After browsing cross validated and several other sources on the web, I still cannot get a grip on McDonald's Omega as a measure of internal consistency. I have a hunch that many fellow social scientists feel similarly insecure about the measure, so I hope to get some clarification on several aspects on this measure:
Assumptions / Prerequisites
While the assumptions for Cronbach's Alpha are commonly discussed (e.g. Cronbach Alpha Assumptions), I haven't managed to get a full picture of the prerequisites for McDonald's Omega. My questions being:
- What are the general assumptions underlying Omega?
- Is there a rule of thumb regarding sample size, or a ratio between variables and observations that should be considered?
- Is Cronbach's Alpha superior to Omega under any circumstances at all?
Coefficients and Interpretation
Secondly, it appears that there still is a great deal of confusion around the different Omega coefficients, perhaps most notably returned by the
psych-package in R. For clarification, maybe someone could offer a full interpretation of coefficients in the following example, in
library(psych) #create 9 variables with a hierarchical structure v9 <- sim.hierarchical() #find omega v9.omega <- omega(v9,digits=2) > v9.omega$omega.group total general group g 0.7984002 0.6857363 0.1126608 F1* 0.7449332 0.6034008 0.1415325 F2* 0.6303512 0.4034189 0.2269323 F3* 0.5022309 0.2460886 0.2561423 > v9.omega$omega.lim  0.858888
My questions regarding this example:
- How does the interpretation between
omega_h(general) differ in this example? Or: What would the correct global measure of internal consistency for the entire measure/questionnaire be?
- What is
- When is
In addition: It appears that
omega_h (general) is getting the most attention in posts/reports, but these values always strike be as surprisingly low in almost every example I have seen. How come?