I must disagree with both this general characterization of the Wilcoxon
test and with the specific example offered. First, we ought to spell the
author's correctly and then clarify that it is the Wilcoxon rank-sum test
that is being considered. Next, the WRS test is a test for differences in
the location parameter of independent samples conditional on the samples
having been drawn from the same distribution. The WRS test would have no
discriminatory power for samples drawn from the same distribution having
equal location parameters but only different with respect to unequal
dispersion. Look at the formula, for Pete's sake. It summarizes
differences in ranking, so it is in fact designed NOT to be sensitive to
the spread of the values in the sample. It would have no power, for
instance, to test the variances of two samples, both with a mean of 0, and
one having a variance of 1 with the other having a variance of 3. One can
think of the WRS as a test for unequal medians.
--
David Winsemius, MD. MPH
Heritage Laboratories
On Feb 13, 2009, at 7:48 PM, Murray Cooper wrote:
Charlotta,
I'm not sure what you mean when you say simple linear
regression. From your description you have two groups
of people, for which you recorded contaminant concentration.
Thus, I would think you would do something like a t-test to
compare the mean concentration level. Where does the
regression part come in? What are you regressing?
As for the Wilcoxnin test, it is often thought of as a
nonparametric t-test equivalent. This is only true if the
observations were drawn, from a population with the
same probability distribution. The null hypothesis of
the Wilcoxin test is actually "the observations were
drawn, from the same probability distribution".
Thus if your two samples had say different variances,
there means could be the same, but since the variances
are different, the Wilcoxin could give you a significant result.
Don't know if this all makes sense, but if you have more
questions, please e-mail your data and a more detailed
description of what analysis you used and I'd be happy
to try and help out.
Murray M Cooper, Ph.D.
Richland Statistics
9800 N 24th St
Richland, MI, USA 49083
Mail: richstat at earthlink.net
----- Original Message ----- From: "Charlotta Rylander" <zcr at nilu.no>
To: <r-help at r-project.org>
Sent: Friday, February 13, 2009 3:24 AM
Subject: [R] Bootstrap or Wilcoxons' test?
Hi!
I'm comparing the differences in contaminant concentration between 2
different groups of people ( N=36, N=37). When using a simple linear
regression model I found no differences between groups, but when
evaluating
the diagnostic plots of the residuals I found my independent variable
to
have deviations from normality (even after log transformation).
Therefore I
have used bootstrap on the regression parameters ( R= 1000 & R=10000)
and
this confirms my results , i.e., no differences between groups ( and
the
distribution is log-normal). However, when using wilcoxons' rank sum
test on
the same data set I find differences between groups.
Should I trust the results from bootstrapping or from wilcoxons' test?
Thanks!
Regards
Lotta Rylander
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