This stems from the fact that Bonferroni correction is effectively designed to prevent any false positives, but FDR control is designed to prevent a large proportion of false positives and can afford to be less conservative. The advantage of FDR over Bonferroni correction is that FDR is generally more powerful (i.e., better at detecting true effects) than Bonferroni. FDR control, like Bonferroni correction, reduces the probability of false positive results by using a more conservative alpha level for each test.

However, if one were to perform 10 tests using an alpha level of 5% for each test, there is a 40% chance of one or more false positive results (again assuming that the factor being analyzed has no effect). For example, if one were to perform a single test using an alpha level of 5% and there truly is no effect of the factor being tested, there is only a 5% chance of a false positive result. As you may recall from your introductory statistics course, when you perform multiple statistical tests, the probability of false positive results rapidly increases. FDR is simply the mean proportion of statistically significant test results that are really false positives. Massive increases in the amount of data scientists are able to acquire and analyze over the past two decades have driven the development of new statistical tools that can better deal with the challenges of “big data.” One such set of tools is ways of controlling the “false discovery rate” (FDR) in a set of statistical tests.

Sigmaplot 11 do not test bonferroni