The NPAR1WAY Procedure

## Example 47.2: The Exact Wilcoxon Two-Sample Test

Researchers conducted an experiment to compare the effects of two stimulants. Thirteen randomly selected subjects received the first stimulant and six randomly selected subjects received the second stimulant. The reaction times (in minutes) were measured while the subjects were under the influence of the stimulants.

The following SAS statements create the data set React, which contains the observed reaction times for each stimulant. The variable Stim represents Stimulant 1 or 2. The variable Time contains the reaction times observed for subjects under the stimulant.

```   data React;
input Stim Time @@;
datalines;
1 1.94   1 1.94   1 2.92   1 2.92   1 2.92   1 2.92   1 3.27
1 3.27   1 3.27   1 3.27   1 3.70   1 3.70   1 3.74
2 3.27   2 3.27   2 3.27   2 3.70   2 3.70   2 3.74
;
```

PROC NPAR1WAY tests the null hypothesis that there is no difference between the effects of the two stimulants against an alternative hypothesis that stimulant 1 has smaller reaction times than stimulant 2. The WILCOXON option specifies that Wilcoxon scores are to be used. The CLASS statement specifies that the variable Stim determines the classes. The VAR statement identifies Time as the response variable. The EXACT option requests the exact p-values. Since the sample size is small, the normal approximation may not be completely accurate, and it is appropriate to compute the exact test.

```   proc npar1way wilcoxon data=React;
class Stim;
var Time;
exact;
run;
```

Output 47.2.1: Results of the Wilcoxon Two-Sample Test

 The NPAR1WAY Procedure

 Wilcoxon Scores (Rank Sums) for Variable TimeClassified by Variable Stim Stim N Sum ofScores ExpectedUnder H0 Std DevUnder H0 MeanScore 1 13 110.50 130.0 11.004784 8.500 2 6 79.50 60.0 11.004784 13.250 Average scores were used for ties.

 Wilcoxon Two-Sample Test Statistic (S) 79.5000 Normal Approximation Z 1.7265 One-Sided Pr > Z 0.0421 Two-Sided Pr > |Z| 0.0843 t Approximation One-Sided Pr > Z 0.0507 Two-Sided Pr > |Z| 0.1014 Exact Test One-Sided Pr >= S 0.0527 Two-Sided Pr >= |S - Mean| 0.1054 Z includes a continuity correction of0.5.

 Kruskal-Wallis Test Chi-Square 3.1398 DF 1 Pr > Chi-Square 0.0764

Output 47.2.1 displays the results of the Wilcoxon two-sample test. The Wilcoxon statistic equals 79.50. Since this value is greater than 60.0, the expected value under the null hypothesis, PROC NPAR1WAY displays the right-sided p-values. The one-sided exact p-value equals 0.0527, which is not significant at the 0.05 level. The normal approximation yields a one-sided p-value of 0.0421, which is significant at the 0.05 level. Thus, the normal approximation may result in rejection of the null hypothesis, while the exact test may result in acceptance.