Question

a) What are the similarities (state one) and differences (state two) between the two-samples t-Test and the ANOVA?

b) Chi-Square Tests is one of those tests that are both parametric and non-parametric depending on what one intends to do. What is the difference between Chi-square test (as parametric and Chi-square (as non-parametric)?

Answer 1

Part a

The two samples t-test and ANOVA both are used for testing the significant difference between the population means. By using these two tests, we find out whether there is any statistically significant difference in the population means or not.

A two samples t-test is used for comparing or testing the significant difference between only two population means while the ANOVA test is used for comparison or testing the significant difference between more than two population means. In two samples t-test, we use the technique of difference between sample means and pooled variance, while in ANOVA we use the analysis of variance for the given variables under study. For a comparison of more than two population means, we need to conduct t-tests more times, while we conduct only one ANOVA test for more than two population means. We do not need to conduct ANOVA test multiple times even though we want to test for several population means.

Part b

We use the Chi-square test as a parametric test for testing the goodness of fit in which variables are quantitative in nature while we use the Chi-square test as a non-parametric test for checking whether given two qualitative variables are independent or not. For this non-parametric test, we use the qualitative variables under study.