This is one of the topics in Meta Analysis and perhaps has several good
sources. Here's a relevant wiki page
http://en.wikipedia.org/wiki/Fisher%27s_methodNagaraj
On Sun, January 11, 2015 8:32 pm, Michael Morton via American Statistical
Association wrote:
> Please Do Not Forward, use the options to the right to forward or reply.
>
> The product of the two p-values does not correspond to a legitimate way to
> directly combine the two p-values. If it were the correct approach, then
> imagine an extension of the approach to 5 experiments each of which with
> p=0.5 (i.e., absolutely no indication that the null hypothesis is false).
> By the obvious extension of the hypothesized approach
> pcombined=0.5^5=0.031<0.05. I.e., if you were to combine a series of
> experiments in the described manner, the p-values would all be <1 and the
> product of enough of them would eventually be less than any chosen alpha.
> I believe the gamma distribution you described is a reasonable approach.
> I don't know if it is optimal in any sense. Mike Morton
>
> ------Original Message------
>
> I am stuck on a probability question. I have run two experiments that
> measure the same thing and have two pvalues. The experiments are
> independent, so I was thinking that the probability of seeing two pvalues
> of the sizes that I found is the product of the two pvalues. But minus
> the log of the product of two uniform random variables, which pvalues are
> under the null hypothesis, is distributed gamma(2,1), which gives a larger
> value pvalue than the product of the pvalues. What am I not seeing?
>
>
> -------------------------------------------
> Margot Tollefson
> Consultant
> Vanward Statistics
> -------------------------------------------
>
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Nagaraj K. Neerchal, PhD.
Professor of Statistics
Chair, Dept of Math and Stat
Director, Center for Interdisciplinary Research and Consulting
UMBC, Baltimore, MD 21250
Skill in Action is Yoga. (BG 2:50)
------Original Message------
The product of the two p-values does not correspond to a legitimate way to directly combine the two p-values.
If it were the correct approach, then imagine an extension of the approach to 5 experiments each of which with p=0.5 (i.e., absolutely no indication that the null hypothesis is false). By the obvious extension of the hypothesized approach pcombined=0.5^5=0.031<0.05. I.e., if you were to combine a series of experiments in the described manner, the p-values would all be <1 and the product of enough of them would eventually be less than any chosen alpha.
I believe the gamma distribution you described is a reasonable approach. I don't know if it is optimal in any sense.
Mike Morton