Robust estimation of Cronbachʹs alpha

Cronbachʹs alpha is a popular method to measure reliability, e.g. in quantifying the reliability of a score to summarize the information of several items in questionnaires. The alpha coefficient is known to be non-robust. We study the behavior of this coefficient in different settings to identify situations where Cronbachʹs alpha is extremely sensitive to violations of the classical model assumptions. Furthermore, we construct a robust version of Cronbachʹs alpha which is insensitive to a small proportion of data that belong to a different source. The idea is that the robust Cronbachʹs alpha reflects the reliability of the bulk of the data. For example, it should not be possible that some small amount of outliers makes a score look reliable if it is not.