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In statistical models applied to psychometrics, congeneric reliability ("rho C") [1] a single-administration test score reliability (i.e., the reliability of persons over items holding occasion fixed) coefficient, commonly referred to as composite reliability, construct reliability, and coefficient omega.
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.
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 .
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.
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.
The standard errors are normally produced as a by-product of the estimation process. The separation index is typically very close in value to Cronbach's alpha. [28] IRT is sometimes called strong true score theory or modern mental test theory because it is a more recent body of theory and makes more explicit the hypotheses that are implicit ...
In mathematics, the method of characteristics is a technique for solving partial differential equations.Typically, it applies to first-order equations, though in general characteristic curves can also be found for hyperbolic and parabolic partial differential equation.