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Correction for multiple tests (a lot of...)


I will start by saying that I am novice in Bayesian statistics, so I am really sorry if I mixed up some notion. I’m currently doing a research on the effect of heat on some bone microstructure. I want to test if there is any difference on the size of structure when exposed to heat. I have 45 bone, and each of these 45 bones has N=120 non-heated microstructure and N=120 heated microstructure, approximately. I wanted to do a Bayesian Mann-Whitney U test (in JASP) for non-heated structure vs heated structure of my 45 bones and for 5 variables (area, diameter, circularity, etc.), but I’m concerned about the multiplicity of tests and how to handle it.

In what I’ve seen so far, a correction can be applied by changing prior odds and then multiplying those with BF10 to get corrected posterior odd. My first question is: How important are the posterior odds in the interpretation of a Bayesian Mann-Whitney U test, since they are not reported in JASP for individual test (only with a post-hoc ANOVA) and for what I understand, BF are not concerned with the correction. With that many tests, I will certainly get a very important correction that will favor the null hypothesis. Are they any limits to the correction?

I choose to test each bone separately because bone microstructure is really variable across individuals and bone type. My goal by doing so many tests is to see if there is a global tendency and I’m worried that I would lose all evidence of an effect if I applied a correction. My argument for not doing a correction is : with that many tests, even if I have some false positive, my goal is to see the global tendency and those would not matter as much as if I would rely on each individual test alone to answer my question.  Does that make any sense? I’m kind of lost here and any help would be very much appreciated. 

Thanks a lot




  • Hi Fred,

    Well, this is indeed a difficult conceptual issue. The Bayesian correction for multiplicity is in the prior odds (not in the BF). When you specify these prior odds subjectively, based on background knowledge, separately for each test, then there is no multiplicity issue. This approach is advocated for instance by Zoltan Dienes (see his 2008 book and this paper:

    On the other hand, you could include an "objective" correction; some of the relevant material is summarized in this master thesis:

    You could first report the BFs and then discuss the issue of multiple comparisons explicitly...



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