# 12.7: Critical Values for the Wilcoxson Ranked Sum Test


The following table provides critical values at $$\alpha = 0.05$$ for the Wilcoxson ranked sum test where $$n_1$$ and $$n_2$$ are the number of samples in the two sets of data where $$n_1 \le n_2$$. An entry of NA means the test cannot be applied. The null hypothesis of no difference between the samples can be rejected when the test statistic is less than or equal to the critical values for the number of samples.

$$\PageIndex{1}$$: Critical Values for Wilcoxson Ranked Sum Test with $$\alpha = 0.05$$
$$n_1$$ $$n_2$$ one-tailed test two-tailed test
3 3 0 NA
3 4 0 NA
3 5 1 0
3 6 2 1
4 4 1 0
4 5 2 1
4 6 3 2
4 7 4 3
5 5 4 2
5 6 5 3
5 7 6 5
5 8 8 6
6 6 7 5
6 7 8 6
6 8 10 8
6 9 12 10
7 7 11 8
7 8 13 10
7 9 15 12
7 10 17 14

12.7: Critical Values for the Wilcoxson Ranked Sum Test is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.