Two-Stage Procedures for Multiple Comparisons with a Control

Abstract

SYNOPTIC ABSTRACTGiven p + 1 populations πi which are distributed N(μi, σi2), comparisons are made between π0 and π1, …, πp by constructing joint confidence intervals, both one and two-sided, for the differences μi – μ0, based on two-stage sampling, the first stage being used to estimate the σi2. Such intervals are used to solve selection problems. It is shown that, for the case of symmetric two-sided intervals, procedures based on sample means are always preferred to those based on other linear combinations of observations, designed to control the confidence coefficient. For other intervals the P* requirement may not be met (using sample means), but an investigation of confidence conditional on first stage sample variances indicates that sample means may still be preferable. A hybrid procedure where sample means are used except for the control population has advantages for one sided intervals.