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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.
Internal consistency is usually measured with Cronbach's alpha, a statistic calculated from the pairwise correlations between items. Internal consistency ranges between negative infinity and one. Coefficient alpha will be negative whenever there is greater within-subject variability than between-subject variability. [1]
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 ...
is a structural equation model (SEM)-based reliability coefficients and is obtained from on a unidimensional model. ρ C {\displaystyle \rho _{C}} is the second most commonly used reliability factor after tau-equivalent reliability ( ρ T {\displaystyle \rho _{T}} ; also known as Cronbach's alpha), and is often recommended as its alternative.
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 CFA is also called as latent structure analysis, which considers factor as latent variables causing actual observable variables. The basic equation of the CFA is X = Λξ + δ where, X is observed variables, Λ are structural coefficients, ξ are latent variables (factors) and δ are errors.
Cronbach's can be shown to provide a lower bound for reliability under rather mild assumptions. [citation needed] Thus, the reliability of test scores in a population is always higher than the value of Cronbach's in that population. Thus, this method is empirically feasible and, as a result, it is very popular among researchers.
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 ...