#### Non-Parametric
Statistics

The non-parametric equivalents of the t-test can be
requested with the NP=Y option. Either the Wilcoxon test or the Mann-Whitney
U test will be printed
depending on whether you are performing a matched pairs or independent groups t-test.

The Wilcoxon test for correlated samples is the
non-parametric equivalent of the matched pairs t-test. The data is assigned rank
values and the differences between the ranks are computed. The Wilcoxon test statistic is the
minimum of positive and negative differences in ranks. If the number of cases is
greater than or equal to ten, the probability is calculated from the normal
distribution. When there are fewer
than ten cases, refer to the appendix to determine the probability.

Example of Wilcoxon Statistic Printout

The Mann-Whitney U test is the non-parametric equivalent of the
t-test for independent groups. It may be used to
evaluate the difference between two population distributions. The data is first ranked. The
Mann-Whitney U is the number of times that one group is smaller than the
other.

For sample sizes of less than twenty, refer to the appendix
to find the probability of U. If the sample size is twenty or more, the
distribution approximates the normal distribution, and the normal deviate will be used to calculate
the probability. The Mann-Whitney U may be
selected by using MW=Y or suppressed by using MW=N.

Example of Mann-Whitney U Statistic Printout