Some Sequential Procedures for Selecting the Better Bernoulli Treatment by Using a Matched Samples Design

Abstract

The problem of selecting the better Bernoulli treatment by using a matched samples design is considered in the framework of the indifference-zone approach. In Tamhane (1980) a fixed sample procedure (FSP) for this problem was proposed. Here three sequential procedures are considered: (a) a curtailed sampling procedure (CSP), (b) a procedure based on the Wald sequential probability ratio test (SPRT), and (c) a procedure based on the 2-SPRT proposed by Lorden (1976). Comparisons are made between these procedures based on their expected total (tied and untied) sample sizes. It is pointed out that the CSP is the only closed procedure (in terms of the total number of observations) among the three. In addition, for any parameter configuration, the CSP is at least as efficient as the FSP, whereas the SPRT and 2-SPRT can be less efficient than the FSP when success probabilities of the treatments are close. Thus the CSP is a useful practical procedure.

Key Words:

• Ranking
• Selection
• Indifference-zone approach
• Curtailed sampling
• Sequential probability ratio test
• 2-Sequential probability ratio test