Sample size determination for step-down multiple test procedures: Orthogonal contrasts and comparisons with a control

Abstrucr; We address the problem of sample size determination for step-down multiple comparison procedures (MCP’s) for two nonhierarchical families orthogonal contrasts and comparisons with a control, in order to guarantee a specified requirement on their power. The results for the corresponding single-step MCP’s are obtained as special cases. Numerical calculations of the sample sizes to guarantee a specified power requirement are carried out for the one-sided comparisons with a control problem in selected cases. These calculations show that for the cases considered, about 10% to 20% savings can be achieved in the total sample size by using the step-down MCP of Miller (1966, pp. 85-86) instead of the single-step MCP of Dunnett (1955). The percentage savings increase, as expected, with the number of treatments being compared with the control. In the process of determining the smallest total sample size for each MCP to guarantee the specified power requirement, we also determine the optimum allocation of this sample size among the treatments and the control. We find that the square root allocation rule recommended by Dunnett (1955) provides a reasonable approximation to the optimum allocation for both the MCP’s.