Q-values are the name given to the adjusted p-values found using an optimised FDR approach.
The sequential method works like this. If you are comparing three pairs, with .05 as the threshold p value (alpha level) then:
the most significant of the three p values has to be smaller than .05/3 = .017 to be sig
the second most significant p value of the three has to be smaller than .05/2 = .025 to be sig
and the third most significant has to be smaller than .05/1 = .05 to be sig.
False positives skew results. Suppose you are searching for something really rare (1 in a million). Even with a good test, it’s likely that a positive result is really a false positive on somebody in the 999,999.