[R] Bootstrap or Wilcoxons' test?

[Murray Cooper]

First of all, sorry for my typing mistakes.

Second, the WRS test is most certainly not a test for unequal medians.
Although under specified models it would be. Just as under specified
models it can be a test for other measures of location. Perhaps I did not
word my explanation correctly, but I did not mean to imply that it would
be a test of equality of variance. It is plain and simple a test for the 
equality
of distributions. When the results of a properly applied parametric test do
not agree with the WRS, it is usually do to a difference in the empirical
density function of the two samples.

Murray M Cooper, Ph.D.
Richland Statistics
9800 N 24th St
Richland, MI, USA 49083
Mail: richstat at earthlink.net

----- Original Message ----- 
From: "David Winsemius" <dwinsemius at comcast.net>
To: "Murray Cooper" <myrmail at earthlink.net>
Cc: "Charlotta Rylander" <zcr at nilu.no>; <r-help at r-project.org>
Sent: Friday, February 13, 2009 9:19 PM
Subject: 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".
>> 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
>>>
>>>
>>> [[alternative HTML version deleted]]
>>>
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>>>
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide 
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>
>