Multiple tests with discrete distributions

We review special issues in multiplicity adjustment where the sampling distributions are discrete. These include (1) incorporating discreteness into the multiplicity adjustments, (2) incorporating correlations versus using Bonferroni or independence-based approximations, and (3) using discrete tails in two-sided tests. Incorporating discrete characteristics can greatly improve the power of the tests that maintain a given familywise error rate, Use of correlations also can improve the power, but it is shown that independence-based multiplicity adjustment is not necessarily a conservative procedure, Exact methods that incorporate discreteness and correlations are generally recommended.