The Estimation of Proportions in m Groups
- 1 March 1973
- journal article
- Published by Cambridge University Press (CUP) in Psychometrika
- Vol. 38 (1) , 19-46
- https://doi.org/10.1007/bf02291172
Abstract
In many applications, it is desirable to estimate binomial proportions in m groups where it is anticipated that these proportions are similar but not identical. Following a general approach due to Lindley, a Bayesian Model II aposteriori modal estimate is derived that estimates the inverse sine transform of each proportion by a weighted average of the inverse sine transform of the observed proportion in the individual group and the average of the estimated values. Comparison with a classical method due to Jackson spotlights some desirable features of Model II analyses. The simplicity of the present formulation makes it possible to study the behavior of the Bayesian Model II approach more closely than in more complex formulations. Also, it is possible to estimate the amount of gain afforded by the Model II analyses.Keywords
This publication has 14 references indexed in Scilit:
- ESTIMATING MULTIPLE REGRESSIONS IN m GROUPS: A CROSS‐VALIDATION STUDYBritish Journal of Mathematical and Statistical Psychology, 1972
- ESTIMATING REGRESSIONS IN m GROUPSBritish Journal of Mathematical and Statistical Psychology, 1971
- Bayesian inference and the classical test theory model: Reliability and true scoresPsychometrika, 1971
- The Assessment of Prior Distributions in Bayesian AnalysisJournal of the American Statistical Association, 1967
- A Bayesian Indifference ProcedureJournal of the American Statistical Association, 1965
- A Bayesian Approach to the Analysis of Data from Clinical TrialsJournal of the American Statistical Association, 1965
- Tables of the Freeman-Tukey transformations for the binomial and Poisson distributionsBiometrika, 1961
- Symmetric measures on Cartesian productsTransactions of the American Mathematical Society, 1955
- Transformations Related to the Angular and the Square RootThe Annals of Mathematical Statistics, 1950
- THE TRANSFORMATION OF POISSON, BINOMIAL AND NEGATIVE-BINOMIAL DATABiometrika, 1948