I am looking for some advice regarding the Mann-Whitney U test. I have a dataset consisting of two indices (Index_1 and Index_2) measured under two conditions (A and B). The sample sizes are small ($n=$5 for each condition).
Condition Index_1 Index_2 A 1.0040242 1.2553715 A 1.3520534 1.74602 A 0.9449538 1.1698796 A 0.9852742 1.3240154 A 1.5320312 2.0959063 B 0.4457907 0.7175904 B 0.3815555 0.5997045 B 0.3720059 0.5654503 B 0.4648043 0.6231635 B 0.4833657 0.723848
When I apply a Mann-Whitney U test for each index I find that the output from the two tests is identical:
> wilcox.test(Index_1~Condition) Wilcoxon rank sum test data: Index_1 by Condition W = 25, p-value = 0.007937 alternative hypothesis: true location shift is not equal to 0 > wilcox.test(Index_2~Condition) Wilcoxon rank sum test data: Index_2 by Condition W = 25, p-value = 0.007937 alternative hypothesis: true location shift is not equal to 0
This is puzzling to me, as no other statistical test applied to this data (Kruskal-Wallis or t test) gives two identical outputs. Specifying
paired=F does not make a difference.
Is this a result of the small sample sizes? Unfortunately this can't be remedied and I have to present some sort of result for this dataset.