Robust generalizations of classical test reliability and Cronbach's alpha

This paper describes a general class of reliability measures that contains the classical‐test‐theory measure as a special case. A particular member of this class is suggested for applied work, and some of its properties are studied. A lower bound for this new measure of reliability is derived which is a robust analogue of Cronbach's alpha. Here the term ‘robust’ is being used to describe a measure of reliability that is relatively insensitive to small fluctuations in the tails of the distributions under study. The idea is that the value of a parameter , intended to reflect reliability, should be determined by the bulk of the distribution associated with whatever is being measured. If, for example, a test is considered unreliable when test scores have a normal distribution, it should not be possible to make the test appear to be reliable with a trivial change in the tails of the distributions. It is illustrated that Cronbach's alpha does not have this characteristic. In statistical jargon, Cronbach's alpha is not a resistant measure of reliability, while the reverse is true for the new measure of reliability introduced here. Included in this paper is a method for computing a confidence interval for the new lower bound.