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Alpha is also a function of the number of items, so shorter scales will often have lower reliability estimates yet still be preferable in many situations because they are lower burden. 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 .
Cronbach's alpha (Cronbach's ), also known as tau-equivalent reliability or coefficient alpha (coefficient ), is a reliability coefficient and a measure of the internal consistency of tests and measures. [1] [2] [3] It was named after the American psychologist Lee Cronbach.
It is a special case of Cronbach's α, computed for dichotomous scores. [2] [3] It is often claimed that a high KR-20 coefficient (e.g., > 0.90) indicates a homogeneous test. However, like Cronbach's α, homogeneity (that is, unidimensionality) is actually an assumption, not a conclusion, of reliability coefficients.
Aickin's α; Andres and Marzo's delta; Bangdiwala's B; Bennett, Alpert, and Goldstein’s S; Brennan and Prediger’s κ; Coefficient of colligation - Yule's Y; Coefficient of consistency
The most common internal consistency measure is Cronbach's alpha, which is usually interpreted as the mean of all possible split-half coefficients. [9] Cronbach's alpha is a generalization of an earlier form of estimating internal consistency, Kuder–Richardson Formula 20. [9]
The Cronbach's alpha was used to obtain reliability measures. Across one group of nine studies, alpha measures were 0.71-0.89, reflecting good internal consistency. The test adequately measures for depressive symptoms. [1] In another group of 16 studies of test-retest reliability, alpha measures were reported as 0.38–0.87. [1]
In a 1978 published analysis of 86 responses, Thomas and Kilmann determined that the TKI exhibited moderate test-retest repeatability, moderate internal consistency (measured by Cronbach's alpha), and low to moderate correlation with three other instruments. [2]
The separation index is typically very close in value to Cronbach's alpha. [ 28 ] IRT is sometimes called strong true score theory or modern mental test theory because it is a more recent body of theory and makes more explicit the hypotheses that are implicit within CTT.