Coefficient Alpha and Beyond: Issues and Alternatives for Educational Research
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BRIEF REPORT
Coefficient Alpha and Beyond: Issues and Alternatives for Educational Research Timothy Teo • Xitao Fan
Published online: 28 March 2013 Ó De La Salle University 2013
Abstract Cronbach’s coefficient alpha has been widely known and used in educational research. Many education research practitioners, however, may not be aware of the potential issues when the main assumptions for coefficient alpha are violated in research practice. This paper provides a brief discussion about two assumptions that may make the use and interpretation of coefficient alpha less appropriate in education research: violations of the tau-equivalence model assumption and the error independence assumption. Violation of either or both of these assumptions will have negative effects on the precision of coefficient alpha as reliability estimate. The paper further presents two alternative reliability estimates without the assumptions of tau-equivalence or error independence. Research practitioners may consider these and other alternatives, when measurement data may not satisfy the assumptions for coefficient alpha. Keywords Cronbach coefficient alpha Reliability Internal consistency Tau-equivalence Independent errors Latent variable modeling Generalizability theory
Introduction In educational research, data in the form of a composite score consisting of multiple items or subscale scores are often obtained and used. By doing so, researchers believe that the item/subtest scores have an acceptable level of ‘‘inter-connectedness’’, and that each item contributes to the overall measurement of a construct. Reliability is a key attribute in educational measurement, and it is generally considered as a necessary condition for measurement validity. Conceptually, reliability represents the portion of the total score variance that is attributed to the true score variance (Revelle and Zinbarg 2009). True score variance, however, cannot be directly obtained or calculated. As a result, we cannot calculate measurement reliability itself; instead, we can only estimate measurement reliability in a given measurement situation. In educational research, a very widely used estimate of reliability for a multi-item instrument is the Cronbach’s coefficient alpha (a).
Cronbach Coefficient Alpha (a) and Issues in its Use
T. Teo (&) Faculty of Education, School of Learning Development and Professional Practice, University of Auckland, Private Bag 92019, Auckland 1010, New Zealand e-mail: [email protected] X. Fan University of Macau, Macau, China
Coefficient a (Cronbach 1951), which was based on a coefficient by Guttman (1945), is by far the most popular estimate for internal consistency reliability of a scale (Peterson 1994). With boundaries between 0 and 1, a is expressed as the following (Crocker and Algina 2006): P 2 k r a ¼ 1 2i k 1 rx P 2 where k is the number of items, ri is the sum of item variances, and r2x is the total variance of the scale. Although not obvious from the formula, coefficient a represents the estimated ratio of
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