Author: Bi, Jian¹

Source: British Journal of Mathematical and Statistical Psychology, Volume 60, Number 1, May 2007 , pp. 71-83(13)

Abstract:

Conventional Bayesian analysis for proportions is not appropriate for proportions with a background effect, for example, for the proportion of correct responses in a sensory difference test using a forced-choice method with a guessing probability. The main difficulty is that it is not reasonable to assume that a proportion with a background effect has a beta prior distribution. A generalized posterior distribution for proportions is derived in this paper. It includes the standard beta posterior distribution for a proportion without background effect as a special case. Bayesian inference and Bayesian sample size determination for proportions based on the generalized posterior distribution are discussed.

Document Type: Research article

DOI: 10.1348/000711005X86705

Affiliations: 1: Sensometrics Research and Service, Richmond, Virginia, USA