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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.
Note further that Cronbach's alpha is necessarily higher for tests measuring more narrow constructs, and lower when more generic, broad constructs are measured. This phenomenon, along with a number of other reasons, argue against using objective cut-off values for internal consistency measures. [4]
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]
For the reliability of a two-item test, the formula is more appropriate than Cronbach's alpha (used in this way, the Spearman-Brown formula is also called "standardized Cronbach's alpha", as it is the same as Cronbach's alpha computed using the average item intercorrelation and unit-item variance, rather than the average item covariance and ...
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.
The average Cronbach's alpha is .71. It is available in 19 languages and has been used worldwide. Support materials for interpretation and training are available in each language.
A quantity similar (but not mathematically equivalent) to congeneric reliability first appears in the appendix to McDonald's 1970 paper on factor analysis, labeled . [2] In McDonald's work, the new quantity is primarily a mathematical convenience: a well-behaved intermediate that separates two values.
If the correlation between separate administrations of the test is high (e.g. 0.7 or higher as in this Cronbach's alpha-internal consistency-table [6]), then it has good test–retest reliability. The repeatability coefficient is a precision measure which represents the value below which the absolute difference between two repeated test results ...