Decision Procedures for Selecting One of Two Normal Population Variances

• Published in: Sequential analysis Vol. 28; no. 1; pp. 82 - 91
• Main Author: Mady, Afaf M.
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 26.01.2009
• Subjects: Bayesian approach; Maximin approach; Minimax approach; Population variances
• ISSN: 0747-4946; 1532-4176
• DOI: 10.1080/07474940802619378

The populations are usually compared with respect to their means to establish superiority of one population over the other or to check if the two populations are equivalent. In this paper we shall compare two normal populations with respect to their variances. The two populations might be two different lots of ammunition and might be the (population) target dispersion of the ith lot, or the two populations might be two different measuring instruments and might be the (population) variance of measurement of the ith instrument. This variance, which characterizes the reproducibility of repeated measurements of the same quantity, can be used as an index of the precision of the measuring instrument. There has been only one paper on this subject (Bechhofer and Sobel, 1954 ). In this paper we introduce a new approach for choosing between two normal population variances. When a choice has to be made in favor of one of two populations, the cost of sampling (experimenting) in order to obtain information on which to base the decision must be balanced against the cost of making the wrong choice. The cost of sampling is assumed to be the cost of an incorrect choice for half the sample (which is divided between the two populations). Fixed sample size and sequential experiments are considered. Bayesian approaches are used for determining the optimal size of a fixed sample experiment and the optimal position of the boundaries of a sequential experiment.