Is there any way to compare two or more than three using mann-whitney-wilcoxon test? that will also give Z and R values?

  • $\begingroup$ It's not clear what you mean by "R values" $\endgroup$ – Glen_b Apr 17 '17 at 17:13

The Wilcoxon-Mann-Whitney test is for two groups. If you want to compare locations of more than two groups with a similar test, then you would usually go to the Kruskal-Wallis test.

The same thing happens with the usual tests under the normality assumption -- for a location comparison (means in that case) on two samples you have a t-test but if you have more than two samples you'd use one-way ANOVA.

The Wilcoxon-Mann-Whitney test doesn't of itself provide Z values (the Mann-Whitney statistic is $U$, while the corresponding Wilcoxon statistic is usually denoted either $W$ or $T$); one can standardize $U$ and call that $Z$, of course (and in large samples it is indeed approximately normal). Some programs will produce such a $Z$ statistic by default, but it's not inherent to the test itself.

[As I mention in comments it's not clear what you mean by "R values". Is it intended to be the proportion of times an observation from sample 1 exceeds one from sample 2?]

When you move to more than two samples, there's no longer a single comparison being made; indeed, it's not even quite the same as performing all possible pairwise comparisons (it's possible with 3 or more groups to have A>B, B>C and C>A on pairwise tests, which the K-W is not sensitive to -- See [1]).

With the Kruskal-Wallis, the usual statistic is in large samples approximately distributed as chi-squared (in the same sense that the ANOVA is F by comparison with the t-statistic in the two sample case).

So a "Z" would not normally be available. You could compute Z's for pairwise comparisons of course, but as outlined above you might have a surprising outcome in that instance (where there is a cycle of differences on pairwise comparisons; you would normally not get a significant Kruskal-Wallis in that instance).

[1] Brown, B.M. and Hettmansperger, T.P. (2002),
"Kruskal–Wallis, Multiple Comparisons and Efron Dice,"
Australian & New Zealand Journal of Statistics, Vol.44 (4), p 427-438


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.