It is widely recognized that the reliability of a difference score depends on the reliabilities of the constituent scores and their intercorrelation. Authors often use a well‐known identity to express the reliability of a difference as a function of the reliabilities of the components, assuming that the intercorrelation remains constant. This approach is misleading, because the familiar formula is a composite function in which the correlation between components is a function of reliability. An alternative formula, containing the correlation between true scores instead of the correlation between observed scores, provides more useful information and yields values that are not quite as anomalous as the ones usually obtained Copyright

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Journal Journal of Educational Measurement
Zimmerman, D.W. (Donald W.). (1994). A Note on Interpretation of Formulas for the Reliability of Differences. Journal of Educational Measurement, 31(2), 143–147. doi:10.1111/j.1745-3984.1994.tb00439.x