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Unbiased Estimators of Ability Parameters, and of Their Parallel-Forms Reliability

Lord, Frederic M.
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Office of Naval Research, Analysis of Variance (ANOVA), Item Response Theory, Mathematical Formulas, Statistical Analysis, Statistical Bias, Test Reliability


This paper is primarily concerned with determining the statistical bias in the maximum likelihood estimate of the examinee ability parameter in item response theory, and of certain functions of such parameters. Given known item parameters, unbiased estimators are derived for (1) an examinee's ability parameter and proportion-correct true score; (2) the variance of ability parameters across examinees in the group tested and the variance of proportion-correct true scores; and (3) the parallel-forms reliability of the observed test score, the maximum likelihood estimator. These formulas apply in situations where the item parameters are known; they are not adequate for situations where the item parameters and ability parameters are estimated simultaneously from a single data set. (Author/BW). (38pp.)

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