http://www.aaos.org/news/aaosnow/apr12/research7.asp For example, a researcher is testing 20 hypotheses simultaneously, with a critical P value of 0.05. In this case, the following would be true: P (at least one significant result) = 1 – P (no significant results) P (at least one significant result) = 1 – (1-0.05) 20 P (at least one significant result) = 0.64 Thus, performing 20 tests on a data set yields a 64 percent chance of identifying at least one significant result , even if all of the tests are actually not significant . Therefore, while a given α may be appropriate for each individual comparison, it may not be appropriate for the set of all comparisons. http://www.fon.hum.uva.nl/praat/manual/Bonferroni_correction.html In general, if we have k independent significance tests at the α level, the probability p that we will get no significant differences in all these tests is simply the product of the individual probabilities: (1 - α) k . For exampl