# [R] Bootstrap or Wilcoxons' test?

Daniel Malter daniel at umd.edu
Sat Feb 14 04:16:54 CET 2009

```
Hi Charlotta, to be more constructive toward your goal. If you bootstrap the
regression when the regression is ill-specified, the bootstrap may not help
you. Further, a test as "difficult" as a regression does not seem to be
(approxiamately) normal for both groups and if variances are equal or a
Wilcoxon test if your dependent variable is not normal should do.

The bootstrap should be very powerful if you do NOT perform it on the
regression (again, bootstrapping the regression may just mean to do the
wrong thing over and over again, which is no improvement). Just bootstrap
sample means for the two groups and compare them appropriately (see:
http://www.stat.berkeley.edu/users/rodwong/Stat131a/boot_diff_twomeans.pdf
). Otherwise, rely on the result of the Wilcoxon test as it is likely more
appropriate if your dependent variable is not normal in the two groups.

Daniel

-------------------------
cuncta stricte discussurus
-------------------------

-----Ursprüngliche Nachricht-----
Von: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] Im
Auftrag von David Winsemius
Gesendet: Friday, February 13, 2009 9:19 PM
An: Murray Cooper
Cc: r-help at r-project.org
Betreff: Re: [R] Bootstrap or Wilcoxons' test?

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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>>
>
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