the statistics that have been chosen. The statistics coach feature in SPSS

has a similar function. Of particular note is the fact that much of this software, which at one time

required a mainframe computer, is available on personal computers.

CAVEAT EMPTOR

One excellent primer on statistics saw fit to entitle the last chapter "Caveat Emptor" ("let the buyer

beware") (Franzblau, 1958, pp. 129-132). This is quite apt advice, particularly to those whose

primary role will be a consumer of research and statistical information. The field of criminal justice,

particularly because of the ready availability of research funds beginning in the seventies, has at times

been awash in a sea of sometimes inappropriate mathematical wizardry. Sophisticated statistical

analysis of inappropriate data can often lead to unfounded conclusions. More dangerous is the fact

that the very intimidating nature of the apparent complexity of these techniques may hide faulty judgment.

With the ready availability of computer packages, it becomes a simple technical matter to run

statistical tests sometimes without paying proper attention to logic, substantive issues, and the many

potential sources of error we have discussed throughout this text. It is hoped that the general overview

of statistics in this chapter will begin to prepare the reader to become a more alert and vigilant consumer.

The consumer of statistical findings should pay special attention to the following:

1. Statistical significance should by no means be taken as indicative of substantive significance.

One might find a highly statistically significant relationship between foot size and

intelligence, but not place any meaningful or important value on such findings.

2. Beware of statistics of convenience or types of analyses that may have been chosen by the

researcher on the basis that they would most likely shed the best possible light on the data.

3. Be wary of discussion and generalization that goes far beyond the limited statistical findings.

Sometimes studies that are done on one atypical group suddenly are assumed to be generalizable

to larger populations. For example, Kinsey et al's study ofFemale (1953) was primarily a purposive sample of white American females. Niederhoffer's

(1967) conclusions regarding the nature of cynicism among police, which was subtitled "The

Police in Urban Society," was a study of the New York City Police Department.

4. Readers should be particularly vigilant regarding the misapplication of statistical techniques

to data that do not meet such required assumptions as normal distributions, random

samples, interval measurement, and the like.

THE ECOLOGICAL FALLACY

The "ecological fallacy" appears to have been noted independently in psychology (Thorndike, 1929)

and in statistics (Yule and Kendall, 1950), but it was Robinson's (1950) paper on the subject that

attracted the most attention and has the greatest relevance to criminal justice research. The

ecological fallacy is the error of assuming that relationships based on groups (aggregate, ecological,

or areal data) can be validly assumed to be true of individual correlations. A correlation coefficient

(*r*) is a measure of relationship that ranges from -1.0 (a perfect negative or inverse association), to

0.0 (no relationship), to 1.0 (a perfect positive relationship). Robinson demonstrated his point by

showing that the relationships between illiteracy and being foreign-born and between illiteracy and

race varied greatly depending on the unit of analysis (Table 13.12).

When the data on illiteracy and being foreign-born were grouped by nine census areas,

there was a moderate negative relationship (-.62); when these same data were regrouped by

ISBN 0-558-58864-6

364 Chapter 13 • Data Analysis

forty-eight states, there was a slightly smaller negative relationship (-.53). Finally, when the data

were ungrouped, the individual correlation was a very small positive one (.12).

Similarly, when the relationship between illiteracy and race (Black) was grouped by nine

census areas, the relationship was a very high positive one (.95); clustered by forty-eight states the

relationship was reduced but still high positive (.77); and when ungrouped, the association was

only a small one (.20). Although individual correlations use persons as the unit of analysis, ecological

correlations use groups of persons. In our previous tabular analyses it would be similar to using

only the marginal totals to obtain ecological correlations, while individual correlations make use of

the internal cell frequencies.

Much research in criminal justice, particularly the early literature in criminology and

juvenile delinquency, has been plagued by shifts in these units of analysis which often lead to

confusion. In their review of such research Hirschi and Selvin (1973, p. 269) indicate that "the

researcher should analyze and present his data so as to avoid suggesting that the relations he

observes are stronger than they actually are. One way of avoiding such suggestions is to distinguish

carefully between properties of individuals and properties of the distribution of individual

traits over a group or class." Particularly, the researcher should be cautions and make sure that, if

the units of analysis are individuals, then the results of data aggregated into groups are not likely

to reflect the real relationships.

Summary

The purpose of this chapter has been to provide the

student of criminal justice with an overview of the primary

types of statistical techniques one confronts in

the literature today. Statistics are simply tools, means

of summarizing and analyzing data. One need not

have extensive training in statistics to be able to generally

interpret reported statistical findings. Without

such a capacity, it is becoming increasingly more difficult

to read most of the latest literature in the field,

which is more and more quantitative in nature.

There are two basic types of statistics: descriptive

and inferential. Descriptive statistics are intended

to summarize, describe, or show relationships

between data; inferential statistics infer or generalize

sample findings to larger populations. Basic descriptive

techniques such as measures of central tendency

(mean, median, and mode) were illustrated, as were

measures of dispersion such as the range and standard

deviation. *Z *scores, or standard deviation scores, are

quite useful in assessing probability so long as we can

TABLE 13.12 Relationship Between Ecological Correlations and Individual Correlations

Unit of Analysis

Illiteracy

By Foreign-Born

Illiteracy

By Race (Black)

Nine census areas *re * -.62 *re * .95

Forty-eight states *re * -.53 *re * .78

Individuals *r * .12 *r * .20

Review 15 (June 15, 1950): 351-357. ISBN 0-558-58864-6

Chapter 13 • Data Analysis **365**

assume the data are normally distributed. Chi-square

was presented as an inferential technique (test of independence)

appropriate for nominal level data. As with

other tests of significance, a calculated value is compared

at appropriate degrees of freedom with a calculated

table of expected values. If a calculated value

exceeds the expected value at the .05 probability

level (*p * .05), this means that in fewer than five of

one hundred trials could such a result be caused by

sampling error. Chi-square is not a measure of

relationship, although there are a number of chisquare-

based measures of association such as phi,

phi-square, contingency coefficient, and Cramer's *V.*

Of these, phi-square is of the greatest utility in that it

is a PRE measure. A PRE (proportional reduction in

error) measure is most useful in that it has in common

with other such statistics a direct operational interpretation-

variance explained.

In addition to having descriptive or inferential

functions, statistics can also be either parametric or

nonparametric in nature. Parametric statistics assume

interval level measurement, normal distributions, and

linearity. Nonparametric statistics are "distribution

free"; that is, they make few assumptions regarding

the distribution of the population. Pearson's *r*, *Z*, and

F tests (ANOVA) are examples of parametric statistics,

whereas gamma, Spearman's rho, and chi-square

are examples of nonparametric statistics.

In inferential statistics, researchers do not

directly test the research hypothesis or relationship

they are attempting to demonstrate, but instead statistically

assess the null hypothesis, a statement of nonrelationship.

Tests of significance measure whether

results are due to chance or are so highly improbable

of resulting from chance that they are significant at

given levels of probability. The *t *test is a test of significance

that compares sample means where the *N*

of either sample is less than 30. For larger samples

the *Z *test is more appropriate.

ANOVA (analysis of variance) is appropriate

for testing, by means of the *F *ratio, three or more

samples. It assumes that the variance between

groups should be large, and the variance within

groups small. At appropriate degrees of freedom, the

F ratio is compared with a table of expected values

to test statistical significance. All of the statistical

procedures that have been discussed in this chapter

are applicable to only certain types of data, and the

researcher is advised to check these assumptions

carefully prior to choice of the statistical measure.

Central to much scientific investigation is the

notion of relationship indicates that, as one variable

increases, the other increases; a negative relationship

(inverse) indicates that, as one variable increases, the

other decreases in value. Finally, if one variable has

absolutely no impact on another, this is indicative of

no relationship. Pearson's correlation coefficient (*r*)

is one of the most widely used measures of relationship.

It is appropriate for interval level data that exhibit

linearity and varies from -1.00 (perfect inverse

relationship) to 1.00 (perfect positive relationship).

The square of *r *(*r*2) is a PRE measure and indicates

variance explained. A regression equation enables

one to predict values of one variable (*Y*), given

knowledge of a predictor variable (*X*).

Some measures of relationship that are alternatives

to Pearson's *r *for working with ordinal (ranked)

data are Spearman's rho and gamma. Both calculations

can have PRE interpretation. Multivariate analysis

includes partial correlation, in which controls for a

third or more variables exist, as well as multiple correlation

and regression. Multiple correlation (*R*) looks at

the impact of multiple predictors (independent variables)

on the dependent variable. Multiple regression

provides a formula that enables the calculation of predicted

values of the dependent variable, given values

of independent variables.

Finally, the reader is urged to follow the

maxim "caveat emptor" ("let the buyer beware") in

reading statistical findings. Be wary of assumptions

regarding the meaning of statistical significance, the

misuse of statistical techniques, overgeneralizations

beyond the data in discussions, and overlooked

assumptions that are required in appropriately

utilizing statistical measures.

Ecological fallacy is the error that occurs

when the researcher's target is individuals, but the

analysis is of groups. If the units of an analysis are

individuals, then data aggregated into groups are not

likely to reflect the real relationship.

ISBN 0-558-58864-6

366 Chapter 13 • Data Analysis

About Mathematics: Statistics Tutorials and Resources

http://math.about.com/od/statistics/

Electronic Textbook: StatSoft *http://math.about.com*

psychology/tests_and_testing/psychometrics

Correlation and Reliability Analysis with SPSS for

Windows *www.nyu.edu/its/socsci/Docs/correlate.html*

policymaking.org/Spss_tutor.htm

Review Questions

1. The types of statistics can be classified as descriptive

or inferential and parametric or nonparametric.

Discuss each of these and provide examples.

2. What is the notion of "normal curve" in statistics, and

of what use is it in statistical tests?

3. What is the purpose of a test of significance? What,

for instance, does *p * .05 indicate?

4. "Caveat emptor"-what are some suggestions for

consumers of statistical findings to guard against

being misled?

Key Concepts

Descriptive statistics *333*

Inferential statistics *333*

Measures of central

tendency *334*

Mode *334*

Median *334*

Mean *335*

Measures of dispersion *336*

Range *336*

Standard deviation *336*

Z scores *340*

Chi-square *341*

Degrees of freedom *343*

Phi coefficient *344*

Phi-square *344*

Contingency coefficient *345*

Cramer's *V 345*

Parametric statistics *345*

Nonparametric statistics *345*

Null hypothesis *346*

t Test *347*

ANOVA *350*

Positive relationship *353*

Negative relationship *353*

Pearson's *r 353*

Regression equation *355*

Spearman's rho *356*

PRE measure *358*

Gamma *358*

SPSS *360*

Partial correlation *361*

Multiple correlation *361*

Multiple regression *361*

Ecological fallacy *363*

APPENDIX A

How to Write the Research Report

The nature, style, and substance of the research report will vary with audience and purpose.

A number of the features of a research report have been discussed previously, first in our analysis

of the steps in research and then in our analysis of the steps in evaluation research and proposal

writing. Does the audience consist of other professionals or laypersons? Is it a paper for a course,

for professional meetings, for a popular publication, a professional journal, or a funding agency?

Although differences will exist depending on the answers to these questions, enough similarities

exist that similar guidelines with minor modifications will suit each situation.

GENERAL ADVICE

The best way to start to learn how to do anything is to "*just do it*"-practice. Getting started by

putting pencil to pad or fingers to keyboard is often the worst part. Howard Becker (1986, p. 167)

advises: "Try it! As a friend once said to me, the worst that can happen is that people will think

you're a jerk. It could be worse." Before examining specifics of the research report here is some

general advice:

- Read some journal articles in the field for a sense of style, language, and format.
- Do not be afraid to start putting your thoughts on paper (or screen). Just assume that you

will have to rewrite and polish later.

- Avoid plagiarism by giving proper acknowledgment-provide a citation for the words,

ideas, or paraphrases of others. To avoid plagiarism, be careful to record sources in your

notetaking, while preparing to write the paper.

- Avoid sexist language. Avoid nouns ending in "man," such as
*policeman*or*chairman.*Use

police officer or *chair*, for example. When using a pronoun for an antecedent that applies

to neither sex specifically, use *he *or *she *or *him *or *her *(Macmillan, 1988, pp. 9-10).

- Avoid prejudicial language. Be careful to guard against stereotypes or attributions that are

offensive to any race, creed, or nation.

- Avoid libel, that is, writing something that is not truthful and could be interpreted as damaging

to another party. A publisher once talked this author out of including a section on a

prominent child sexual abuse case in a book he had written because the case had not been

adjudicated. Fortunately, it was eliminated, but it turned out to be the longest such trial in

American history, and the defendants were eventually found not guilty.

- Generally avoid using the first person pronoun "I" in formal papers.
- Proofread the paper. This can be done efficiently with spell-checking software, which is

available for most word-processing programs.

The function of scientific writing is not so much to entertain as it is to objectively inform, and

although the style need not be boring, it is generally more technical and geared to a professional

audience.

ISBN 0-558-58864-6

STEPS IN THE RESEARCH REPORT

There are a number of variations in steps in a research report, depending on whether the report is

qualitative or quantitative and depending on its intended audience. The steps in a research report

include:

- The Research Problem and Literature Review
- The Methodology: Research Design and Data Collection
- The Analysis and Presentation of Findings
- Discussion and Conclusions
- References

Preceding the actual body of the paper are the title and abstract. A good title and abstract

are succinct and to the point. Abstracts should be less than 200 words. The following is an example

(McElrath, 1990, p. 135):

Standing in the Shadows: Academic Mentoring in Criminology

by Karen McElrath

Abstract

Survey data were used to explore the effect of mentoring on publications by faculty members in

criminology and criminal justice. The initial analysis showed that mentored faculty were significantly

more successful at publishing than nonmentored faculty. Further examination revealed

gender differences with respect to being mentored: among new faculty members, publication

success was associated with being mentored by males. Explanations for these findings focused on

the well-established male network in criminal justice and criminology and on structural disadvantages

encountered by female faculty members.

Because many reviewers scanning bibliographic abstracts in search of information will

decide on the basis of the abstract's content what the report deals with, it is essential that the

abstract be a succinct rendering of the paper's content. Abstracts are written after the entire

report has been completed.

Research Problem and Literature Review

Included in this initial section of the research paper is a clear identification of the purpose of the

research project. The writer should address why this research and its findings may be useful to

criminal justice and/or criminology. A beginning topic is narrowed down to a formalized and

specific research problem. The introduction should also include a brief overview of what is to

come.

Howard Becker (1986, p. 135) uses the phrase "terrorized by the literature" to refer to the

tendency of some researchers to become so overwhelmed by and deferential to the past literature

that they become almost immobilized when trying to get on with their own work. As discussed in

Chapter 1, a good literature review can be considerably enhanced by the use of a computerized

search service such as DIALOG or the National Criminal Justice Reference Service. Because

research papers, unlike books, must be succinct, the literature review must, by necessity, be

abbreviated to permit space for the other sections of the report. In most instances, research report

writers should avoid relying upon the mass media and popular literature-for example *Time *or

Newsweek-and they should, as much as possible, use sources from professional journals such

as *Criminology *or *Justice Quarterly.*

If there is a specific hypothesis to be examined in the paper, the writer should state this as

clearly as possible. In the methodology section, one can describe how the measurements are

intended to address and test the hypothesis. Kerlinger (1973, p. 694) indicates: "The report

should be so written that the reader himself can reach his own conclusions as to the adequacy of

the research and the validity of the reported results and conclusions."

Methodology

The methodology section, which includes descriptions of research design and data gathering,

should be as specific as possible in order to permit replication. Actual instruments used, such as

questionnaires, may be added at the end of the report if they are brief enough. Student reports for

class may require that instruments as well as calculations and raw data be appended.

The methodology section should also detail the sampling procedures, the subjects and setting,

ethical protections, operationalization of key variables, and the measuring instruments that

were employed. The writer basically explains how the study was done. If the report is also to be

submitted to the media, it is advisable to cut some of the professional jargon and methodological

detail that might not be understood by a general audience. These items should be retained in the

original report for submission to a professional audience. Finally, an important question to be

discussed is whether the research intends to replicate in any way previous research.

Analysis and Presentation of Findings

Presentation of tables and results are the subject of this portion of the research report. Berg

(1989, p. 150) explains that this section might vary with qualitative data. In some cases, the data

might be presented throughout the report because qualitative studies are often organized around

conceptual themes, ethnographic narratives, and observations.

For quantitative analysis, researchers should explain in detail any scoring and analysis procedures

that were used. For qualitative analysis, researchers select quotes and indirectly connote

the field experience to the reader (Lofland, 1988).

Discussion and Conclusions

The discussion section usually reiterates the initial research problem and how the analysis and

findings addressed it. The writer now goes beyond reporting findings and speaks to how these

findings bear upon broader theoretical and substantive concerns. Some typical questions include:

What are the limitations of the study?

Of what significance are these results to issues in the field or to practical criminal justice

concerns?

What should future research of this type address?

What conclusions can be drawn?

Writers should avoid getting carried away and generalizing beyond the level of the data that they

have gathered. Such sweeping generalizations should be avoided.

References

Most social science journals and writers prefer using what is called the APA style or some variation

for referencing materials. This style is spelled out in the *Publication Manual *of the

American Psychological Association (2001). This approach eliminates the traditional style of footnotes at the bottom of the page in addition to a separate bibliography. Instead references are

cited directly in the body of the text as has been the case throughout this textbook. For example:

The number of doctoral programs remain small (Flanagan, 1990, p. 195).

For the reference section, the item would be included in an alphabetized list that has some

variation:

Flanagan, Timothy J. "Criminal Justice Doctoral Programs in the United States and Canada:

Findings From a National Survey." *Journal of Criminal Justice Education *1 (Fall 1990):

195-213.

Such formats are usually detailed near the front or back of journals. The research report

should provide a reference for each source that is actually cited in the report.

Appendix

The Appendix contains any tables or figures that are considered too detailed or distracting to

include in the main body of the text. While most published journal articles are slim on appendixes

because of page space limitations, student research reports that fulfill class requirements

should include as much supporting material as possible. For more detail on preparing a research

report, the reader is referred to: XXXXX XXXXX Curtis (1987), Strunk and White (1979), and

Turabian (1967).

A final piece of advice for academic writers is offered by Howard Becker (1986, p. 121)-

"get it out the door." There is something to be said for completing a project within a reasonable

period of time. If one is afraid of criticism or seeks absolute perfection, he or she should not

write. Research is a dynamic process and critiques and reviews can be very helpful in improving

a research report.

370 Appendix A

ISBN 0-558-58864-6

444 References

Orenstein, Alan, and William R. F. Phillips.

Understanding Social Research. Boston, MA:

Allyn and Bacon, 1978.

Osgood, Charles, et al. The Measurement of

Meaning. Urbana, IL: University of Illinois

Press, 1957.

XXXXX, XXXXX P., Phillip R. Shaver, and

Lawrence S. Wrightsman, eds. Measures of

Personality and Social Psychological Attitudes.

San Diego, CA: Academic Press, 1991.

Rossi, Peter H., and J. Patrick Henry.

"Seriousness as a Measure for All

Purposes?" InEvaluation, edited by M. Klein and K.

Teilmann, 489-505. Beverly Hills, CA:

Sage, 1980.

Rossi, Peter H., et al. "The Seriousness of

Crimes: Normative Structure and

Individual Differences."Sociological Review 39 (April 1974): 224-237.

Samuelson, R. "Riding the Monthly Escalator:

Times Magazine (December 8, 1974): 34-35.

Scheussler, Karl B., and Donald B. Cressey.

"Personality Characteristics of Criminals."

American Journal of Sociology 55 (1950):

476-484.

XXXXX, XXXXX F. "Two Dimensions of

Sociological Review 24 (April 1959): 240-243.

Sellin, Thorsten, and Marvin E. Wolfgang.

The Measurement of Delinquency. New York:

Wiley, 1966.

Shaw, Marvin E., and Jack M. Wright. Scales

for the Measurement of Attitudes. New York:

McGraw-Hill, 1967.

File. Rockville, MD: National Institute of

Justice, 1985.

Sherman, Lawrence W., et al. Preventing

Crime: What Works, What Doesn't, What's

Promising.Washington, DC: Office of

Justice Programs, 1997, NCJ 165366.

---. eds. *Evidence-Based Crime Prevention.*

London: Routledge, 2002.

Short, James F., Jr., and Fred L. Strodtbeck.

Group Process and Gang Delinquency.

Chicago, IL: University of Chicago Press,

1965.

Simon, Frances H. Prediction Methods in

Criminology. Home Office Research

Studies, No. 7. London: Her Majesty's

Stationery Office, 1971.

Snider, James G., and Charles E. Osgood, eds.

Semantic Differential Technique. Chicago, IL:

Aldine, 1969.

Stephenson, W. The Study of Behavior:

Q-Technique and Its Methodology. Chicago,

IL: University of Chicago Press, 1953.

Straus, Murray A., and Richard J. Gelles.

"Societal Change and Change in Family

Violence from 1975 to 1985 As Revealed in

Two National Surveys."and the Family 48 (1986): 466-479.

Summers, Gene F., ed. Attitude Measurement.

Chicago, IL: Rand McNally, 1970.

Tennenbaum, David J. "Research Studies of

Personality and Criminality: A Summary

and Implications of the Literature."

Journal of Criminal Justice 5 (Spring 1977):

1-19.

Thielbar, Gerald W., and Saul D. Feldman.

"Images of Deviants and Their Behavior:

Stereotypes and Social Context." In

Deciphering Deviance, edited by Saul D.

Feldman, 265-281. Boston, MA: Little,

Brown, 1978.

Thurstone, Louis L., and Ernest J. Chave. The

Measurement of Attitudes. Chicago, IL:

University of Chicago Press, 1929.

Torgerson, Warren. Theory and Methods of

Scaling. New York: Wiley, 1958.

Vito, Gennaro F. "Felony Probation and

Recidivism: Replication and Response."

Federal Probation 50, no. 4 (1986): 17-25.

Waldo, Gordon P., and Simon Dinitz.

"Personality Attributes of Criminals: An

Analysis of Research Studies, 1950-1965."

Journal of Research in Crime and Delinquency

4 (1967): 185-202.

ISBN 0-558-58864-6

**THIS IS THE END OF THE SOURCE READINGS FOR THIS CLASS SESSION!**

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