On the Behavior of the Reliability Index Coefficient Alpha and its Variance: Analytical Results for One and Two Samples

Coefficient alpha is a frequently used index of survey reliability, reflecting the internal consistency of a measurement scale. Coefficient alpha is a function of scale length and item correlation. Its variance estimator is a function of these components and the corresponding standard error also a function of sample size. This research presents analytical results which systematically examine the influence of these components' sample size, scale length, and item correlation on the behavior of coefficient alpha and its variance and standard error. While coefficient alpha is half a century old, these analytics have not yet been documented. The variance and standard error are newer developments, and here too, the analytics offer the first such demonstrations of the effects of the formulae components. This paper then proceeds to extend the investigation to the assessment of the difference between coefficient alphas derived from independent samples. In the generalization to two samples, we consider the differential effects of the two sample sizes, their comparative respective scale lengths, and the possibility that the items may be more highly correlated for one sample than the other.