Tests for means/medians (related samples)

Assumes the population differences are normally distributed. Due to the central limit theorem, the test may still be useful when this assumption is not true if the sample size is moderate. However, in this case, the Wilcoxon test may be more powerful.

Assumes the population differences are normally distributed. Due to the central limit theorem, the test may still be useful when this assumption is not true if the sample size is moderate. However, in this case, the Wilcoxon test may be more powerful.

Under the assumption that the population distribution of the differences is symmetric, the hypotheses can be stated in terms of a difference between means/medians.

Under the less strict hypotheses, requiring no distributional assumptions, the hypotheses can be stated as the probability that the sum of a randomly chosen pair of differences exceeds zero is 0.5.

Under the more general hypotheses, tests if given a random pair of observations (xi, yi), that xi and yi are equally likely to be larger than the other.

Has few assumptions, but lacks power compared to the Wilcoxon and Student's t test.

Assumes the populations are normally distributed. Due to the central limit theorem, the test may still be useful when this assumption is not true if the sample sizes are equal, moderate size, and the distributions have a similar shape.

Assumes the populations are normally distributed. Due to the central limit theorem, the test may still be useful when the assumption is violated if the sample sizes are equal and moderate size. However, in this situation the Friedman test is may be more powerful.

Has few assumptions, and is equivalent to a two-sided Sign test in the case of two samples.