Question

There are numerous times when the information collected from a real organization will not conform to the requirements of a parametric analysis. That is, a practitioner would not be able to analyze the data with a t-test or f-test (ANOVA). Presume that a young professional had read about tests—such as the Chi-Square, the Mann-Whitney U test, the Wilcoxon Signed-Rank test, and Kruskal-Wallis one-way analysis of variance—and wants to know when it is appropriate to use each test, what each test is used for, and why each would be used instead of the t-tests and ANOVA. How would you address this person’s concerns?

Answer 1

The said tests that are mentioned in the question are all non-parametric tests wherein, one can analyze the information collected by the organization that does not conform to the requirements of a parametric analysis such as a t-test or a F-test.

The concept of the non-parametric analysis is to perform statistical analysis on the data that is not in any way quantifiable but qualitative in nature. In such cases, one does need inferences and non-parametric hypothesis testing is the best foot forward.

Given are the following tests that are non-parametric tests:

a) Chi-square test: The category of a chi-square test is very broad and one can use it on both qualitative as well as quantitative data. The versatility of the chi-square test makes it accommodate with the form of data given. It is best used in cases where the data is categorical and one has to analyze the dependence of these categories on one another.

b) Mann-Whitney U test: Using this test one can interpret whether the two chosen values from the two datasets come from the population with the same distribution. It is best used when we have a small dataset and parametric analysis is not possible. Further, when the sample data is highly skewed or does not represent any given statistical distribution, Mann-Whitney U test is the best non-parametric test to perform to test the independence of the two samples.

c) Wilcoxon signed rank test: It is a non-parametric substitute to the paired t-test wherein the one uses signed rank test since the underlying population distribution of the sample is not normally distributed. It requires assigning ranks to the datasets and then analyzing then in order to verify whether the mean ranks of the two samples are same or not.

d) Kruskal -Wallis one way analysis of variance: A non-parametric version of one way ANOVA, this test is an extension to the Mann-Whitney U test where instead of just two samples one can analyze more than two samples in order to undertsand whether they come from the same population or not. It is used whenever the underlying population does not follow a normal distribution.