Dear Carlos Salavera

Alpha is the estimation of lower bound of reliability. It gives true reliability in under one condition, congeneric measures. On the other hand omega coefficient can give reliability under tau- equivalence. Consequently omega corrects the underestimation bias of α when the assumption of tau-equivalence is violated (Dunn et al., 2014) and different studies show that it is one of the best alternatives for estimating reliability (Zinbarg et al., 2005, 2006; Revelle and Zinbarg, 2009), although to date its functioning in conditions of skewness is unknown.

For more information:

Trizano-Hermosilla I and Alvarado JM (2016) Best Alternatives to Cronbach's Alpha Reliability in Realistic Conditions: Congeneric and Asymmetrical Measurements. Front. Psychol. 7:769. doi: 10.3389/fpsyg.2016.00769

Deng, L., & Chan, W. (2017). Testing the difference between reliability coefficients alpha and omega. Educational and psychological measurement, 77(2), 185-203.

Hope it helps

Hello Hakan,

as far as I know, alpha presumes *essential* tau-equivalence (i.e, congeneric measurement of a shared underlying factor AND equal factor loadings) whereas omega assumes only congeneric measurement but not equal loadings.

Overall, I remember that measurement models increase in rigidity from congeneric (same factor) to essential tau-equivalence (same factor + equal loadings) to tau-equivalence (all of them + equal intercepts) to parallel (all of them + equal error variances).

Omega is preferable as it has weaker and thus more realistic assumptions (i.e., the items only have to measure the same thing). I am no psychometrician, this was just memory. Is that wrong?

All the best,

Holger

Carlos, as Holger already explained, alpha is based on quite restrictive assumptions that are generally violated in empirical research, i.e., unidimensionality, essential tau-equivalence (equal factor loadings), and uncorrelated errors. If the assumptions are met, alpha can of course be used. If the assumption of tau-equivalence is violated, then omega would be preferable. However, when factor loadings are not equal but quite high, alpha generally leads to similar reliability value compared to omega.

If the assumption of uncorrelated errors is violated, error covariances can be included in the denominator of the omega equation. Alpha treats this error covariance as true variance. If there is a positive error covariance in the data, alpha overestimates the population reliability. However, if there is a negative covariance, alpha underestimates the true value. Therefore, alpha is not generally a lower bound of the population reliability when the assumptions are violated.

Alpha is often used because it is included in text books and it is the first option in the SPSS program.

Therefore, omega is almost always the better alternative.

HTH, Karin

Estimado Carlos Salavera

En estudios de corte psicométrico, el alfa de Cronbach presenta diversas limitaciones, está afectado por la naturaleza de ítems (dicotómico u ordinal), número de ítems, tipo de escala de respuesta y proporción de varianza. Se utiliza frecuentemente porque se encuentra integrado a software de mayor uso como SPSS. Ante sus limitaciones, se aconseja utilizar el coeficiente Omega que trabaja directamente con cargas factoriales y por ende, no subestima la fiabilidad.

Para calcular el Omega utilizo el software Jomavi (https://www.jamovi.org/download.html)

Algunos estudios:

Viladrich, C., Angulo-Brunet, A., & Doval, E. (2017). Un viaje alrededor de alfa y omega para estimar la fiabilidad de consistencia interna. Anales de Psicología, 33(3), 755. doi:10.6018/analesps.33.3.268401 

Ventura-León, J.L. y Caycho, T. (2017). El coeficiente omega: un método alternativo para la estimación de la fiabilidad [carta al Editor]. Revista Latinoamérica de Ciencias Sociales, Niñez y Juventud, 15, 625-627.