This probability is essentially 1 when more than 100 tests are conducted with an individual significance level of 0.05. An equivalent way of assessing the magnitude of the problem is that the number of false positive associations that are expected by chance when testing 500,000 null hypotheses, assuming all of the null hypotheses are true, is α × 500,000. For example, this number is 25,000 when α = 0.05. The Bonferroni correction attempts to limit this number by reducing the individual significance of each test so that the overall number of expected false positive associations is 5% of the number of tests that are conducted [48]. In practice, the Bonferroni correction consists of dividing the usual significance level by the number of tests that are conducted and requires dramatic P-values < 10−6 or smaller to meet genome-wide significance [47]. Figure 5 shows an example taken from a study of the response of fetal hemoglobin to treatment with hydroxyurea in patients with in sickle cell anemia [87].
