As with most non-parametric tests, the Mann-Whitney U is more powerful than its parametric counterpart when parametric assumptions are not met. Also, the Mann-Whitney U will provide the same results under any monotonic transformation of the data; the results of the test are therefore more generalizable.

A Mann-Whitney U test statistic can be calculated using the following steps:

• Rank all of the observations (N total) regardless of group membership, whereby tie scores are given the average rank for the whole rank of ranks that would be subsummed by those scores.
• Sum the ranks independently for each group (R1 and R2).
• Calculate U1 and U2 by the following formulas:

• Use the smaller of U1 and U2 and compare to the critical value given in the table (available in most statistics texts).

• When n > 20, the distribution of the Mann-Whitney U approaches the normal curve and a z-test can be used:

The Median test is a less powerful non-parametric test than the Mann-Whitney because the dependent variable is dichotomized at the median (hence the name). In other words, there are two groupsfor the dependent variable: those who scored higher than the median score and those who scored lower than the median score. The data becomes simply the number of individuals who fall into each group. Thus, this technique tends to discard most of the information inherent in the data and is rarely used.

In order to evaluate the frequencies, a simple 2 x 2 contingency table is used. In essence, this test becomes simply a 2 x 2 chi square test of independence with 1 df.