Question

Nonparametric Tests

a. Which of the following terms is sometimes used instead of “nonparametric test”: normality test; abnormality test; distribution-free test; last testament; test of patience?

b. Why is the term that is the answer to part (a) better than “nonparametric test”?

Short answer

a.The term “distribution free-test” is synonymous withthe nonparametric test.

b.The term “distribution-free test” is better than the term “nonparametric test”because it does not provide incorrect information about the parameters.

Step-by-step solution

Given information

Nonparametric tests are commonly used to test different hypotheses when the distribution of the population from which the sample is extracted is not known.

Synonym of “nonparametric test”

a.

Out of the given words, the term “distribution-free test” is also used to describe a nonparametric test.

The most important characteristic of a nonparametric test is that there is no requirement to know the exact probability distribution of the population from which the sample is selected.

As the name signifies, a nonparametric test can accurately be called a distribution-free test.

b.

The term “nonparametric test” may suggest that the procedure of the test does not require any parameters. In reality, many of the nonparametric tests involve the computation of median, which is a parameter.

The phrase "distribution free-test" better represents how and why the test is used and its important feature.

Therefore, the term “distribution-free test” is better than the term “nonparametric test.”