Cronbach Alpha is very used for assessing internal consistence of a scale. It is very much used for scales with items scored with a Likert scale. I wonder if the number of the Likert scale points affect the value of Alpha. I have not been able to find any article tackling on this issue.
Hello Rosa,
The arithmetic associated with estimation of Cronbach's alpha makes no distinction for how many score points are possible with polytomous items.
However, do note that, because both item variances and total variances are computed, the implicit assumption is that the polytomous scores are of interval strength. That said, as you noted, people routinely apply it to the scores from Likert-type response scales.
Good luck with your work.
Cronbach's alpha is based on covariances/Pearson correlations, which are not really appropriate for Likert-type (ordinal) data with few categories. I'd suggest checking out the following papers for an approach to ordinal reliability estimation:
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, 21-29.
https://scholarworks.umass.edu/pare/vol17/iss1/3/
https://scholarworks.umass.edu/cgi/viewcontent.cgi?article=1247&context=pare
An alternative would be to conduct confirmatory factor analysis for ordinal items (based on polychoric correlations) and estimate composite reliability on the basis of the parameters of the factor model. This would have the advantage that it would allow you to also test underlying assumptions, for example, concerning the unidimensionality of the items.
Hi Rosa,
here are some articles that investigate the effect of number of categories on reliability of a scale. As can be expected, the results show that reliability increases when the number of categories increases.
Green, S. B., & Yang, Y. (2009). Reliability of summed item scores using structural equation modeling: An alternative to coefficient alpha. Psychometrika, 74(1), 155–167. https://doi.org/10.1007/s11336-008-9099-3
Lissitz, R. W., & Green, S. B. (1975). Effect of the number of scale points on reliability: A Monte Carlo approach. Journal of Applied Psychology, 60(1), 10–13. https://doi.org/10.1037/h0076268
Lozano, L. M., García-Cueto, E., & Muñiz, J. (2008). Effect of the number of response categories on the reliability and validity of rating scales. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 4(2), 73–79. https://doi.org/10.1027/1614-2241.4.2.73
Kind regards, Karin
David Morse and Karin Schermelleh-Engel I really appreciate your answers. Now let´s wait for the statistical software to include these recommendations.
@Rosa, how do you suppose those recommendations came about? David Booth
Rosa Eugenia Jiménez what do you mean with "let´s wait for the statistical software to include these recommendations"?? Software like R offers a lot of possibilities to calculate ordinal versions of alpha and McDonald's omega, to use polychoric correlation approaches or to use ULS or DWLS etimators in SEM appropriate for ordinal data (e.g. "lavaan" and/or "psych" package). An I am pretty sure other programs like MPlus are also capable if not even better equipped. So what are you waiting for? And I am also pretty sure there are lots of tutorial online.
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