[MUSIC] How can you control the false discovery rate? Well the Benjamini-Hochberg Procedure gives you a way to do this, and so here's how it works. You compute the p-value of your hypotheses. And then you sort them in descending order, such that the with the lowest p-value, which are the most likely hypotheses, the ones that are best supportive by the evidence, come first. Okay, and then you apply this condition where the p-value is subject to a more stringent condition than just alpha. Remember alpha is your 0.05, your cut off, and what we're trying to do is correct for the multiple hypothesis testing. So we want a much more stringent alpha. And so that more stringent alpha is this ratio i over m. And so i is just the rank order of the hypothesis you're testing. And m is your total number of hypotheses that you're testing, number of hypotheses. All right and the procedure says, well, find the highest i for which this condition holds, and then reject the null hypotheses for all i lower than that, accept everything up until that point, okay. And so here's what it might look like with 50 and 0.05. I suppose I should put that. So your first hypothesis has to. The first hypothesis is compared with a pretty stringent condition, 1 in 1000. And the second one is double that, and the third one is triple that, and so on, all the way up to the 50th one. Which would be 50 over 50 which is just your original alpha, 0.05, okay? So this is a much tighter condition. And so what they're able to prove is that the under these conditions, following this procedure, the false discovery rate is less than T over m. Times alpha, where if you remember T was the total number of cases where the null hypothesis is true. Okay, so here's what it looks like graphically. The little xs are above this line and the dots are below this line, and the x-axis is rank order. And these are all your 50 hypotheses sorted in increasing p-value. And the line represents that threshold condition. It slopes up with rank order, as we would expect. Here, we would find the highest i for which this condition holds, and accept everything lower than this. And here we had a pretty good run, we accepted 30 out of 50 hypotheses. And notice that these actually are above the line, but we would still accept them. Okay. [MUSIC]