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Statistical Inferences About True Scores

Lord, Frederic M.
Publication Year:
Report Number:
ETS Research Memorandum
Document Type:
Page Count:
Subject/Key Words:
Office of Naval Research, Statistical Inference, Test Theory, True Scores


This paper was presented at the American Psychological Association Convention in September 1958. It is shown how unbiased estimators may be computed for any moment of the frequency distribution of the true scores on an objective test. From these moments, the shape of the distribution of true scores can be estimated and a least-squares estimate computed for the true score of each examinee. Linear regression of true score on obtained score need not be assumed, as has been usually done, nor normality of the errors of measurement. The shape of the joint distribution of true scores and of errors of measurement can also be inferred by this method.

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