Stats
Sample size calculation for a nonparametric test (March 8, 2005).
Category: Sample size justification
I got an email inquiry about how to calculate power for a Wilcoxon signed ranks test. I
don't have a perfect reference for this, but I do have a brief
discussion on sample size calculations for the Mann Whitney U test as part of my pages on
selecting an appropriate sample size. The same considerations would
apply for the Wilcoxon test. In response, the email author sent me a link to
which offers the following advice:
If you plan to use a nonparametric test, compute the sample size required for a t
test and add 15%.
This assumes a reasonably high number of subjects (at least a few dozen) and a
distribution which is not really unusual. I had not heard this rule; the author cites pages
76-81 of Lehmann, Nonparametrics: Statistical Methods Based on Ranks
[BookFinder4U link]. I don't
have this book, so I can only guess as to the basis for this formula.
This rule could be based, I suppose, on the lower bound for the Asymptotic Relative
Efficiency (ARE) of the Mann Whitney U test versus the t-test, which is 0.864. This says that
no matter what the distribution, the ARE of the Mann Whitney U test can never be worse than
0.864 for a reasonably broad class of probability distributions. Inverting that gives you an
increase in the sample size by a factor of 1.157. The same statement would also apply for the
Wilcoxon Signed Ranks test, which can never have an ARE less than 0.864 compared to the
paired t-test.
07/08/2008.
