Choosing the Q-value in the Benjamini-Hochberg procedure to control false discovery rate I have done 350 independent tests. I need to correct them for the multiple comparisons. I am using the Benjamini-Hochberg (BH) procedure to control FDR. However choosing the Q (the level at which we want to control the FDR) beforehand could be restrictive (say e.g. I find no discovery for Q=0.05 and 40 for Q=0.1: it would be nice tell something about those 36 supposedly true discoveries made with Q=0.1 instead of reporting no discovery).
I have two questions:


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*If I'm doing an exploratory analysis, is it a wrong procedure to have a look at the number of discoveries for varying levels of Q instead of fixing it a priori? If I then need to choose just one Q value I may choose, e.g. the more conservative one that still gives me some true discovery or the one that gives the maximum number of true discovery, etc.

*Am I doing again multiple comparisons in checking different levels of Q? I don't think so since I'm actually not testing new hypothesis but just controlling the FDR to different levels: the original hypothesis keep untouched, what is changed are the criteria in the BH procedure.
 A: Yes, these things are done quite often, at least in genetics. To address your specific points:


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*This is quite commonly done, and I have personally reported results this way. Though, make sure to make it clear at what level of FDR you are reporting. Think of it akin to "marginal" significance; people may find it interesting, but they have to know what they're looking at.

*No, you would not have to do multiple corrections for this, as you mentioned you're simply manipulating the $P$-values in a different way and not changing anything. 
I would also look further into what Dr. Motulsky has mentioned above, if I were you. Reporting the $q$ value is a very common and useful metric.
A: An alternative you might find useful is to report -- for each comparison -- the q value. The q value (lower case) is the Q value (upper case) at which that particular comparison would be right at the border of being a discovery. You can then report the q value for each comparison, rather than just a list of which comparisons are "discoveries" using an arbitrary value of Q. 
A: There's nothing magical about alpha=.05. 
I see nothing wrong with going with alpha/q=.10. I would also report confidence intervals (and adjust these as well). 
Alternatively, use a Bayesian model with priors up to the job of wacking down false positives (horseshoe, laplace)
