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Extension of the Rulon Formula for Test Reliability: The Case of Correlated True and Error Components of Scores

Williams, Richard H.; Zimmerman, Donald W.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Error of Measurement, Mathematical Formulas, Split-Half Test Reliability, Test Reliability, True Scores


It is proved that Rulon's formula, estimating reliability from split-halves of a test, can be applied in its usual form even though true scores and error scores are correlated. It is seen, however, that the variance of difference scores in Rulon's formula is not equivalent to error variance and that the standard deviation of difference scores cannot be used as an estimate of the standard error of measurement when true scores and error scores are correlated. Values predicted by the equations presented in this paper are compared to the corresponding values generated by a computer simulation method.

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