A Note on the Relation between Coefficient Alpha and Guttman’s “split-half” Lower Bounds

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Abstract
Use of the same term “split-half” for division of an n-item test into two subtests containing equal [Cronbach], and possibly unequal [Guttman], numbers of items sometimes leads to a misunderstanding about the relation between Guttman’s maximum split-half bound and Cronbach’s coefficient alpha.Coefficient alpha is the average of split-half bounds in the Cronbach sense and so is not larger than the maximum split-half bound in either sense when n is even. When n is odd, however, splithalf bounds exist only in the Guttman sense and the largest of these may be smaller than coefficient alpha.