skip to main content skip to footer

Use of True-Score Theory to Predict Moments of Univariate and Bivariate Observed Score Distributions

Lord, Frederic M.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Office of Naval Research, Mathematical Formulas, Test Format, Test Length, Test Theory, True Scores


Formulas are derived for using the available item statistics and score statistics on a test to estimate the moments (or cumulants) of the score distribution of a lengthened (or shortened) form of the same test. Other formulas are derived for estimating the bivariate moments (or cumulants) of the scatterplot between two parallel test forms from the data available on either form alone. An empirical study is made showing in each case satisfactory agreement between the theoretical values predicted from the formulas and the values actually observed. These results suggest the utility of the true-score model used in deriving the formulas for the estimates.

Read More