Consider testing H1,..., Hs, with Hi specifying i = 0 against twosided alternatives. In order to control

Consider testing H1,..., Hs, with Hi specifying θi = 0 against twosided alternatives. In order to control the mixed directional familywise error rate in

(9.15), a simple device it to consider the 2s one-sided hypotheses defined as follows.

For i = 1,...,s, let Hi be the null hypothesis θi ≤ 0 (tested against θi > 0, and for j = i + s, let H j be the null hypothesis θi ≥ 0 (tested against θi < 0). Explain how, if you apply the Holm method to the 2s hypotheses, one gets an improvement over Bonferroni. Compare with the method which applies Holm to the original hypotheses.

Section9.2