Empirical Bayes Estimation of Proportions in Several Groups.
PORTLAND STATE UNIV OR DEPT OF PSYCHOLOGY
Pagination or Media Count:
The problem of estimating binomial proportions in several similar but not necessarily identical groups occurs frequently in psychological and educational settings. A straightforward empirical Bayes approach to this problem using a slight extension of the standard Bayesian method for estimating a single proportion is proposed. Novick, Lewis, and Jackson 1973 suggest a purely Bayesian solution to the problem which uses a root arcsine transformation of the proportions. They contrast their method with a similar approach using the same transformation, due to Jackson 1972 using examples to show that the Bayesian approach is better. This note shows that an improved version of Jacksons approach yields much more satisfactory results than the original, so the advantage of the purely Bayesian approach is questionable. But the revised version of Jacksons approach and the new beta-binomial approach yield practically identical results, so even the need for using the root-arcsine transformation is questionable, except when the proportions are concentrated near zero or one.
- Statistics and Probability