Two (k + 1)-Decision Selection Procedures for Comparing k Normal Means with a Specified Standard

Abstract

The problem of comparing k normal means with a specified (absolute) standard is considered. A single-stage and a two-stage (k + 1)-decision procedure are proposed for the cases of common known variance and common unknown variance, respectively. The procedures guarantee that (1) with probability at least P ₀* (specified), no population is selected when the largest population mean is sufficiently less than the standard, and (2) with probability at least P ₁* (specified), the population with the largest population mean is selected when that mean is sufficiently greater than its closest competitor and the standard. Tables to implement the procedures are provided. Applications and generalizations are described.

Key Words:

• Ranking procedures
• Selection procedures
• Two-stage procedures
• Comparisons with specified standard
• Indifference-zone approach
• Sampling plans