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I need a good reference for the methods and/or the difficulties that arise when attempting such a combination.

I've found Loughin, TM, A systematic comparison of methods for combining p-values from independent tests, Computational Statistics & Data Analysis (2004) 47(3):467–485, for example. Is there a better/more precise one?

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  • $\begingroup$ Is this for multiple test correction or something else? $\endgroup$
    – Bitwise
    Commented Sep 27, 2012 at 15:33
  • $\begingroup$ It's pretty long to explain but basically I have 3 p-values obtained through the same process (the kde.test function of R's ks package cran.r-project.org/web/packages/ks/ks.pdf) but applied to three different sets of 2 columns each (all 6 columns are linked because they belong to the same 'observation') $\endgroup$
    – Gabriel
    Commented Sep 27, 2012 at 15:44
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    $\begingroup$ It sounds like you want to do a meta analysis. Fisher's combination test is one method for combining p-values. There are many books on meta analysis that could be useful to you. I will give you an answer with links to several books if you tell me I am on the right track. $\endgroup$
    – Michael R. Chernick
    Commented Sep 27, 2012 at 20:42
  • $\begingroup$ Well I'm not a statistician so I have no idea what a meta analysis is :) (sorry) I actually do not want to perform such a combination, I just need references for the various methods of doing so and/or its difficulties (like the article I presented, to which I have no access sadly) $\endgroup$
    – Gabriel
    Commented Sep 27, 2012 at 20:59
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    $\begingroup$ I guess I don't know why you are interested in the article. They talk in the abstract about combining p-values for a combined hypothesis. If you are combining independent data set to reach strong conclusion because of the increased sample size. That is all that us meant by a meta analysis. One way to do meta analysis (also called data synthesis) is to combined p-values from independent tests of the individual data sets. Fisher's combination test is one of many that could be tried. Apparently the paper compares 6 such methods. Meta analysis is in the list of key words in the abstract. $\endgroup$
    – Michael R. Chernick
    Commented Sep 28, 2012 at 3:35

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One useful entry into this literature is an annotated bibliography by R D Cousins which considers most of the well-known methods for combining $p$-values and which is freely available from arXiv.

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    $\begingroup$ (+1) What is the benefit of using BibTeX on this forum? Presumably that one can copy-paste it into one's .bib file. How often do you think this is happening? I would guess that many many more people would find a hyper-link more useful; my own preference is to put a hyperlink on a short citation, e.g. Cousins, 2008, Annotated bibliography of some papers on combining significances or $p$-values or something like that. Perhaps a BibTeX citation can be provided extra in the end of an answer. I am saying this because this is not the first time you are using BibTeX and I am always wondering... $\endgroup$
    – amoeba
    Commented Aug 21, 2016 at 21:24
  • $\begingroup$ Thank you for the article mdewey. I edited your answer to add a link since I also wondered (as @amoeba did) why you left the bibtex instead (or without) the link. $\endgroup$
    – Gabriel
    Commented Aug 21, 2016 at 23:55
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    $\begingroup$ I would suggest to follow the advice of @amoeba and not embed BibTex for citations here. Assuming you actually do want a BibTeX citation to be available, you could cite via a Google Scholar hyperlink. If you click that link, then click Cite, then BibTex, you can get the same result. $\endgroup$
    – GeoMatt22
    Commented Aug 22, 2016 at 4:34
  • $\begingroup$ @amoeba (and other commenters) apologies, I had no idea I was going to perturb so many people. I have removed the formatting. $\endgroup$
    – mdewey
    Commented Aug 23, 2016 at 9:00

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