Hi

I was wondering if anyone could help me with the following. Of 353 detected miRNAs 74 were statistically significant (FDR 10%), if I recall correctly at 10% FDR I should expect 3.53 significant miRNAs, but what is the probability of observing 74 at this threshold. The FDR is calculated using benjamini-hochberg procedure using limma. My supervisor has asked me for this.

Thanks.

You are confusing FDR with p-values. You would expect 10% of the miRNAs to have p < 0.1 if actually there were none significant, but FDRs are different. You will notice that limma gives you both p-value and FDR columns in the output and the FDR values are higher than the p-values.

The question shows that your supervisor is not familiar with false discovery rates or else he or she wouldn't ask this question. Let me just say that FDR is a type of multiple testing correction and the whole point of multiple testing adjustments is that they take into account the fact that you have done 353 tests.

The bottom line is this: if there is actually no DE, then you would expect to find no genes at all with FDR < 10%.

To give a more technical answer, for any cutoff 'q', the probability of getting any genes at all with FDR <  q is less than q if there are actually no DE genes.