|Title||Improving Holm's procedure using pairwise dependencies|
|Year of Publication||2014|
For Holm's multiple testing procedure controlling the familywise error rate (FWER), Seneta and Chen (2005) sharpened its critical values providing tighter control of the FWER by incorporating pairwise dependencies among the underlying p-values into the derivation of these critical values. The second-order Bonferroni approximation for the distribution of the minimum of a set of null p-values given by the Kounias (1968) inequality was used in the process. We propose further sharpening of the critical values when the distribution functions of the pairwise maximum p-values are convex, a property shared by p-values arising in many applications of Holm's method. These newer critical values are uniformly larger than Seneta-Chen's, significantly so under high pairwise positive dependencies, as numerically seen, and maintain a tighter control over the FWER. These critical values are further improved under exchangeable null p-values with modest additional computation.