A hypothesis test formally tests if two or more population means/medians are equal.
Inferences about related samples are complicated by the fact that the observations are correlated. Therefore the tests for independent samples are of no use. Instead, tests for related samples focus on the differences within each sampling unit.
The hypotheses to test depends on the number of samples:
- For two samples, the null hypothesis states that the difference between the mean/medians of the populations is equal to a hypothesized value (0 indicating no difference), against the alternative hypothesis that it is not equal to (or less than, or greater than) the hypothesized value.
- For more than two samples, the null hypothesis states that the means/medians of the populations are equal, against the alternative hypothesis that at least one population mean/median is different.
When the test p-value is small, you can reject the null hypothesis and conclude that the populations differ in means/medians.