Use Omega Rather than Cronbach’s Alpha for Estimating Reliability. But…

ABSTRACT

Cronbach’s alpha (α) is a widely-used measure of reliability used to quantify the amount of random measurement error that exists in a sum score or average generated by a multi-item measurement scale. Yet methodologists have warned that α is not an optimal measure of reliability relative to its more general form, McDonald’s omega ($\omega$). Among other reasons, that the computation of $\omega$ is not available as an option in many popular statistics programs and requires items loadings from a confirmatory factor analysis (CFA) have probably hindered more widespread adoption. After a bit of discussion of α versus $\omega$, we illustrate the computation of $\omega$ using two structural equation modeling programs (Mplus and AMOS) and the MBESS package for R. We then describe a macro for SPSS and SAS (OMEGA) that calculates $\omega$ in two ways without relying on the estimation of loadings or error variances using CFA. We show that it produces estimates of $\omega$ that are nearly identical to when using CFA-based estimates of item loadings and error variances. We also discuss the use of the OMEGA macro for certain forms of item analysis and brief form construction based on the removal of items from a longer scale.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. When the response scales for the k indicators are the same, the arithmetic average of the k indicators is also frequently used as a proxy for T. The use of the average does not change the argument we make here or the estimate of reliability that results, but it will change a little bit of the math that we describe.

2. As Raykov and Marcoulides (2019) point out, this definition is problematic as a general definition of reliability. It is possible for data to be highly reliable in circumstances in which there is no variation in T, yet reliability would be 0 (or undefined, depending on the variance in O) by this definition. They argue that this definition of reliability should be conditioned on V(T) > 0.

3. McDonald (1999) refers to Equation 3 as Guttman-Cronbach α. Although Cronbach popularized Equation 3, Guttman (1945) invented this measure of reliability before Cronbach’s influential paper was published.

4. The ML extraction method does not allow for the factor analysis of a covariance matrix.

5. The output from the factor routine generated by the omega macro should be examined to make sure that the factor analysis converged and generated a solution. The rest of the output should not be interpreted if an error is generated by the factor command.

6. The subsets option is also available in the OMEGA macro when using Cronbach’s α as the measure of reliability. Note that we are not the first either to suggest maximizing reliability through selective item deletion or to provide software that implements such an all subsets approach. See Morris (1978a, 1978b) and Serlin and Kaiser (1976) for some earlier treatments of this topic that focus on maximizing Cronbach’s α.

7. The sort option can be used to change the sorting of the rows of this table by reliability (the default, sort = 0) to sorting by r_m (sort = 1) or the number of items m (sort = 2). This table can also be saved as a data file with the use of the save option. See the documentation for details.