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Inferring the Shape of the Frequency Distribution of True Scores and of Errors of Measurement

Lord, Frederic M.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Error of Measurement, Statistical Distributions, Test Interpretation, True Scores


Given k parallel, fallible measures on each individual in a group, all the multivariate cumulants of kth and lower orders for the joint distribution of true scores and errors of measurement may be expressed as simple linear functions of the multivariate cumulants of the fallible measures. It is assumed only that the number of examinees is large; that over a very large number of different testings, the average error of measurement will be zero for each examinee; and that the errors of measurement for two different examinees, or for two different testings of the same examinee, are independently distributed. The form of the frequency distribution of the errors is unspecified and may be different for different individuals. The results of a numerical application to psychological test data are given.

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