Accession Number : ADA118667

Title :   Empirical Bayes Estimation of Proportions in Several Groups.

Descriptive Note : Technical rept.,


Personal Author(s) : Paulson,James A

PDF Url : ADA118667

Report Date : Jan 1981

Pagination or Media Count : 36

Abstract : 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 Jackson's approach yields much more satisfactory results than the original, so the advantage of the purely Bayesian approach is questionable. But the revised version of Jackson's 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.

Descriptors :   *Bayes theorem, *Groups(Mathematics), *Biometry, *Biostatistics, Estimates, Comparison, Variations, Population(Mathematics), Group dynamics, Binomials, Transformations(Mathematics), Test methods, Theory, Performance(Human), Scoring

Subject Categories : Psychology
      Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE