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Coefficient Alpha and the Reliability of Composite Measurements

Novick, Melvin R.; Lewis, Charles
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Office of Naval Research, Alpha Coefficient, Test Reliability, Test Theory


Following a general approach due to Guttman, coefficient alpha is derived as a lower bound on the reliability of a test. The necessary and sufficient condition under which equality is attained in this inequality and hence that alpha is equal to the reliability of the test is derived and shown to be closely related to the recent redefinition of the concept of parallel measurements due to Novick. This condition is then also shown to be closely related to the unit rank assumption originally adopted by Kuder and Richardson in the derivation of their formula 20. The assumption later adopted by Jackson and Ferguson and the one adopted by Gulliksen are shown to be related to the necessary and sufficient condition derived here. It is then pointed out that the statement that "coefficient alpha is equal to the mean of the split-half reliabilities" is true only under the condition assumed by Cronbach in the body of his derivation of this result. Finally some limitations on the uses of any function of alpha as a measure of internal consistency are noted.

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