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Does Brain Size Matter? Is the...

Does Brain Size Matter?

Is the size of your brain an indicator of your mental capacity? Are human brain size and intelligence related to each other? The relationship between brain size and intelligence has been a topic of a scientific debate since at least 1830s. The first researchers in this area often used external skull measurements or waited until a person died to estimate brain size. The most recent advances in technology, in particular Magnetic Resonance Imaging (MRI) allowed to obtain very accurate brain size measurements. In 1991, Willerman et. al. used the technology to examine the relationship between brain size and intelligence for a random sample of university students. Brain size of the subjects selected for the study was determined by MRI scans and intelligence was measured with several standardized intelligence tests. For detailed information about the study, refer to the paper by Willerman, L., Schultz, R., Rutledge, J. N., and Bigler, E. "In Vivo Brain Size and Intelligence", Intelligence, 1991, 15, 223-228.

The study was conducted at a large southwestern university in USA. Researchers randomly selected a sample of 40 students from a larger pool of right-handed Anglo introductory psychology students, who had indicated no history of alcoholism, unconsciousness, brain damage, epilepsy, or heart disease and had volunteered to participate in the study.

MRI was used to determine the brain size of the subjects. The MRI scans were performed at the same facility for all 40 subjects. The scans consisted of 18 horizontal MR images. The computer counted all pixels with non-zero gray scale (indicating the presence of gray matter) in each of the 18 images and the total count served as an index for brain size. Information about gender and body weight is also included.

With prior approval of the University's research review board, students selected for MRI were required to obtain prorated full-scale IQs of greater than 130 or less than 103, and were equally divided by sex and IQ classification.

In this assignment, you will use the data to explore the relationship between brain size and intelligence for male and female students, and you will use a simple linear regression model to make predictions about IQ score for a student of a given brain size.

The following is the description of the variables in the data file:

Description of Variable

GENDER 0 = Female, 1 = Male

PIQ Performance IQ scores based on the four Wechsler (1981) sub-tests

(Vocabulary, Similarities, Block Design, and Picture Completion)

WEIGHT Body weight in pounds

MRI Total pixel count from the 18 MRI scans

Answer the following questions:

1) Describe the PIQ for each gender using the values listed in the Descriptive Statistics (in the worksheet data file).

2) Perform a pooled variance t-test to see for the difference in mean PIQ scores between females and males. Show the analysis and state the conclusion.

3) Examine the relationship between i) PIQ and WEIGHT and ii) PIQ and MRI for all the subjects. Use the scatter plots as reference (in the worksheet data file). Describe the overall pattern in the plot including shape, direction, and strength of the relationship in (i) and (ii) for all subjects. Also, describe the pattern separately for males and females.

4) Now run separate regressions of PIQ versus MRI for males and females. Then use the Regression tool in Excel to perform the regression for each gender separately and use the output to answer the following questions:

i) What is the estimated regression line for each gender? Interpret the values of the y-intercept and slope for each model.

ii) What percent of the variation in PIQ is explained by MRI for each gender?

iii) Is the MRI variable significant for each gender?

5) Synthesize your statistical findings carried out in question 1 until 4. Given your findings, what conclusion can be drawn with regards to the beliefs? Write no more than 300 words.

Is the size of your brain an indicator of your mental capacity? Are human brain size and intelligence related to each other? The relationship between brain size and intelligence has been a topic of a scientific debate since at least 1830s. The first researchers in this area often used external skull measurements or waited until a person died to estimate brain size. The most recent advances in technology, in particular Magnetic Resonance Imaging (MRI) allowed to obtain very accurate brain size measurements. In 1991, Willerman et. al. used the technology to examine the relationship between brain size and intelligence for a random sample of university students. Brain size of the subjects selected for the study was determined by MRI scans and intelligence was measured with several standardized intelligence tests. For detailed information about the study, refer to the paper by Willerman, L., Schultz, R., Rutledge, J. N., and Bigler, E. "In Vivo Brain Size and Intelligence", Intelligence, 1991, 15, 223-228.

The study was conducted at a large southwestern university in USA. Researchers randomly selected a sample of 40 students from a larger pool of right-handed Anglo introductory psychology students, who had indicated no history of alcoholism, unconsciousness, brain damage, epilepsy, or heart disease and had volunteered to participate in the study.

MRI was used to determine the brain size of the subjects. The MRI scans were performed at the same facility for all 40 subjects. The scans consisted of 18 horizontal MR images. The computer counted all pixels with non-zero gray scale (indicating the presence of gray matter) in each of the 18 images and the total count served as an index for brain size. Information about gender and body weight is also included.

With prior approval of the University's research review board, students selected for MRI were required to obtain prorated full-scale IQs of greater than 130 or less than 103, and were equally divided by sex and IQ classification.

In this assignment, you will use the data to explore the relationship between brain size and intelligence for male and female students, and you will use a simple linear regression model to make predictions about IQ score for a student of a given brain size.

The following is the description of the variables in the data file:

Description of Variable

GENDER 0 = Female, 1 = Male

PIQ Performance IQ scores based on the four Wechsler (1981) sub-tests

(Vocabulary, Similarities, Block Design, and Picture Completion)

WEIGHT Body weight in pounds

MRI Total pixel count from the 18 MRI scans

Answer the following questions:

1) Describe the PIQ for each gender using the values listed in the Descriptive Statistics (in the worksheet data file).

2) Perform a pooled variance t-test to see for the difference in mean PIQ scores between females and males. Show the analysis and state the conclusion.

3) Examine the relationship between i) PIQ and WEIGHT and ii) PIQ and MRI for all the subjects. Use the scatter plots as reference (in the worksheet data file). Describe the overall pattern in the plot including shape, direction, and strength of the relationship in (i) and (ii) for all subjects. Also, describe the pattern separately for males and females.

4) Now run separate regressions of PIQ versus MRI for males and females. Then use the Regression tool in Excel to perform the regression for each gender separately and use the output to answer the following questions:

i) What is the estimated regression line for each gender? Interpret the values of the y-intercept and slope for each model.

ii) What percent of the variation in PIQ is explained by MRI for each gender?

iii) Is the MRI variable significant for each gender?

5) Synthesize your statistical findings carried out in question 1 until 4. Given your findings, what conclusion can be drawn with regards to the beliefs? Write no more than 300 words.

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