I've been trying to clarify for myself how to interpret the p values produced by p.adjust with method="fdr/BH".
I'm aware of this question: https://stackoverflow.com/questions/10323817/r-unexpected-results-from-p-adjust-fdr and Multiple hypothesis testing with FDR in R – FDRtool and p.adjust and other similar discussions online, e.g. https://support.bioconductor.org/p/49864/
However, from this it's not clear how to interpret the values produced. It seems like the values this method produces are not really probabilities anymore – as are the case with other 'adjusted' p values, e.g. via Holm method. Rather, it's that if choose to reject null hypotheses where the p_fdr < X, then we are maintaining a false discovery rate < X. Is this the correct interpretation?
Best Answer
By my understanding, the question is about what these corrected p-values actually mean. It would be nice to have, like in a case of testing a single hypothesis, a straight forward meaning such as the probability of observing a given outcome assuming that the null hypothesis is true.
I believe that you are correct in your assertions. In case of the BH correction and other corrections based on controlling the False Discovery Rate , correcting the p-values is just a construct to control the FDR. The same way other methods based on FWER control only serve that purpose and p-values loose their original meaning.
I would argue that the process of making and reporting the correction is here out of habit/ for consistency. It is simple for people to interpret a test result based on a p-value and this way they can keep the way of evaluating statistical significance and make a good judgment.