When the assumption of essential -equivalence of the components is violated, alpha is not an unbiased estimator of reliability. A factor analysis may then produce artificial factors that are related to the differential skewnesses of the components.
These circumstances make it unlikely that the items have a linear regression on a common factor. This is caused by the facts that (1) most test developers invariably include items with a range of difficulties (or stimuli that vary in their standing on the latent trait, in the case of personality, attitude or other non-cognitive instruments), and (2) the item scores are usually bounded from above and below. Although the assumption of essential -equivalence may sometimes be met (at least approximately) by testlets, when applied to items it is probably never true. One special case of essential -equivalence is that the components are parallel. Under this condition the components can have different means and different variances, but their covariances should all be equal - which implies that they have 1 common factor in a factor analysis. For this reason the coefficient is also called the internal consistency or the internal consistency reliability of the test.Ĭronbach's alpha in classical test theoryĪlpha is an unbiased estimator of reliability if and only if the components are essentially -equivalent (Lord & Novick, 1968 ). Where N is the number of components (items or testlets), equals the average variance and is the average of all covariances between the components.Ĭronbach's alpha and internal consistencyĬronbach's alpha will generally increase when the correlations between the items increase. Where is the number of components (items or testlets), is the variance of the observed total test scores, and is the variance of component i.Īlternatively, the standardized Cronbach's can also be defined as 7 Cronbach's alpha and other disciplines.5 Cronbach's alpha and the intra-class correlation.4 Cronbach's alpha in generalizability theory.
3 Cronbach's alpha in classical test theory.2 Cronbach's alpha and internal consistency.
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