So i am performing correlation test (pearson) on 500 genes. and getting the r value and p value. In total we get 500*499/2=124750 tests.
I know next step is to perform multiple comparaison check using FDR or Bonferroni procedures. lets say we have chosen FDR for getting adjusted p value.
My question is if we first filter the comparisons based on a specific r value like 0.4. say we have now filtered 1000 comparisons out because the absolute r value was greater than 0.4. Now we run fdr for multiple comparisons. then it is going to use 1000 p values only of course. Are we being biased here? can we do this actually? because actually we performed 124750 tests and I am not sure if i am going the right way?
The method you propose would certainly be unusual, and in some way defeats the point of using FDR. With this many tests, you may want to simply use no correction for multiple hypotheses, and accept that some portion of the correlations you've identified as significant are so just by chance. This makes sense in a screening situation, since likely you want to err on the side of including possible correlations and not worry too much about false positives. By the way, if the sample sizes are all the same, there will be a r value that corresponds to the alpha value of interest (say 0.05). See, e.g.: http://www.webassign.net/bbunderstat9/10-table-06.gif .
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