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Chirag, Master's Degree
Category: Math Homework
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# What is the difference between parametric and nonparametric

### Customer Question

What is the difference between parametric and nonparametric statistical tests?
Submitted: 5 years ago.
Category: Math Homework
Expert:  Chirag replied 5 years ago.

If a statistical variable understudy can be represented on a ratio or at least an

interval scale of measurement, then it is said to have proper units. With some

assumption made about the distribution of the variable (say normality, for example),

the variable is fit to be tested parametrically. The t-test, the z-test etc are a few well-

known parametric testing methods. These tests lay different restrictions on the data.

If a statistical variable is of the nominal or ordinal type only, then it does not qualify to

be parametrically tested. Sometimes we may have obtained a sample which may

not be a part of a well-defined population. In this case, there are no population

parameters to fall back upon since the population is itself nonexistent or not well

defined. Here we conduct a non-parametric test, which is essentially distribution-

free. In this case, there are no requirements of normality or homogeneity in the data.

This also means there can be a few outliers and their effect will be ignored.

An advantage of non-parametric tests is that sometimes, they give quick answers

with little computation work. However, since these tests are non-parametric, it is

difficult to quantitatively justify the observed differences.

Many critical statistical procedures such as regression, hypothesis testing and

ANOVA require the population to be normally distributed. This means if we can

"normalize" the data, we can use use these powerful statistical analysis tools. There

are tests that do not require an assumption of normality, but they are not as sensitive

as the ones based on normal distribution. Parametric tests are many and are more

powerful than their nonparametric counterparts. Not to forget the implementation of

control charts for mean, range etc in statistical quality control, which are also based

on normal distribution.

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Chirag, Master's Degree
Category: Math Homework
Satisfied Customers: 12192
Experience: Excellent Tutor with a long teaching experience at different levels.
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Expert:  dhouse1940 replied 5 years ago.
Nothing said so far is incorrect. However, I believe the answer to the original question is much simpler than that given. That simple answer is that parametric tests assume the observations are drawn from a population with a certain distribution, usually a normal distribution, while nonparametric tests make no such assumption.

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Customer: replied 5 years ago.
Does this mean normal distribution is the only assumption for parametric tests?
Customer: replied 5 years ago.
Relist: Answer came too late.
Expert:  Chirag replied 5 years ago.

Hi,

From the time log on my screen for this posting, I see that I had sent the answer within 5 minutes of your posting the question.

Please see if you can still use the answer.

Thanks.

Expert:  dhouse1940 replied 5 years ago.
Being from a certain distribution also implies knowledge of the variance and equal variance is an assumption of many parametric tests.