Jenny Keating wants help with determining power when using a MannWhitney U
test. This is a long answer and it may be off-topic for this list. If so,
please accept my apologies.
As Ted Harding points out, the power of a nonparametric test is not
nonparametric. In other words the formula for power changes when the
distribution changes. That's not an insurmountable problem, but you do need
to think a bit about why you are using a non-parametric test before you can
properly justify the sample size.
There are several approaches you can take here. The simplest is to buy the
software program: nQuery Advisor, which has power calculations for various
scenarios including the Mann-Whitney-Wilcoxon test. If you do a lot of power
and sample size calculations, this software will save you a lot of time and
effort.
The latest version of StatXact software also has power calculations for
various Exact tests. I bet it has something for the Mann Whitney Wilcoxon
test, but I don't have the software on my system so I can't verify this.
There's lots of other software out there that will do this problem. I'm just
mentioning the two packages I happen to be familiar with.
I don't have good contact information about nQuery Advisor, but you can find
information about StatXact at:
Cytel Software Corporation
675 Massachusettes Ave.
Cambridge, MA 02139 USA
Tel: (617) 661-2011
Fax: (617) 661-4405
Web: http://www.cytel.com
E-M: [log in to unmask]
If you are adventurous you can derive approximate power formulas yourself.
Most people aren't that adventurous, but here are some details anyway.
There's a simple relationship between Asymptotic Relative Efficiency (ARE)
and sample size. If you can calculate a sample size for a parametric test,
and you know the ARE comparing the parametric test to a nonparametric test,
then you can extrapolate to the sample size needed for the nonparametric
test. I don't have details or a reference for this method, but I'm hoping to
dig up all the details and write up a web page about it soon. If you can
send me some specifics about your particular study, perhaps I could include
it as an example on this page.
Machin et al have a formula on page 25-26 that seems to be based on the ARE
method described above, but the details are a bit sketchy.
Machin, David, Campbell, Michael, Fayers, Peter, and Pinol, Alain (1997)
Sample Size Tables for Clinical Studies, Second Edition. Oxford England:
Blackwell Science, Inc. ISBN: 0-86542-870-0.
You might also try looking at the reference suggested in nQuery advisor:
Noether GE (1987) Sample size determination for some common nonparametric
statistics. J. Am Stat. Assn 82:645-647.
Good luck!
Steve Simon, [log in to unmask], Standard Disclaimer.
Ask Professor Mean: http://www.cmh.edu/stats/profmean.htm
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