# Factor analysis and Cronbach's alpha

My research work is based on a questionnaire which includes all types of questions, ordinal as well as nominal, but 80% of the questions are based on Likert scale 1-5. My question is whether Cronbach's alpha can be calculated for all types of questions even if they are not on scale format? Secondly whether Cronbach's alpha or reliability should be done before or after conducting factor analysis and what if it comes to be too low? Also, how do we select questions from the questionnaire for factor analysis, can it be random?

• whether Cronbach's alpha can be calculated for all types of questions even if they are not on scale format No. Classic alpha - only for scale (metrical) data. Or binary (then it is called Kuder-Richardson). Feb 1, 2017 at 7:27
• @ttnphns: want to turn that into an answer? Feb 1, 2017 at 9:42

As mentioned in the comments by @ttnphs, Cronbach's alpha $$\alpha$$ is not appropriate for ordinal$$^1$$ and nominal data, as it was designed for scale (or metrical data). Factor analysis, however, can easily accommodate ordinal and nominal data. When using factor analysis omega, $$\omega$$ is typically used as a measure of internal consistency. Unlike $$\alpha$$, $$\omega$$ is a model-based reliability estimate. Thus, it can only be calculated after the factor analysis has been run (and is returned by default in many software packages) regardless of your item type (just make sure the appropriate link function is used for each item).

I am not sure what you mean by item selection; if you could elaborate on the context, I may be able to help.

For more information, see McNeish (2018) and Raykov & Marcoulides (2019) for a discussion about the use of $$\alpha$$ in scenarios where factor analysis is the appropriate measurement model.

$$^1$$ For ordinal data in particular, a different version of Cronbach's $$\alpha$$ is available called ordinal $$\alpha$$ (Zumbo, Gadermann, & Zeisser, 2007) which I cover in more detail here.

References

McNeish, D. (2018). Thanks coefficient alpha, we'll take it from here. Psychological methods, 23(3), 412.

Raykov, T., & Marcoulides, G. A. (2019). Thanks coefficient alpha, we still need you!. Educational and psychological measurement, 79(1), 200-210.

Zumbo, B. D., Gadermann, A. M., & Zeisser, C. (2007). Ordinal versions of coefficients alpha and theta for Likert rating scales. Journal of modern applied statistical methods, 6(1), 4

Before conducting factor analysis you need to perform the KMO test or Bartlett's test of sphericity to check whether your data is suitable for factor analysis.

You need to perform Cronbach's alpha test after the factor analysis.