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It is shown that if a behavior domain can be described by the common factor model with a finite number of factors, the squared correlation between the sum of a selection of items and the domain total score is actually greater than coefficient alpha. Equality is attained only if the selected items are parallel. Generalizability can be correctly assessed as a function of the item uniquenesses and the test variance.
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Roderick P. McDonald (1978) studied this question.
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