skip to main content skip to footer

Estimating True-Score Distributions in Psychological Testing (An Empirical Bayes Estimation Problem)

Lord, Frederic M.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Bayesian Statistics, Error of Measurement, Estimation (Mathematics), Score Distribution, True Scores


The following problem is considered: Given that the frequency distribution of the errors of measurement is known, determine or estimate the distribution of true scores from the distribution of observed scores for a group of examinees. Typically this problem does not have a unique solution. However, if the true-score distribution is "smooth", then any two smooth solutions to the problem will differ little from each other. Methods for finding smooth solutions are developed a) for a population and b) for a sample of examinees. The results of a number of tryouts on actual test data are summarized.

Read More