Median test

The median test is a special case of Pearson's chi-square test. It tests the null hypothesis that the medians of the populations from which two samples are drawn are identical. The data in each sample are assigned to two groups, one consisting of data whose values are higher than the median value in the two groups combined, and the other consisting of data whose values are at the median or below. A Pearson's chi-square test is then used to determine whether the observed frequencies in each group differ from expected frequencies derived from a distribution combining the two groups.

The statistical power of this test may sometimes be improved by using a value other than the median to define the groups – that is, by using a value which divides the groups into more nearly equal groups than the median would.

This test is useful when the distributions of data differ markedly from normality, for example when raw scores have been arbitrarily classified into inappropriate ranges before being recorded. For this reason it is often useful as an initial step in exploratory analysis.