Despite much criticism, almost all of it criticising people for using Cronbach’s alpha without really understanding it and either overclaiming for what it does or tacitly implying it does more than it does, Cronbach’s alpha remains the most used index of internal reliability in our fields.
Details #
Let’s keep this simple. This is all about multi-item measures, whether structured interviews, observational checklist rating scales or the ubiquitous multi-item self-completion questionnaires that so dominate our research field.
The idea behind internal reliability is that if the items in the rating scale or questionnaire do reflect something we want to measure as a dimension on which the participants vary, then the scores on the items, across a group of participants, should show strong intercorrelation with each other.
Cronbach’s alpha is the proportion of the covariance between the scores on the items of a multi-item measure to the variance of the item total score across a dataset of completions of the measure. Thus its upper limit is 1.0 and would indicate that the responses to all the items across the dataset were perfectly correlated, its doesn’t have a general lower limit but a value of zero would show that there was no covariance shared across all the items so their total could not be a reliable (or useful) measure of anything.
Cronbach’s alpha tells you nothing about the dimensionality of the responses so a high value could arise from a perfect unidimensional source of variance across the responses from the participants suggesting that the measure is a very pure measure of one latent variable. However, high values can also be seen when multiple latent variables contribute to the covariance of the responses to the items and alpha could be high even if these latent variables were completely uncorrelated: alpha is only an (near) upper bound of possible unidimensional reliability. It tells you nothing about the construct validity and the dimensionality of the responses. Cronbach was perfectly clear about this in the original 1951 paper (Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297–334. It’s not an easy read but it is a great paper!)
It is also only a “near” upper bound for unidimensional internal reliability and where the variances of the items is not pretty uniform and where the area is not unidimensional, whether importantly not or trivially, unimportantly, not there are arguments that McDonald’s Omega is a better measure. In my experience, for most fairly usable measures, the difference between the two for any particular dataset is generally not huge but that’s starting to get us into more detail than we need here!
Try also #
- Internal reliability
- McDonald’s Omega
- Psychometrics
- Reliability
Chapters #
Chapter 3, “How to judge the quality of an outcome measure” in the OMbook.
Online resources #
None yet.
Dates #
First created 30.viii.25, tweaked 2.ix.25 to improve explanation and 3.ix.95 to add link to new internal reliability glossary item.
