(i) Under the assumptions of Theorem 9.1.1, suppose also that the pvalues are mutually independent. Show that the Sidák procedure which rejects any Hi for which pˆi < c(α,s) = 1 − (1 − α)1/s controls the FWER at level α.

(ii) Compare α/s with c(α,s) and show lim s→∞

c(α,s)

(α/s) = − log(1 − α)

α .

For α = .05, this limiting value to 3 decimals is 1.026, so the increase in cutoff value is not substantial.

(iii) Derive the adjusted p-values for Sidák’s method.