Cronbach's alpha

In statistics (classical test theory), Cronbach's ${\displaystyle \alpha }$ (alpha) is used as a (lowerbound) estimate of the reliability of a psychometric test.

It has been proposed that ${\displaystyle \alpha }$ can be viewed as the expected correlation of two tests that measure the same construct. By using this definition, it is implicitly assumed that the average correlation of a set of items is an accurate estimate of the average correlation of all items that pertain to a certain construct.

Cronbach's ${\displaystyle \alpha }$ is a function of the number of items in a test, the average covariance between item-pairs, and the variance of the total score.

It was first named alpha by Lee Cronbach in 1951, as he had intended to continue with further coefficients. The measure can be viewed as an extension of the Kuder–Richardson Formula 20 (KR-20), which is an equivalent measure for dichotomous items. Alpha is not robust against missing data. Several other Greek letters have been used by later researchers to designate other measures used in a similar context. Somewhat related is the average variance extracted (AVE).

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