Hi friends, I am facing a problem understanding the concept of FDR or False Discovery Rate in Multiple Hypothesis Testing. May be the question is silly, please try to bear with me. Actually, when we are talking about P-Value for a single hypothesis test, a value below 0.05 is considered as 5% result is false positive regarding that particular hypothesis. So far, no problem. But, whenever there is suppose 20,000 tests why there will be 5% of the tests is false positive? The P-value we are talking about is for a single hypothesis, why we are connecting that with 20,000 tests? Here, each of the hypothesis is a separate entity, they are independent of each other. Then 5% of 30,000 will be false positive?

Actually even this is not strictly correct. P-value < 0.05 does not tell you almost anything about the probability of the hypothesis different from null.

I provide a Bayesian view - there are other views (e.g. likelihood) so without informative priors (like "toss-up" here) - and it sill is not interpreted as the probability of an alternative hypothesis.

You may start reading from here: http://daniellakens.blogspot.com/2015/09/how-can-p-005-lead-to-wrong-conclusions.html

Very nice slide, thanks! It implicates that as a scientist you should think about the plausibility of your new hypotheses

beforeyou obtain new data. But this is difficult, of course...with FDR correction and many tests it is magically resolved because of magic (I've asked at stats.stackexchange and this was the answer) - but for small number of tests sure, prior beliefs and expected effect size are important...

(the full answer here https://stats.stackexchange.com/questions/402176/how-is-it-possible-to-control-false-discovery-rate-fdr-without-knowing-the-pow )

Hi, I am trying to understand FDR in the following way. Please let me know whether my understanding right or wrong. Suppose, 100 people are tossing a biased coin (95% probability of Head and 5% probability of Tail). When each person is tossing, most of the time he will get Head, rarely Tail. But, when 100 people will toss, definitely any 5 people will get Tail. These 5 people are like FDR in our case, Right? This 5% will become a huge number when we are testing 1000 genes, i.e., 1000 people are tossing? Please let me know if my understanding is true or not. Thanks

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