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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.
The name of this formula stems from the fact that is the twentieth formula discussed in Kuder and Richardson's seminal paper on test reliability. [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 ...
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. The ...
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 ...
Related coefficients are tau-equivalent reliability (; traditionally known as "Cronbach's ") and congeneric reliability (; also known as composite reliability) which can be used to evaluate the reliability of tau-equivalent and congeneric measurement models, respectively.
Unfortunately, there is no way to directly observe or calculate the true score, so a variety of methods are used to estimate the reliability of a test. Some examples of the methods to estimate reliability include test-retest reliability, internal consistency reliability, and parallel-test reliability. Each method comes at the problem of ...
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 ...
where is the separation index of the set of estimates of , which is analogous to Cronbach's alpha; that is, in terms of classical test theory, is analogous to a reliability coefficient. Specifically, the separation index is given as follows: