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The Variance of Rasch Ability Estimates From Partially-Known Item Parameters

Mislevy, Robert J.
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Office of Naval Research, Analysis of Variance (ANOVA), Item Analysis, Rasch Model, Statistical Analysis, Test Difficulty


A closed-form approximation is given for the variance of examinee proficiency estimates in the Rasch model for dichotomous items, under the condition that only estimates, rather than true values, of item difficulty parameters are available. The term that must be added to the usual response-sampling variance is inversely proportional to both the number of examinees in the item calibration sample and the length of the test. Illustrative numerical values suggest that the impact of uncertainty about Rasch item parameters on subsequent estimtes of examinee proficiencies is less than has been observed in the 2- and 3- parameter logistic IRT models. (17pp.)

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