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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References
1.
Cronbach, L. J., Rajaratnam, N., and Gleser, G. C.Theory of generalizability : A liberalization of reliability theory. British Journal of Statistical Psychology, 1963, 16, 137-163.
2.
Guttman, L.The determinacy of factor score matrices with implications for five other basic problems of common-factor theory. British Journal of Statistical Psychology, 1955, 8, 65-82.
3.
Kaiser, H. J. and Caffrey, J.Alpha factor analysis. Psychometrika, 1965, 30, 1-14.
4.
Kaiser, H. J. and Michael, W. B.Domain validity and generalizability. EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT, 1975, 35, 31-35.
5.
McDonald, R. P.The theoretical foundations of principal factor analysis, canonical factor analysis, and alpha factor analysis. Brit ish Journal of Mathematical and Statistical Psychology, 1970, 23, 1-21.
6.
Novick, M. R. and Lewis, C.Coefficient alpha and the reliability of composite measurements . Psychometrika, 1967, 32, 1-13.
7.
Tryon, R. C.Reliability and behavior domain validity: Reformulation and historical critique. Psychological Bulletin, 1957, 54, 229-249.