R help - Oct 2013 - Interpreting the result of a Wilcoxon (Mann-Whitney U) test

Hello everyone,

I'm having some trouble interpreting the results of a Wilcoxon
(Mann-Whitney U) test. Hope you can help.

This is the R script that I am running:

a <- c(1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 5, 1, 1, 1, 3, 1, 1,
1, 1, 1, 1, 3, 1, 1)
b <- c(1, 2, 1, 1, 2, 3, 2, 2, 1, 2, 1, 1, 1, 2)
wilcox.test(a, b, alternative="t", mu=0, exact=FALSE, paired=FALSE) 
#1st
wilcox.test(a, b, alternative="l", mu=0, exact=FALSE, paired=FALSE) 
#2nd
wilcox.test(a, b, alternative="g", mu=0, exact=FALSE, paired=FALSE) 
#3rd

... and it's returning:

Wilcoxon rank sum test with continuity correction data:  a and b
W = 145, p-value = 0.08969
alternative hypothesis: true location shift is not equal to 0

Wilcoxon rank sum test with continuity correction data:  a and b
W = 145, p-value = 0.04485
alternative hypothesis: true location shift is less than 0

Wilcoxon rank sum test with continuity correction data:  a and b
W = 145, p-value = 0.9582
alternative hypothesis: true location shift is greater than 0

The null hypothesis is that the populations are equivalent (mu=0). The
alternative hypothesis are that they differ, with the 2nd and 3rd runs
of the test above considering respectively that a<b and b>a. Plus, I'm
considering an alfa of 0.05.

My issue is that from the first run I could not conclude that there
was a difference between the two populations (0.08969>0.05), but the
second run leads me to think that a<b (because 0.04485<0.05).

Am I misinterpreting the results?

Thanks!

Filipe

Filipe,

When you chose a different alternative argument you are asking a different
null hypothesis.  You are looking at a two-tailed, lesser than, and greater
than hypotheses.  Which one you chose is dependent upon your initial
question.  Are you asking generically if your two populations (a and b) are
different?  Are you asking if a > b or a < b?  It is my understanding that
you shouldn't just do all of them to see which fits, it depends on what you
initially were intending to test.  If you can answer that question then you
can determine if your appropriate run is significant.

Regards,

-- 
Charles Determan
Integrated Biosciences PhD Candidate
University of Minnesota


On Wed, Oct 2, 2013 at 10:33 AM, Filipe Correia <fcorreia@gmail.com>
wrote:
> Hello everyone,
>
> I'm having some trouble interpreting the results of a Wilcoxon
> (Mann-Whitney U) test. Hope you can help.
>
> This is the R script that I am running:
>
> a <- c(1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 5, 1, 1, 1, 3, 1, 1,
> 1, 1, 1, 1, 3, 1, 1)
> b <- c(1, 2, 1, 1, 2, 3, 2, 2, 1, 2, 1, 1, 1, 2)
> wilcox.test(a, b, alternative="t", mu=0, exact=FALSE,
paired=FALSE)  #1st
> wilcox.test(a, b, alternative="l", mu=0, exact=FALSE,
paired=FALSE)  #2nd
> wilcox.test(a, b, alternative="g", mu=0, exact=FALSE,
paired=FALSE)  #3rd
>
> ... and it's returning:
>
> Wilcoxon rank sum test with continuity correction data:  a and b
> W = 145, p-value = 0.08969
> alternative hypothesis: true location shift is not equal to 0
>
> Wilcoxon rank sum test with continuity correction data:  a and b
> W = 145, p-value = 0.04485
> alternative hypothesis: true location shift is less than 0
>
> Wilcoxon rank sum test with continuity correction data:  a and b
> W = 145, p-value = 0.9582
> alternative hypothesis: true location shift is greater than 0
>
> The null hypothesis is that the populations are equivalent (mu=0). The
> alternative hypothesis are that they differ, with the 2nd and 3rd runs
> of the test above considering respectively that a<b and b>a. Plus,
I'm
> considering an alfa of 0.05.
>
> My issue is that from the first run I could not conclude that there
> was a difference between the two populations (0.08969>0.05), but the
> second run leads me to think that a<b (because 0.04485<0.05).
>
> Am I misinterpreting the results?
>
> Thanks!
>
> Filipe
>
> ______________________________________________
> R-help@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.
>
	[[alternative HTML version deleted]]

On Oct 2, 2013, at 8:33 AM, Filipe Correia wrote:
> Hello everyone,
> 
> I'm having some trouble interpreting the results of a Wilcoxon
> (Mann-Whitney U) test. Hope you can help.
> 
> This is the R script that I am running:
> 
> a <- c(1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 5, 1, 1, 1, 3, 1, 1,
> 1, 1, 1, 1, 3, 1, 1)
> b <- c(1, 2, 1, 1, 2, 3, 2, 2, 1, 2, 1, 1, 1, 2)
> wilcox.test(a, b, alternative="t", mu=0, exact=FALSE,
paired=FALSE)  #1st
> wilcox.test(a, b, alternative="l", mu=0, exact=FALSE,
paired=FALSE)  #2nd
> wilcox.test(a, b, alternative="g", mu=0, exact=FALSE,
paired=FALSE)  #3rd
> 
> ... and it's returning:
> 
> Wilcoxon rank sum test with continuity correction data:  a and b
> W = 145, p-value = 0.08969
> alternative hypothesis: true location shift is not equal to 0
> 
> Wilcoxon rank sum test with continuity correction data:  a and b
> W = 145, p-value = 0.04485
> alternative hypothesis: true location shift is less than 0
> 
> Wilcoxon rank sum test with continuity correction data:  a and b
> W = 145, p-value = 0.9582
> alternative hypothesis: true location shift is greater than 0
> 
> The null hypothesis is that the populations are equivalent (mu=0). The
> alternative hypothesis are that they differ, with the 2nd and 3rd runs
> of the test above considering respectively that a<b and b>a. Plus,
I'm
> considering an alfa of 0.05.
> 
> My issue is that from the first run I could not conclude that there
> was a difference between the two populations (0.08969>0.05), but the
> second run leads me to think that a<b (because 0.04485<0.05).
This is not an appropriate question for R-help. You should ask your statistics
instructor or pose the question in a venue where explanations of purely
statistical problems are on-topic. (Just because you used R to get results that
confused you does not make this an R-help-problem.)
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html

-- 

David Winsemius
Alameda, CA, USA

> I'm having some trouble interpreting the results of a Wilcoxon
> (Mann-Whitney U) test. Hope you can help.
Two-tailed and one tailed tests generally give different p-values, with the
two-tailed p-value twice (one of) the one-tailed values for rather obvious
reasons. You need to sort out which question you wanted the answer to.

Having said that, if a factor of two in the p-value changes your interpretation,
you probably haven't got a really compelling result.

S Ellison


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> -----Original Message-----
> Got it! I agree it should had been more obvious to me... :)
I wouldn't feel too bad about that. I've spent most of the last 25 years
discovering the hard way that statistics is very much a field where things are
'obvious' only _after_ you know the answer...

S



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This email and any attachments are confidential. Any use...{{dropped:8}}

+1

John Kane
Kingston ON Canada

> -----Original Message-----
> From: jim at bitwrit.com.au
> Sent: Sat, 05 Oct 2013 17:16:35 +1000
> To: r-help at r-project.org
> Subject: Re: [R] Interpreting the result of a Wilcoxon (Mann-Whitney U)
> test
> 
> On 10/04/2013 11:34 PM, S Ellison wrote:
>> ...
>  >> Got it! I agree it should had been more obvious to me... :)
>> I wouldn't feel too bad about that. I've spent most of the last
25 years
>> discovering the hard way that statistics is very much a field where
>> things are 'obvious' only _after_ you know the answer...
>> 
> A fortune ("hindsight") if I ever saw one.
> 
> Jim
> 
> ______________________________________________
> 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.
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