### One-Way ANOVA Tests

PROC NPAR1WAY computes a one-way ANOVA test for each
score type that you specify. Under the null hypothesis
of no difference among class levels (or samples),
this test statistic has an asymptotic chi-square
distribution with *r*-1 degrees of freedom, where
*r* is the number of class levels. For Wilcoxon
scores, this test is known as the Kruskal-Wallis
test.
Exact one-way ANOVA tests are also available for
multisample data (where the data are classified
into more than two levels). For two-sample 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 "Exact Tests" section for details on exact tests.

PROC NPAR1WAY computes the one-way ANOVA test
statistic as

where *T*_{i} is the total of scores for the class level *i*,
*E*_{0}(*T*_{i}) is the expected total for level *i* under the
null hypothesis of no difference among levels, *n*_{i} is
the number of observations in level *i*, and
*S*^{2} is the sample variance of the scores.

where *a*(*R*_{j}) is the score for observation *j*,
and *c*_{ij} indicates whether observation *j* is in
level *i*.

where is the average score,

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.