A Probability Model for Forced Binary Choices

1 February 1978

journal article
research article
Published by Taylor & Francis in The American Statistician

Vol. 32 (1) , 23-25
https://doi.org/10.1080/00031305.1978.10479238

Abstract

In this article a natural extension of the beta-binomial distribution is developed. Forced binary choice situations are modeled such that each individual has a probability p of knowing the correct answer. (This probability is distributed f(p) across the population.) Hence each individual will guess at the correct answer with probability 1 – p. The observable random variable R, the total number of correct answers (both by knowing and guessing) out of k trials has a rather complicated distribution. However, when f(p) is distributed beta with parameters m and n, the distribution P(r; k, m, n) can be expressed in terms of the well-known Gaussian hypergeometric function. This distribution has implications for true-false tests, taste tests, and virtually every other forced binary choice situation.

Keywords

This publication has 1 reference indexed in Scilit:

Estimating the Proportion of "Always Buy" and "Never Buy" Consumers: A Likelihood Ratio Test with Sample Size Implications
Journal of Marketing Research, 1977