Journal of Applied Mathematics and Decision Sciences
Volume 8 (2004), Issue 1, Pages 33-42

Sample size for testing homogeneity of two a priori dependent binomial populations using the Bayesian approach

Athanassios Katsis

Department of Statistics and Actuarial Science, University of the Aegean, 68 Dikearhou Street, Athens 116 36, Greece

Copyright © 2004 Athanassios Katsis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper establishes new methodology for calculating the optimal sample size when a hypothesis test between two binomial populations is performed. The problem is addressed from the Bayesian point of view, with prior information expressed through a Dirichlet distribution. The approach of this paper sets an upper bound for the posterior risk and then chooses as ‘optimum’ the combined sample size for which the likelihood of the data does not satisfy this bound. The combined sample size is divided equally between the two binomials. Numerical examples are discussed for which the two proportions are equal to either a fixed or to a random value.