USE OF TRUE‐SCORE THEORY TO PREDICT MOMENTS OF UNIVARIATE AND BIVARIATE OBSERVED SCORE DISTRIBUTIONS*

Abstract

ABSTRACT 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.

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