On Cronbach’s Alpha as the Mean of All Possible k-Split Alphas

Coefficient alpha is the most commonly used internal consistency reliability coefficient. Alpha is the mean of all possible k-split alphas if the items are divided into k parts of equal size. This result gives proper interpretations of alpha: interpretations that also hold if (some of) its assumptions are not valid. Here we consider the cases where the items cannot be split into parts of equal size. It is shown that if a k-split is made such that the items are divided as evenly as possible, the difference between alpha and the mean of all possible k-split alphas can be made arbitrarily small by increasing the number of items.