A problem of considerable importance in certain educational settings is determining how many items to include on a mastery test. Applying ranking and selection procedures, a solution is given which includes as a special case all existing single-stage, non-Bayesian solutions based on a strong true-score model. Illustrations are given for the binomial and compound binomial distributions.
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References
1.
Barr, D. R. and Rizvi, M. H.An introduction to ranking and selection. Journal of the American Statistical Association, 1966, 61, 640-646.
2.
Fhanér, S.Item sampling and decision making in achievement testing. British Journal of Mathematical and Statistical Psychology, 1974, 27, 172-175.
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 : Center for the Study of Evaluation, University of California, 1974.
4.
Huynh, H.Statistical consideration of mastery scores. Psychometrika, 1976, 41, 65-78.
5.
IBM Application Program, System/360. Scientific subroutines package (360-CM-03X) Version III, programmer's manual. White Plains, New York : IBM Corporation Technical Publications Department , 1971.
6.
Lehmann, E. L.Testing statistical hypotheses . New York: John Wiley, 1959.
7.
Lord, F. M.A strong true-score theory, with applications. Psychometrika, 1965, 30, 239-270.
8.
Lord, F. M. and Novick, M. R.Statistical theories of mental test scores. Reading, MA: Addison-Wesley, 1968 .
9.
Macready, G. B. and Dayton, C. M.The use of probabilistic models in the assessment of mastery. Journal of Educational Statistics, 1977, 2, 99-120.
10.
Millman, J.Passing scores and test lengths for domain-referenced measures. Review of Educational Research , 1973, 43, 205-216.
11.
Novick, M. R. and 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 : Center for the Study of Evaluation, University of California, 1974.
12.
Tong, Y. L.On partitioning a set of normal populations by their locations with respect to a control. Annals of Mathematical Statistics, 1969, 40, 1300-1324.
13.
Wald, Abraham.Sequential analysis. New York: John Wiley, 1947.
14.
Wilcox, R. R.A note on the length and passing score of a mastery test. Journal of Educational Statistics , 1976, 1, 359-364.
15.
Wilcox, R. R.Estimating the likelihood of a false-positive or false-negative decision with a mastery test: An empirical Bayes approach. Journal of Educational Statistics, 1977, 2, 289-307.