Thank you, Peter. They are empirical quantities, that's why I felt confused as being requested to give the power of my test. Could you please clarify the reason why power calculations are not fit for empirical quantities? So that I can defend my test for such request.

BTW, the correlation of the two samples is -0.053.

Thanks,
Tianchan

From: Peter Dalgaard-2 [via R] [mailto:ml-node+s789695n3815852h43@n4.nabble.com]
Sent: Thursday, September 15, 2011 11:04 AM
To: Tianchan Niu
Subject: Re: How to compute the power of a wilcoxon test?


On Sep 15, 2011, at 15:47 , tn85 wrote:

> Hello All,
>
> I posted a similar question before, but the direction was driven to whether
> my case is suitable for a wilcoxon test. After research about the
> appropriateness, I am pretty sure that a wilcoxon test is the right tool for
> my case. But how to compute the power of the test is still an unanswered
> question bothering me.
>
> The basic stats of my two paired samples are:
> mean1 = 0.0032,   sd1 = 0.012
> mean2 = 0.00042, sd2 = 0.0016
> sample size = 366
>
> Could anyone help? Thank you in advance.

Thing is, you can't really do that. Nonparametic tests are only distribution-free under the null hypothesis. For power, you need the distribution of the test statistic under the alternative.

First: Do you really mean "paired"? If so, there would seem to be some information missing, namely the magnitude of the correlation. Also, do you really mean that the sd's differ by a factor of 10?? (And, if those are empirical quantities, don't do power calculations at all).

Assuming that you have two independent samples of size 366, and parameters as above, you might do

> pval <- replicate(1000, wilcox.test(rnorm(366,.0032,.012), rnorm(366,.00042,.0016))$p.value)
> summary(pval)
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max.
0.0000000 0.0000004 0.0000185 0.0064520 0.0003877 0.8997000
> sum(pval < .05)
[1] 979

suggesting a power of around 98%. Adjust as necessary.

>
> --
> View this message in context: http://r.789695.n4.nabble.com/How-to-compute-the-power-of-a-wilcoxon-test-tp3815616p3815616.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> [hidden email]</user/SendEmail.jtp?type=node&node=3815852&i=0> 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.

--
Peter Dalgaard, Professor
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: [hidden email]</user/SendEmail.jtp?type=node&node=3815852&i=1>  Priv: [hidden email]</user/SendEmail.jtp?type=node&node=3815852&i=2>

______________________________________________
[hidden email]</user/SendEmail.jtp?type=node&node=3815852&i=3> 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.

________________________________
If you reply to this email, your message will be added to the discussion below:
http://r.789695.n4.nabble.com/How-to-compute-the-power-of-a-wilcoxon-test-tp3815616p3815852.html
To unsubscribe from How to compute the power of a wilcoxon test?, click here<http://r.789695.n4.nabble.com/template/NamlServlet.jtp?macro=unsubscribe_by_code&node=3815616&code=bml1QGlzaXMuZ2VvcmdldG93bi5lZHV8MzgxNTYxNnwtMTI4NTg5ODAwMQ==>.


--
View this message in context: http://r.789695.n4.nabble.com/How-to-compute-the-power-of-a-wilcoxon-test-tp3815616p3815893.html
Sent from the R help mailing list archive at Nabble.com.
	[[alternative HTML version deleted]]

