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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.
Internal consistency is usually measured with Cronbach's alpha, a statistic calculated from the pairwise correlations between items. Internal consistency ranges between negative infinity and one. Coefficient alpha will be negative whenever there is greater within-subject variability than between-subject variability. [1]
[3] [4] Seemingly unaware of McDonald's work, Jöreskog first analyzed a quantity equivalent to congeneric reliability in a paper the following year. [4] [5] Jöreskog defined congeneric reliability (now labeled ρ) with coordinate-free notation, [5] and three years later, Werts gave the modern, coordinatized formula for the same. [6]
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 ]
Cronbach's can be shown to provide a lower bound for reliability under rather mild assumptions. [citation needed] Thus, the reliability of test scores in a population is always higher than the value of Cronbach's in that population. Thus, this method is empirically feasible and, as a result, it is very popular among researchers.
[1] 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.
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The range of the ICC may be between 0.0 and 1.0 (an early definition of ICC could be between −1 and +1). The ICC will be high when there is little variation between the scores given to each item by the raters, e.g. if all raters give the same or similar scores to each of the items.