Replicated difference and preference tests: how to account for inter-trial variation

Binomial tests are often used in sensory difference and preference testing. Two assumptions underlie this use: (1) responses are independent and (2) choice probabilities do not vary from trial to trial. In many applications, the latter assumption is violated. In this paper we account for variation in inter-trial choice probabilities using the beta distribution. The result of combining the binomial with the beta distribution is a compound distribution known as the beta-binomial. We show how to use the betabinomial model for replicated difference and preference tests such as those used to support product claims.