PROC NPAR1WAY computes a oneway ANOVA test for each score type that you specify. Under the null hypothesis of no difference among class levels (samples), this test statistic has an asymptotic chisquare distribution with r – 1 degrees of freedom, where r is the number of class levels. For Wilcoxon scores, this test is known as the KruskalWallis test.
Exact oneway ANOVA tests are also available for multisample data (where the data are classified into more than two levels). For twosample data, exact simple linear rank tests are available. PROC NPAR1WAY computes exact tests for each score type that you specify in the EXACT statement. See the section Exact Tests for details.
PROC NPAR1WAY computes the oneway ANOVA test statistic as

where is the total of scores for class level i, is the expected total for level i under the null hypothesis of no difference among levels, is the number of observations in level i, and is the sample variance of the scores. The total of scores for class level i is given by

where is the score for observation j, and indicates whether observation j is in level i. The expected total of scores for class level i under the null hypothesis is equal to

The sample variance of the scores is computed as

where is the average score,
