Abstract
As usually interpreted, the standard error of measurement is assumed to be constant throughout the test-score range. In this investigation the standard error of measurement was assumed to be not higher than a second-degree function of the test score. By conceiving a test score to be made up of the scores on two parallel tests, an equation was derived for predicting the standard error of measurement from the test score. In the derivation the corresponding first four moments of the score distributions for the parallel tests were assumed to be identical, and certain errors of estimate involved in predicting the second test score from the first were assumed to be uncorrelated with powers of the score on the first test. An empirical verification was carried out, using nine synthetic tests and a 1000-case sample, and showed good agreement between predicted and observed results. The findings indicated that the standard error of measurement was constant only for a symmetrical, mesokurtic distribution of scores.
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References
Conrad, H. S. A statistical evaluation of the basic classification test battery (Form I),O.S.R.D. Report 4346. Washington: Applied Psychology Panel, N.D.R.C., 1945, 93 pp.
Isserlis, L. On certain probable errors and correlation coefficients of multiple frequency distributions with skew regression.Biometrika, 1916,11, 185–190.
Pearson, K. On the probable errors of frequency constants.Biometrika, 1913,9, 1–10.
Thurstone, T. G. The difficulty of a test and its diagnostic value.J. educ. Psychol., 1932,23, 335–343.
Wilkins, J. E. A note on skewness and kurtosis.Ann. math. Stat., 1944,15, 333–335.
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This study was carried out while the author was a National Research Council Predoctoral Fellow in psychology at Princeton University.
The author wishes to express his appreciation for the guidance given by his thesis adviser, Professor Harold Gulliksen. He wishes also to acknowledge his gratitude to the Educational Testing Service for extensive assistance in the empirical phase of the study, and to Dr. Ledyard Tucker for suggesting efficient methods of handling special computational problems.
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Mollenkopf, W.G. Variation of the standard error of measurement. Psychometrika 14, 189–229 (1949). https://doi.org/10.1007/BF02289153
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DOI: https://doi.org/10.1007/BF02289153