Question

If we are comparing two independent samples and are not convinced that our data is normally distributed or that our variances are equal, what statistical test should we use to test our hypothesis of equivalent means across the two groups?

Answer 1

If we are comparing two independent samples and are not convinced that our data is normally distributed or that our variances are equal then we use Z-test for testing the hypothesis of equivalent means across the two groups.

Some key points regarding the above is-

If the variances are known & equal then we go through t-test.

If variances are known but unequal then we use Z-test.

The test is accurate if the populations are normally distributed but if not i.e. the population are non-normal then the test may be regarded as approximate and the test statistic for the respective test may be compared with the standard normal distribution using either a one - or two - tailed test.