Solved – the correct use of Cronbach’s alpha

Question

I am trying to use Cronbach's alpha in order to see if some variables are measuring the "same", but I have some doubts about the correct use:

1. Can I compute alpha for numerical, ordinal or dichotomous variables? If it is correct to do that, then may I mix dichotomous, ordinal and numerical variables?

2. If Cronbach's alpha cannot be used for numerical, should I turn these variables into ordinal, or not?

3. If all my variables are ordinal, do they have to be on the same scale? I mean if variable 1 goes from 1 to 5, and variable 2 goes from 1 to 3, may I use Cronbach's alpha for these 2 variables?

Answer 1

First, alpha is a quantity for a scale (a set of items).

Ad 1: Strictly speaking, alpha only makes sense for metric items (which, I believe, you mean by numerical variables). However, it is often used on (sum) scales of ordinal items too (there the general rule of thumb is a sum of more than 7 items and more than 4 levels of the item). I believe this is bad practice though.

Ad 2: You can use alpha in this case. Generally, it is rarely a good idea to make a numeric variable ordinal.

Ad 3: I would not use it in this case (but mainly because they are ordinal).