Recently it was suggested that the Bayes risk might be used to characterize tests. To conform to common practices about indexes, a rescaling of the Bayes risk was proposed. The motivation for this new coefficient, d, was to provide an index that has a large value when the Bayes risk is small and that has a value in the closed interval [0, 1]. However, since d might have a value outside this range, a modification of d is described which yields an index that always has a value between zero and one.
Get full access to this article
View all access options for this article.
References
1.
Fhanér, S.Item sampling and decision making in achievement testing. British Journal of Mathematical Statistical Psychology, 1974 , 27, 172-175.
2.
Griffin, B.S., & Krutchkoff, R.G.Optimal linear estimators: An empirical Bayes version with application to the binomial distribution. Biometrika , 1971, 58, 195-201.
3.
Harris, C.W.Some technical characteristics of mastery tests. In C. W. Harris, M. C. Alkin , & W. J. Popham (Eds.), Problems in criterion-referenced measurement (CSE Monograph Series in Evaluation, No. 3. Los Angeles: University of California, Center for the Study of Evaluation, 1974 .
Lord, F.M., & Novick, M.R.Statistical theories of mental test scores. Reading, MA : Addison-Wesley, 1968.
6.
Novick, M.R., & Lewis, C.Prescribing test length for criterion-referenced measurement. In C. W. Harris, M. C. Alkin , & W. J. Popham (Eds.), Problems in criterion-referenced measurement (CSE Monograph Series in Evaluation, No. 3. Los Angeles: University of California, Center for the Study of Evaluation, 1974.
7.
Skibinsky, M.The maximum probability on an interval when the mean and variance are known . Sankhya, Series A, 1977, 39, 144-159.
8.
van der Linden, W.J., & Mellenbergh, G.J.Coefficients for tests from a decision theoretic point of view. Applied Psychological Measurement, 1978, 2, 119-134.
9.
Wilcox, R.R.Estimating the likelihood of false-positive and false-negative decisions in mastery testing : An empirical Bayes approach. Journal of Educational Statistics, 1977, 2, 289-307.
10.
Wilcox, R.R.Applying ranking and selection techniques to determine the length of a mastery test. Educational and Psychological Measurement , in press.
