# statistical power for Wilcoxon rank sum test

In Matlab I did run a Wilkoxon rank sum test to compare two variables. The number of observation -for each variable- was very small (N=7; for this reason I did not run a t-test, as I could not reasonably assume normality of data). I don't know how to evaluate the result of Wilkoxon test: response is significant but I'm worried about the very small sample size (only 7 observation...did I run a meaningful test?). For this reason I computed the statistical power of the test which, as far as I know, is the correct way to evaluate the "goodness" of test response (Am I right?). I used the Matlab function sampsizepwr which wants as argument the type-of-test (for example z-test, t-test, Chi-square, etc...). I guess it is 'z' but I'm not sure (Matlab page on Wilcoxon seems to suggests that ranksum uses z-statistics).

Question 1: is it meaningful to compute the statistical power of Wilcoxon test, when I have very small samples size?

Question 2: is it correct to use z-statistics (as argument of function sampsizepwr) for computing power of Wilcoxon test?

• Its not clear what the question is – Kozolovska Jan 25 '18 at 18:09
• I apologise and try to make it clearer: is it correct to use 'z-statistic' as argument of function 'sampsizepwr' when testing the power of Wilkoxon test? – valerio_sperati Jan 25 '18 at 18:15
• Let me guess: the result was not significant... a power analysis is rarely useful after peeking at the results. – Michael M Jan 25 '18 at 18:22
• @MichaelM on the contrary! The Wilcoxon test was significant and power was beyond 95%!!! This very high power value was suspicious to me, because of the small sample size (N=7). But maybe only because I'm not used to compute this measure... – valerio_sperati Jan 26 '18 at 11:06

• Well, the issue is, if you're going to specify an effect (such as a location shift) at which you compute the power, simulation doesn't avoid distributional assumptions (the power very much depends on the distribution!). You still make distributional assumptions, what it saves you from is both needing to be able to compute it algebraically, and having to assume normality. e.g. we could compute the power at n1=20,n2=15, data having a t(5) distribution with scale parameter $σ$ and, and a location shift of $½σ$. Or you could assume exponential samples and the second sample with twice the scale. – Glen_b Jan 27 '18 at 4:09