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The NPAR1WAY Procedure |
In addition to the score types described in this section, you can specify the SCORES=DATA option to use the input data observations as scores. This enables you to produce a very wide variety of tests. You can construct any scores using the DATA step, and then PROC NPAR1WAY computes the corresponding linear rank and one-way ANOVA tests. You can also analyze the raw data with the SCORES=DATA option; for two-sample data, this permutation test is known as Pitman's test.
Using Wilcoxon scores in the linear rank statistic for two-sample data produces the rank sum statistic of the Mann-Whitney-Wilcoxon test. Using Wilcoxon scores in the one-way ANOVA statistic produces the Kruskal-Wallis test. Wilcoxon scores are locally most powerful for location shifts of a logistic distribution.
When computing the asymptotic Wilcoxon two-sample test, PROC NPAR1WAY uses a continuity correction by default, as described in the "Simple Linear Rank Tests for Two-Sample Data" section. If you specify CORRECT=NO in the PROC NPAR1WAY statement, the procedure does not use a continuity correction.
Using median scores in the linear rank statistic for two-sample data produces the two-sample median test. The one-way ANOVA statistic with median scores is equivalent to the Brown-Mood test. Median scores are particularly powerful for distributions that are symmetric and heavy-tailed.
Savage scores are powerful for comparing scale differences in exponential distributions or location shifts in extreme value distributions (Hajek 1969, p. 83).
where the score values continue to increase in this pattern towards the middle ranks until all observations have been assigned a score.
Equivalently, Ansari-Bradley scores are defined as
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