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Variation of the Standard Error of Measurement

Published online by Cambridge University Press:  01 January 2025

William G. Mollenkopf
William G. Mollenkopf*
Affiliation:
Princeton University And Educational Testing Service
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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.

Type
Original Paper
Information
Psychometrika , Volume 14 , Issue 3 , September 1949 , pp. 189 - 229
Copyright
Copyright © 1949 Psychometric Society

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Footnotes

*

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.

References

Conrad, H. S. A statistical evaluation of the basic classification test battery (Form I), Washington: Applied Psychology Panel, N.D.R.C., 1945.Google Scholar
Isserlis, L. On certain probable errors and correlation coefficients of multiple frequency distributions with skew regression. Biometrika, 1916, 11, 185–190.CrossRefGoogle Scholar
Pearson, K. On the probable errors of frequency constants. Biometrika, 1913, 9, 1–10.Google Scholar
Thurstone, T. G. The difficulty of a test and its diagnostic value. J. educ. Psychol., 1932, 23, 335–343.CrossRefGoogle Scholar
Wilkins, J. E. A note on skewness and kurtosis. Ann. math. Stat., 1944, 15, 333–335.CrossRefGoogle Scholar