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A Test of the Equality of Standard Errors of Measurement

Published online by Cambridge University Press:  01 January 2025

Bert F. Green Jr.
Bert F. Green Jr.*
Affiliation:
Educational Testing Service
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Abstract

A procedure is proposed for testing the significance of group differences in the standard error of measurement of a psychological test. Wilks' criterion is used to assure that the tests used in ascertaining reliability and hence variance of errors of measurement may be assumed parallel for each group. Votaw's criterion may be used to check whether the test scores of all the groups have the same mean, variance, and covariance. It is possible, however, for the variance and reliability of the test to differ widely from group to group, so that Votaw's criterion is not satisfied even though the variance of errors of measurement stays relatively constant. For this case a modification of Neyman and Pearson's criterion is developed to test agreement among standard errors of measurement despite group differences in mean, variance, and reliability of the test.

Type
Original Paper
Information
Psychometrika , Volume 15 , Issue 3 , September 1950 , pp. 251 - 257
Copyright
Copyright © 1950 The Psychometric Society

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Footnotes

*

The author wishes to acknowledge the helpful criticisms of Dr. Harold Gulliksen, who suggested the problem.

References

Bartlett, M. S. Properties of sufficiency and statistical tests. Proc. Roy. Soc., 1937, 160, 268–282.Google Scholar
Jackson, R. W. B., and Ferguson, G. A.Studies on the reliability of tests. Bulletin No. 12, Department of Educational Research, University of Toronto, Toronto, Canada.Google Scholar
Kelley, T. L. The reliability of test scores. J. educ. Res., 1921, 3, 370–379.CrossRefGoogle Scholar
Neyman, J., and Pearson, E. S.On the problem of k samples. Bulletin de l'Academie Polonaise des Sciences et des Lettres, Série A, Sciences Mathematique, 1931, 460–481.Google Scholar
Otis, A. S. A method of inferring the change in a coefficient of correlation resulting from a change in the heterogeneity of the group. J. educ. Psych., 1922, 13, 293–294.CrossRefGoogle Scholar
Votaw, D. F. Jr.. Testing compound symmetry in a normal multivariate distribution. Ann. math. Stat., 1948, 19, 447–473.CrossRefGoogle Scholar
Wilks, S. S. Sample criteria for testing equality of means, equality of variances and equality of covariances in a normal multivariate distribution. Ann. math. Stat., 1946, 17, 257–281.CrossRefGoogle Scholar
Wilks, S. S. Mathematical Statistics, Princeton: Princeton University Press, 1943.Google Scholar