Coefficient Alpha and the Reliability of Composite Measurements
- 1 March 1967
- journal article
- Published by Cambridge University Press (CUP) in Psychometrika
- Vol. 32 (1) , 1-13
- https://doi.org/10.1007/bf02289400
Abstract
Following a general approach due to Guttman, coefficientα is rederived as a lower bound on the reliability of a test. A necessary and sufficient condition under which equality is attained in this inequality and hence that α 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 α is equal to the mean of the split-half reliabilities” is true only under the restricted condition assumed by Cronbach in the body of his derivation of this result. Finally some limitations on the uses of any function of α as a measure of internal consistency are noted.Keywords
This publication has 11 references indexed in Scilit:
- THEORY OF GENERALIZABILITY: A LIBERALIZATION OF RELIABILITY THEORY†British Journal of Statistical Psychology, 1963
- Statistical Inferences About True ScoresPsychometrika, 1959
- The Definition and Estimation of Test ReliabilityEducational and Psychological Measurement, 1958
- The Kuder-Richardson formula (21) as a Split-Half Coefficient, and Some Remarks on its Basic AssumptionPsychometrika, 1958
- Reliability Formulas that do not Assume Experimental IndependencePsychometrika, 1953
- Coefficient alpha and the internal structure of testsPsychometrika, 1951
- Theory of mental tests.Published by American Psychological Association (APA) ,1950
- Test Reliability Estimated by Analysis of VariancePsychometrika, 1941
- Some Remarks on the Kuder-Richardson Reliability CoefficientPsychometrika, 1940
- The Theory of the Estimation of Test ReliabilityPsychometrika, 1937