Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-01-07T18:22:57.687Z Has data issue: false hasContentIssue false
  • English
  • Français

Marginal Distributions for the Estimation of Proportions in m Groups

Published online by Cambridge University Press:  01 January 2025

Charles Lewis ,
Ming-mei Wang  and
Melvin R. Novick
Charles Lewis
Affiliation:
The University of Illinois
Ming-mei Wang
Affiliation:
The University of Iowa
Melvin R. Novick
Affiliation:
The University of Iowa The American college Testing program
Get access Rights & Permissions [Opens in a new window]

Abstract

A Bayesian Model II approach to the estimation of proportions in m groups (discussed by Novick, Lewis, and Jackson) is extended to obtain posterior marginal distributions for the proportions. It is anticipated that these will be useful in applications (such as Individually Prescribed Instruction) where decisions are to be made separately for each proportion, rather than jointly for the set of proportions. In addition, the approach is extended to allow greater use of prior information than previously and the specification of this prior information is discussed.

Type
Original Paper
Information
Psychometrika , Volume 40 , Issue 1 , March 1975 , pp. 63 - 75
Copyright
Copyright © 1975 Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

We are grateful to a reviewer for suggestions that made possible a more concise and complete presentation of our work.

References

Box, G. E. P., and Tiao, G. C.. Bayesian estimation of means for the random effect model. Journal of the American Statistical Association, 1968, 63, 174–181.CrossRefGoogle Scholar
Box, G. E. P., and Tiao, G. C.. Bayesian Inference in Statistical Analysis, 1973, Reading, Mass.: Addison-Wesley.Google Scholar
Cronbach, L. J., Gleser, G. C., Nanda, H., and Rajaratnam, N.. The Dependability of Behavioral Measurements: Theory of Generalizability for Scores and Profiles, 1972, New York: McGraw-Hill.Google Scholar
De Finetti, B.. Foresight: its logical laws, its subjective sources (The original French version appeared in Ann. de L' Inst. Henri Poincaré, 1937, 7.). In Kyburg, H. E. Jr., and Smokler, G. E. (Eds.), Studies in Subjective Probability. New York: Wiley. 1964, 93–105.Google Scholar
Freeman, M. F., and Tukey, J. W.. Transformations related to the angular and the square root. The Annals of Mathematical Statistics, 1950, 21, 607–611.CrossRefGoogle Scholar
Hambleton, R. K., and Novick, M. R.. Toward an integration of theory and method for criterion-referenced tests. Journal of Educational Measurement, 1973, 10, 159–170.CrossRefGoogle Scholar
Hewitt, E., and Savage, L. J.. Symmetric measures on cartesian products. Transactions of the American Mathematical Society, 1955, 80, 470–501.CrossRefGoogle Scholar
Hill, B. M.. Inference about variance components in the one-way model. Journal of the American Statistical Association, 1965, 60, 806–825.CrossRefGoogle Scholar
Kelley, T. L.. Statistical Method, 1923, New York: MacMillan.Google Scholar
Kelley, T. L.. Interpretation of Educational Measurements, 1927, Yonkers on Hudson, New York: World Book.Google Scholar
Leonard, T.. Bayesian methods for binomial data: Some computational methods and further ideas, 1972, Iowa City, Iowa: The American College Testing Program.CrossRefGoogle Scholar
Leonard, T.. Comment on “Estimation of proportions in m groups. Psychometrika, 1974, 39, 521–523.CrossRefGoogle Scholar
Lindley, D. V., and Smith, A. F. M.. Bayes estimates for the linear model. Journal of the Royal Statistical Society, Series B, 1972, 34, 1–41.CrossRefGoogle Scholar
Novick, M. R.. In Glass, G. V. (Eds.), Bayesian considerations in educational information systems, 1970, Princeton, New Jersey: Educational Testing Service.Google Scholar
Novick, M. R., and Jackson, P. H.. Bayesian guidance technology. The Review of Educational Research, 1970, 40(4), 459–494.CrossRefGoogle Scholar
Novick, M. R., and Jackson, P. H.. Statistical Methods for Educational and Psychological Research, 1974, New York: McGraw-Hill.Google Scholar
Novick, M. R., Lewis, C., and Jackson, P. H.. The estimation of proportions in m groups. Psychometrika, 1973, 38, 19–45.CrossRefGoogle Scholar
Tiao, G. C., and Tan, W. Y.. Bayesian analysis of random-effect models in the analysis of variance. I. Posterior distribution of variance components. Biometrika, 1965, 52, 37–54.CrossRefGoogle Scholar