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Concept
Cronbach's alpha
Summary
Cronbach's alpha (Cronbach's ), also known as rho-equivalent reliability () or coefficient alpha (coefficient ), is a reliability coefficient and a measure of the internal consistency of tests and measures.
Numerous studies warn against using it unconditionally. Reliability coefficients based on structural equation modeling (SEM) or generalizability theory are superior alternatives in many situations.
Lee Cronbach first named the coefficient in 1951 with his initial publication, Cronbach's alpha. The publication also conceived an additional method to derive it, after implicit use in previous studies. His interpretation of the coefficient was thought to be more intuitively attractive compared to those of previous studies. This made them quite popular.
In 1967, Melvin Novick and Charles Lewis proved that is equal to reliability if the true scores of the compared tests or measures vary by a constant, which is independent of the persons measured. In this case, the tests or measurements are said to be "essentially tau-equivalent".
In 1978, Cronbach asserted that the reason his initial 1951 publication was widely cited was "mostly because [he] put a brand name on a common-place coefficient." He explained that he had originally planned to name other types of reliability coefficients, such as those used in inter-rater reliability and test-retest reliability, after consecutive Greek letters (i.e., , , etc.), but later changed his mind.
Later, in 2004, Cronbach and Richard Shavelson encouraged readers to use generalizability theory rather than . Cronbach opposed the use of the name "Cronbach's alpha" and explicitly denied the existence of studies that had published the general formula of KR-20 prior to Cronbach's 1951 publication of the same name.
In order to use Cronbach's alpha as a reliability coefficient, the following conditions must be met:
The data is normally distributed and linear;
The compared tests or measures are essentially tau-equivalent;
Errors in the measurements are independent.
Official source
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