Solved – Cronbach’s alpha in R

Question

I am pretty new to Cronbach's Alpha, so I have a question about how to find it using R.

As far as I am aware, Cronbach's alpha is a measure of internal consistency, but to use the alpha() function in R (in the psych package) you need a dataframe or matrix – which has two+ variables. Why is this the case? Shouldn't you only need a list? Or am I understanding Cronbach's Alpha wrong?

Answer 1

Cronbach's $\alpha$ is a measure of internal consistency of a questionnaire or test. It says how correlated the items are that are included in the scale. This is the reason why you need preferably much more than two items: you cannot correlate one item with itself and if you had only two items you could use a "traditional" correlation between the two items. So you need at least a few of them.

You also ask why a matrix or data.frame are needed instead of list. This is a broader topic about R's data types, however, questionnaire data that are used for calculation of Cronbach's $\alpha$ consist of several items, let's say $k$ and responses for those items by a group of $n$ individuals, so $n\times k$ matrix is a natural way of storing this kind of data. If you have this kind of data saved as a list (e.g., $k$ vectors of length $n$) you can always transform the list into a data.frame or a matrix.

What you have to remember with Cronbach's $\alpha$ is that it is a correlation measure, so you would get perfect $\alpha$ for a scale consisting of several items that are identical, while this would be a very poor questionnaire. So the general idea that correlated items are the best ones has its flaws and you have to remember about that. That is one of the reasons why you should rather not use $\alpha$ alone for psychometric analysis, but combine it with other methods, e.g. with Item Response Theory based methods being one of the most popular nowadays (check e.g. Comparison of Classical Test Theory and Item Response Theory and Their Applications to Test Development paper by Ronald K. Hambleton and Russell W. Jones ).

Check out also alpha documentation or the tutorial on personality-project.org (site by psych library developer with a great deal of information about psychometrics and R).