p-value, q-value (FDR)

http://www.nonlinear.com/support/progenesis/samespots/faq/pq-values.aspx

For example, if there are 200 spots on a gel and we apply an ANOVA or t-test to each, then we would expect to get 10 false positives by chance alone. This is known as the multiple testing problem.

Another way to look at the difference is that a p-value of 0.05 implies that 5% of all tests will result in false positives. An FDR adjusted p-value (or q-value) of 0.05 implies that 5% of significant tests will result in false positives. The latter is clearly a far smaller quantity.

a p-value of 0.01 implies a 1% chance of false positives

To interpret the q-values, you need to look at the ordered list of q-values. There are 839 spots in this experiment. If we take spot 52 as an example, we see that it has a p-value of 0.01 and a q-value of 0.0141. Recall that a p-value of 0.01 implies a 1% chance of false positives, and so with 839 spots, we expect between 8 or 9 false positives, on average, i.e. 839*0.01 = 8.39. In this experiment, there are 52 spots with a value of 0.01 or less, and so 8 or 9 of these will be false positives. On the other hand, the q-value is a little greater at 0.0141, which means we should expect 1.41% of all the spots with q-value less than this to be false positives. This is a much better situation. We know that 52 spots have a q-value less than 0.0141 and so we should expect 52*0.0141 = 0.7332 false positives, i.e. less than one false positive. Just to reiterate, false positives according to p-values take all 839 values into account when determining how many false positives we should expect to see while q-values take into account only those tests with q-values less the threshold we choose.