Bayesian analysis for proportions with an independent background effect.
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.
Bi
Jian
J
Sensometrics Research and Service, Richmond, Virginia, USA. bbdjcy@aol.com
D001499:Bayes Theorem; D016010:Binomial Distribution; D002755:Choice Behavior; D004192:Discrimination, Psychological; D006801:Humans; D015233:Models, Statistical; D011336:Probability; D011594:Psychometrics / Q000706:statistics & numerical data*; D012677:Sensation