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

Published online by Cambridge University Press:  01 January 2025

Frederic M. Lord
Frederic M. Lord*
Affiliation:
Educational Testing Service
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Abstract

Formulas are derived for using the available item statistics and score statistics on a test to estimate the moments of the score distribution of a lengthened (or shortened) form of the same test. Other formulas are derived for estimating the bivariate moments of the scatterplot between two parallel test forms using only 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.

Type
Original Paper
Information
Psychometrika , Volume 25 , Issue 4 , December 1960 , pp. 325 - 342
Copyright
Copyright © 1960 The Psychometric Society

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Footnotes

*

This work was supported by contract Nonr-2752(00) between the Office of Naval Research and Educational Testing Service. Reproduction in whole or in part for any purpose of the United States Government is permitted.

References

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