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I am reading paper by Benjamini and Yekutieli (2001) on controlling FDR under dependence. My question is to figure out, in practical applications, whether the PRDS property is fulfilled in a given application, or not. Specifically:

  1. for example, I am running a series of t-tests on a number of variables. When do I run into the danger of violating the PRDS property?
  2. What happens to the FDR when I do?

I get the maths in the paper, technically, but I don't get a feeling for it.

Intuitively, I understand the PRDS property as not having a negative interaction between the p-values; if one test gives a p value rejecting the given hypothesis, then another test is not less likely to reject the hypothesis.

As a practical example, I imagine the following situation violates PRDS: two genes react to a treatment; however, if gene A is expressed, it prevents regulation of gene B, and vice versa. That is, it is unlikely that $H_A$ (gene A is not regulated) wis rejected and at the same time $H_B$ (gene B is not regulated) is rejected. $Pr(p_a \le q | p_b \le q) < Pr(p_a \le q | p_b > q)$.

Does this have any connection to reality?

January
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    +1. Related: http://stats.stackexchange.com/questions/111756 (there was a high bounty on that Q until a day or two ago). See my answer and also user43849's answer. – amoeba Mar 31 '17 at 09:45
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    Thanks, that is a great thread. Should have mentioned it in my question, and actually, my question was prompted by me being *still* quite dim on the two specific (hopefully specific) points after reading the responses. – January Mar 31 '17 at 09:54
  • @amoeba I was never satisfied with my answer in that thread and i think that yours should be marked as the accepted one, since I am still quite foggy on the details myself. Last summer I was working on a mathematical extension to FDR and still got quite confused, so I think the "big picture" approach is the most useful for those who are applying it. – Chris C Apr 01 '17 at 23:36

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