On Cronbach’s alpha as the mean of all split-half reliabilities

Abstract

A famous description of Cronbach’s alpha is that it is the mean of all (Flanagan–Rulon) split-half reliabilities. The result is exact if the test is split into two halves that are equal in size. This requires that the number of items is even, since odd numbers cannot be split into two groups of equal size. In this chapter it is shown that alpha is approximately identical to the mean of all split-half reliabilities, if a test consists of an odd number of items and has at least eleven items.