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I have a sample size of N=63 and 6 items measuring risk tolerance. Now, I want to calculate Cronbachs alpha, however, the 6 items have different scales. For example, the first item has a scale from 1-4, and the second question a scale from 1-2, etc. Does this lead to any problems or can I just use the "alpha" function from the psych package in R? Are there any other points I have to consider when I calculate Cronbachs alpha? Thanks in advance :)

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  • $\begingroup$ you may use "standardized alpha" $\endgroup$
    – ttnphns
    Sep 27, 2020 at 21:32
  • $\begingroup$ That's sounds good. So the "standardized alpha" is created for problems like that or what is the general use of "standardized alpha"? $\endgroup$
    – Jensxy
    Sep 27, 2020 at 21:42

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As @ttphns points out, standardized $\alpha$ (e.g., see Cortina, 1993; and Falk & Savalei, 2011 for more information) is a good choice. The main difference between standardized $\alpha$ and coefficient $\alpha$ is that the former uses inter-item (standardized) correlations, whereas the latter uses inter-item (unstandardized) covariances.

Because your items appear to be ordinal, you could also consider using Zumbo's ordinal $\alpha$ (e.g., Gadermann, Guhn, & Zumbo, 2012; Zumbo, Gadermann, & Zeisser, 2007), which is designed for ordinal data.

References

Cortina, J. M. (1993). What is coefficient alpha? An examination of theory and applications. Journal of applied psychology, 78(1), 98.

Falk, C. F., & Savalei, V. (2011). The relationship between unstandardized and standardized alpha, true reliability, and the underlying measurement model. Journal of personality assessment, 93(5), 445-453.

Gadermann, A. M., Guhn, M., & Zumbo, B. D. (2012). Estimating ordinal reliability for Likert-type and ordinal item response data: A conceptual, empirical, and practical guide. Practical Assessment, Research, and Evaluation, 17(1), 3.

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.

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