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A coefficient derived from communalities of test parts has been proposed as greatest lower bound to Guttman's “immediate retest reliability.” The communalities have at times been calculated from covariances between item sets , which tends to underestimate appreciably. When items are experimentally independent, a consistent estimate of the greatest defensible internal-consistency coefficient is obtained by factoring item covariances. In samples of modest size, this analysis capitalizes on chance; an estimate subject to less upward bias is suggested. For estimating alternate-forms reliability, communality-based coefficients are less appropriate than stratified alpha.
Lee J. Cronbach (Tue,) studied this question.
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