From alpha to omega and back

Abstract

Coefficient α, also known as the coefficient of internal consistency, is one of the most used and at the same time the most misused reliability assessment method of the composite psychological instruments or tests. For the interpretation of results generated through the application of psychological tests, the most important misuse of the coefficient α is the wrong conclusion about homogenity or unidimensionality. One source of this kind of misuse has originated from the very definition of the coefficient α. The other source is insufficient differentiation of the definitions of reliability, homogenity and validity between classical measurement model, also known as theory of the true and error score, and its developed version, the factor-analytic model of measurement. Because of that, there has been for some time an alternative index for the assessment of reliability, homogenity and validity under the socalled spearmanian confirmatory one-factor model, which is known as coefficient ω. Using the data generated with the one scale resembling standard composite psychological test, the usefulness and limitations of the coefficients α and ω are described through the simple algebra. Based on these results and in conjuction with previous analyses, it is showed that the acceptable assessment of the coefficient α is neccesary but not sufficient reason for the conclusion about the reliability and homogenity of the test. For the reasonable and sound conclusion of this kind it is necessary to use other assessments such as coefficient ω, together with the indices of factor validity and goodness of fit under the hypothesis of spearmanian one-factor model.