My questionnaire consists of Dichotomous questions, Numerical Questions, 5 Point Likert scale questions, and 10 points Likert scale questions. I am a bit confused about whether I can apply Cronbach Alpha to the overall questionnaire or if I need to bifurcate them according to the nature of the questions.
Hello Prashantu,
The more important consideration is whether all items in your questionnaire were intended to (and actually do) measure the same overall trait/characteristic/attribute/behavior (e.g., that the items are unidimensional).
The arithmetic underlying Cronbach's alpha does not restrict you from entering items having different maximum point values. However, you should recognize that, all other things equal, maximum item variance (part of the estimation equation) varies as maximum number of points per item varies.
Example: Maximum item variance for a dichotomously scored item (0/1) is 0.25;
Maximum item variance for a 1-7 range, polytomously scored item would be 9 (for even number of cases).
Good luck with your work.
Dear friend, think about what exactly Cronbach's alpha (and in a more general sense, reliability) is and what it is supposed to measure.
As an addendum to the points made by David Morse , difference in item variances means that a multi-item scale will, in effect, be a weighted average of the items, with the highest-variance items weighted most heavily. If you want all items weighted equally in the scale, you can use the "standardized item alpha" (or equivalently, calculate z-scores for every item and run the reliability analysis on the z-scored versions instead of the raw scores). Or you can give all items more nearly equal variances by transforming them all to have approximately the same range (e.g., if the 10-point items are scored 1,2,3,4,5,6,7,8,9,10 you could re-score the dichotomies 1,10 instead of 0,1 or 1,2; and re-score the 5-category items 2,4,6,8,10 or better yet 1, 3.25, 5.5, 7.75, 10). I'm unsure what you mean by "numerical questions," but for example, if one of those has an observed range of about 0 to 100, you could re-score it by dividing every observed score by 10.
Using a multidimensional scale as if it is unidimensional could yield misinterpretations of the relationships among variables of interest. Therefore, you should establish the dimensionality of your scale before looking into other psychometric properties (e.g., internal consistency). In other words, Cronbach’s alpha coefficient should be utilized to measure internal consistency only after unidimensionality is verified. You might find the following article helpful.
Boateng, G. O., Neilands, T. B., Frongillo, E. A., Melgar-Quiñonez, H. R., & Young, S. L. (2018). Best practices for developing and validating scales for health, social, and behavioral research: A primer. Frontiers in Public Health, 6, 149. https://doi.org/10.3389/fpubh.2018.00149
Good luck,