Question

Most people believe you shouldn’t use a Mann-Whitney test if the data is interval/ratio, symmetric, and normal. They think a t-test is better. Why might this be?

When can a z-test successfully be used instead of a chi-square test (for the same data)?

Answer 1

Mann-Whitney test is a non parametric test and the most widely used test as an alternative to the t-test when we do not make the t-test assumptions about the parent population. When the data is interval/ratio, symmetric and normal which is considered as an assumption of the parent population for t-test, then t-test is better.

Chi square test is a general test. It is a non parametric test. That is, it is not based on any parametric assumption on the parent population. It is also used as a parametric test, because it is the test of the significance difference between the true value and the hypothetical value of the population variance i.e. it is also used to test H₀ : . On the other hand Z test is a parametric test. In other words, Z test can successfully used when the parent population is assumed to be normal and the population standard deviation is given or known.