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Estimation of True Score and Error Variance for Tests Under Various Equivalence Assumptions

Published online by Cambridge University Press:  01 January 2025

Walter Kristof
Walter Kristof*
Affiliation:
Educational Testing Service
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Abstract

Maximum-likelihood estimators of true score variance and error variance for mental tests are derived for six different models of equivalent measurements. Statistical properties of the estimators are examined. Main emphasis is placed upon essentially τ-equivalent measurements. A statistical criterion for this type of measurement is given. The solution of the comparatively simple maximum-likelihood equations is effected by means of a rapid Newton-Raphson procedure. Two different initial estimators are considered and their relative merits in terms of second moments evaluated. Four numerical examples are appended by way of illustration.

Type
Original Paper
Information
Psychometrika , Volume 34 , Issue 4 , December 1969 , pp. 489 - 507
Copyright
Copyright © 1969 The Psychometric Society

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Footnotes

*

Paper read at the Mathematical Psychology Meeting, August 28, 1968, at Stanford, Calfornia.

†

This research was supported in part by the National Institute of Child Health and Human Development, Research Grant 1 P01 HD01762.

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