The Logical Structure of Cronbach's Coefficient Alpha, and its Precision in Estimating Reliability under Measurement Models Assumptions

The study examined three main research questions: 1- What is the logical structure of Cronbach's Coefficient Alpha and its implications" 2- Under what measurement models and cicumstances the use of Coefficient Alpha produce either accurate or biased assessment of reliability? 3- What are the alternative Consistency Coefficients that provide the researcher with more accurate estimation of reliability in the absence of assumptions required by Coefficient Alpha? With respect to the first question, it was demonstrated that the total variance , compared with the sum of item variances, and the test length are the most determinant components of Coefficient Alpha. These findings imply that the sample used should be heteregenous and that Coefficient Alpha is not a pure indicator of internal consistency. To deal with the second question, four measurement models were examined' 1- The Parallel Model, 2- The Tau-equivalent Model, 3- The Essentially Tau-equivalent Model, and 4- The Congeneric Model. Coefficient alpha is based on the Essentially Tau-equivalent Model assumptions concerning test item data. It provides precise assessment of reliability under the three first aforementioned measurement models. However, coefficient alpha tends to underestimates reliability under violation of the assumptions of essential tau-equivalence , being usually the case, of test item scores, and tends to overestimate reliability under violation of the assumption of uncorrelated error scores. When test data satisfy the least restrictive and more realistic model: the congeneric model, alpha provides lower bound estimate of reliability. Regarding the third question, Some alternative assessment of reliability in the presence of the congeneric models, and when some restrictive assumptions of the essential tau-equivalence model are not present in the items data, are examined. Therefore, Theta coefficient, Omega coefficient, Construct Reliability coefficient, and Weighted Omega coefficient are succinctly described. For didactic purposes, three coefficients: Alpha, Construct Reliability, and weighted Omega, were computed using data emanating from a research example. The study concluded with some research implications and recommendation