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The NPAR1WAY Procedure |

are called *simple linear rank statistics*, where

*R*_{j}- is the rank of the observation
*j* *a*(*R*_{j})- is the score based on that rank
*c*_{j}- is an indicator variable denoting the class
to which the
*j*th observation belongs *n*- is the total number of observations

For two-sample data (where the observations are classified into two levels), PROC NPAR1WAY calculates simple linear rank statistics for the scores that you specify. The "Scores for Linear Rank and One-Way ANOVA Tests" section describes the available scores, which you can use to test for differences in location and differences in scale.

To compute

For each score that you specify, PROC NPAR1WAY computes an asymptotic test of the null hypothesis of no difference between the two classification levels. Exact tests are also available for these two-sample linear rank statistics. 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.

To compute an asymptotic test for a linear rank sum statistic, PROC NPAR1WAY uses a standardized test statistic

where

where

where

PROC NPAR1WAY computes one-sided and two-sided asymptotic

where

For Wilcoxon scores and Siegel-Tukey scores, PROC NPAR1WAY
incorporates a continuity correction when computing the standardized
test statistic *z*, unless you specify CORRECT=NO.
PROC NPAR1WAY applies the continuity correction by subtracting
0.5 from the numerator *S* - *E _{0}*(

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