Internal Consistency - Cronbach's Alpha

Cronbach's Alpha

Internal consistency is usually measured with Cronbach's alpha, a statistic calculated from the pairwise correlations between items. Internal consistency ranges between zero and one. A commonly accepted rule of thumb for describing internal consistency is as follows:

Very high reliabilities (0.95 or higher) are not necessarily desirable, as this indicates that the items may be entirely redundant. The goal in designing a reliable instrument is for scores on similar items to be related (internally consistent), but for each to contribute some unique information as well.

An alternative way of thinking about internal consistency is that it is the extent to which all of the items of a test measure the same latent variable. The advantage of this perspective over the notion of a high average correlation among the items of a test - the perspective underlying Cronbach's alpha - is that the average item correlation is affected by skewness (in the distribution of item correlations) just as any other average is. Thus, whereas the modal item correlation is zero when the items of a test measure several unrelated latent variables, the average item correlation in such cases will be greater than zero. Thus, whereas the ideal of measurement is for all items of a test to measure the same latent variable, alpha has been demonstrated many times to attain quite high values even when the set of items measures several unrelated latent variables. The hierarchical "Coefficient omega" may be a more appropriate index of the extent to which all of the items in a test measure the same latent variable. Several different measures of internal consistency are reviewed by Revelle & Zinbarg (2009).