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On Accuracy in Reliability Estimation

Published online by Cambridge University Press:  01 January 2025

Walter Kristof
Walter Kristof*
Affiliation:
Educational Testing Service
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Abstract

This study in parametric test theory deals with the statistics of reliability estimation when scores on two parts of a test follow a binormal distribution with equal (Case 1) or unequal (Case 2) expectations. In each case biased maximum-likelihood estimators of reliability are obtained and converted into unbiased estimators. Sampling distributions are derived. Second moments are obtained and utilized in calculating mean square errors of estimation as a measure of accuracy. A rank order of four estimators is established. There is a uniformly best estimator. Tables of absolute and relative accuracies are provided for various reliability parameters and sample sizes.

Keywords

Public PolicyStatistical TheoryReliability EstimationRank OrderParametric Test
Type
Original Paper
Information
Psychometrika , Volume 39 , Issue 1 , March 1974 , pp. 23 - 29
Copyright
Copyright © 1974 The Psychometric Society

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