Question

Provide at least one example of a parametric statistical test and its nonparametric equivalent, and explain how these examples illustrate the comparison of the two types of analysis

Answer 1

Example

A professor wants to know if her introductory statistics class has a good grasp of basic math. Six students are chosen at random from the class and given a math proficiency test. The professor wants the class to be able to score above 75 on the test. The six students get scores of 65, 93, 72, 69, 83, and 97. Can the professor have 90 percent confidence that the mean score for the class on the test would be above 75?

Here we can use either test which defined below

Parametric test : one sample t test

Equivalent Non Parametric test : Wilcoxon one sample signed rank test

For conducting one sample t test the given data should follow some assumptions listed below:

• Parent Population is Normal
• Sample size is reasonably large
• Scale of measurement continuous or ordinal
• Sample taken should be a random sample
• Homogeneity of variance

If the above assumptions not holds then the same situation can be handled on non parametric test.

We can conduct Wilcox one sample signed rank test. The result obtained this test is valid when ever we can't conduct one sample t test.

Usually Power of non parametric test is smaller than that of Parametric test. So Parametric test is preferable and is avoided when we cannot go forward in the violation of assumption is serious one..