The mean difference test is to test the difference between the two populations represented by the mean difference of two samples.

Both populations are normally distributed, and both population variance are known. Use z-test.

Both populations are normally distributed, and both population variance are unknown. Use t-test.

Both populations are non-normal distribution, and the sample size is >; =30, with z' test (approximate z test)

Both populations are non-normal distribution, and the sample size is

Analysis of variance is used to test the average difference of three or more samples.