Coefficient Alpha and the Reliability of Composite Measurements

Abstract

Following a general approach due to Guttman, coef~icient ex 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 ex is equal to the reliability of the test is derived and shown to be closely related to the recent redefinition of the concept op arallel 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 Fergusqn and·the one adopted by Guliiksen are, shown to be related to the neceasarv and sufficient condition derived here. It is then pointed out that the statement that "coefficient ex is equal to the mean of the split-half reliabilities"·is tru~only 'tinder the condition assumed by Cronbacb, in the body of his derivation of this result.Finally some limitations on the uses of any function of ex as a measure of internal consistency are noted.

The estimation of the IRT reliability coefficient and its lower and upper bounds, with comparisons to CTT reliability statistics

“…18 is in form identical to the classical equation for Cronbach's alpha. Thus, as well documented in the literature (e.g., Novick and Lewis 1967),…”

Cronbach’s α, Revelle’s β, and Mcdonald’s ωH: their relations with each other and two alternative conceptualizations of reliability

“…Though the Case IV result that ≤ might appear to contradict the proof originally published by Novick and Lewis (1967) that is a lower bound of reliability with equality holding under conditions of essential tau equivalence, it must be remembered that our reflects a different definition of true score than that used by Novick and Lewis. The Case IV result that = does accord with the Novick and Lewis proof.…”

“…Whereas Lord and Novick (1968) and Novick and Lewis (1967) compared with reliability, they did not consider and h as we have done. McDonald (1970McDonald ( , 1999 considered the relation between and h only and did not consider conditions of multidimensionality as we have done.…”

The PedsQL in pediatric cerebral palsy: reliability and validity of the Chinese version pediatric quality of life inventory 4.0 generic core scales and 3.0 cerebral palsy module

“…The total score of the Emotional Functioning subscales for parent proxy-report, Social Functioning, Fatigue, Speech and Communication subscales for selfreport did not approach or exceed 0.70. Although Cronbach's alpha represents the lower boundary of the reliability of a measurement instrument and is a conservative estimate of actual reliability [34], scales that did not achieve the 0.70 standard should be used only for descriptive analyses.…”