Abstract
Given a set of n individuals and k test items, Hoyt's analysis of variance procedure for estimating reliability assumes that the residual mean square estimates error variability. Based on the assumption that an individual's true score should be allowed to vary across items (rather than remain constant), the present author argues that the residual mean square estimates two components—error and interaction—and hence Winer's modification of Hoyt's formula, (MS exam - m'MS res)/MS exam, underestimates the reliability of the test. Tukey's procedure for partitioning MS res into nonadditive and error components is discussed, with the recommendation made that MS balance be used in place of MS res in the Hoyt formula.
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