The paper considers the problem of selecting the t best of k normal populations and simultaneously determining whether the selected populations have a mean larger than a known standard. Illustrations are given for selecting the t best of k examinees when the binomial error model applies.
Get full access to this article
View all access options for this article.
References
1.
Bechhofer, R.E.A single-sample multiple decision procedure for ranking means of normal populations with known variances. Annals of Mathematical Statistics, 1954, 25, 16-39.
2.
Bechhofer, R.E. and Turnbull, B.W.Two (k + 1) decision selection procedures for comparing k normal means with a specified standard. Journal of the American Statistical Association, 1978, 73, 385-392.
3.
Cronbach, L.J. and Gleser, G.C.Psychological Tests and Personnel Decisions. (2nd Ed.) Urbana, Ill.: University of Illinois Press, 1965.
4.
Dudewicz, E.J., Ramberg, J.S., and Chen, H.J.New tables for multiple comparisons with a control (unknown variances . Biometrische Zeitschrift, 1975, 17, 13-26.
5.
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.
6.
Glass, G.V.Standards and criteria. Journal of Educational Measurement , 1978, 15, 237-261.
Novick, M.R., and Lindley, D.V.The use of more realistic utility functions in educational applications . Journal of Educational Measurement, 1978 , 15, 181-191.
10.
Olkin, I., Sobel, M., and Tong, Y.L.Estimating the true probability of correct selection for location and scale parameter families. Department of Statistics , Stanford, Technical Report No. 110, 1976.
11.
Wilcox, R.R.Applying ranking and selection techniques to determine the length of a mastery test. EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT , 1979, 39, 13-22.
