Multiple hypothesis correction stems from the single hypothesis testing idea that if I perform a statistical test (e.g. t-test or Fischer ratio) I decide before doing the analysis what level of error, due to random fluctuation, I am willing to accept. This defines the probability that I will be wrong, or falsely report a change in a chemical as significant when I compare its concentration from one sample to another. If I accept a 5% false positive rate, but then measure 1000 chemicals at once, statistically I am saying that I will be wrong 50 times (5% of 1000). Multiple hypothesis correction and modeling the distribution of non-changes lets me improve this false positive rate, so I am not wrong as many times.
Parsons BA, Marney LC, Siegler WC, Hoggard JC, Wright BW, Synovec RE.
Anal Chem. 2015 Apr 7;87(7):3812-9. doi: 10.1021/ac504472s. Epub 2015 Mar 26.