# [R] Bootstrap or Wilcoxons' test?

David Winsemius dwinsemius at comcast.net
Sat Feb 14 03:19:03 CET 2009

```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".
> 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
> 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
>
> ----- 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
>>
>>
>> [[alternative HTML version deleted]]
>>
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>> and provide commented, minimal, self-contained, reproducible code.
>>
>
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