We formulated the null hypothesis that, for a subset of participants with bipolar disorder v. controls, the number of hits we observed follows the distribution expected by chance. This hypothesis assumes that the bipolar disorder sample is genetically homogeneous (i.e. minimal variation between individuals), and that the subset of participants with bipolar disorder under investigation is a truly random selection from the full bipolar disorder sample of 1868 individuals. It is important to note that the null hypothesis here is that the genetic effects within the sample with bipolar disorder are homogeneous in the sense that they do not vary according to diagnostic subset. It is not an assumption that there are no genetic effects (i.e. we do not assume that there are no differences between those with bipolar disorder and controls). The one-sided alternative is that we observed more hits than would be expected by chance, i.e. the total sample with bipolar disorder is genetically heterogeneous. Under the alternative hypothesis, the subset under investigation is postulated to have properties that facilitate the detection of genetic effects. Such properties include
