This study was undertaken to answer the following research question: Can standardized achievement test norms be better estimated with a theoretical probability model other than the negative hypergeometric model? Ninety norms distributions from two standardized achievement test batteries (ITBS and ITED) were fitted by six models. The results strongly supported the Pearson Type I model (four moments) as the best-fitting curve. It was concluded that this Type I model could provide a viable alternative to the negative hypergeometric model for use in approximating distributions when moment estimates are obtained from multiple matrix sampling or item sampling procedures.
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References
1.
Brandenburg, D. C.The use of multiple matrix sampling in approximating an entire empirical norms distribution. Unpublished PhD thesis, University of Iowa, 1972.
2.
Elderton, W. P.Frequency curves and correlation . (4th ed.) Washington, D. C. : Harren Press, 1953.
3.
Feldt, L.Personal interview. October 31, 1971.
4.
Keats, J. A. and Lord, F. M.A theoretical distribution for mental test scores. Psychometrika, 1962, 27, 59-72.
5.
Kendall, M. G. and Stuart, A.The advanced theory of statistics, Volume 1. London: Charles Griffin & Company Limited, 1963.
6.
Lord, F. M.Estimating norms by item-sampling . EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT, 1962, 22, 259-267.
7.
Lord, F. M. and Novick, M. R.Statistical theories of mental test scores. Reading: Addison-Wesley, 1968.
8.
Pearson, E. S. and Hartley, H. O.Biometrika tables for statisticians, Volume 1. Cambridge, London : University Press, 1954.
9.
Pearson, E. S. and Johnson, N. L.Tables of the incomplete beta-function. (2nd ed.) Cambridge, London: University Press, 1968.
10.
Shoemaker, D. M.Allocation of items and examinees in estimating a norm distribution by item sampling. Journal of Educational Measurement, 1970, 7, 123-128.
11.
Shoemaker, D. M.Principles and procedures of multiple matrix sampling. Technical Report 34, Southwest Regional Laboratory for Educational Research and Development, August, 1971.
