Cronbach's Alpha

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Description

Calculates Cronbach's alpha (Cronbach, 1951), a coefficient of internal consistency. The coefficient typically serves as an estimate of the reliability of a psychometric test.

Usage

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cronbach.alpha(x, standardized = FALSE)

Arguments

x

A numeric data.frame/matrix with rows and columns corresponding to individuals and items, respectively.

standardized

A logic indicating whether a standardized Cronbach alpha should be calculated (default is FALSE).

Details

For a test consisting of k items that measures a quantity X, Cronbach's alpha is defined as

α = (k/k - 1)(1 - (∑_{i=1}^{k}{σ_Y}_i^2/σ_X^2))

with X = Y_1 + Y_2 + ... + Y_k. {σ_Y}_i^2 is the variance of item i, and σ_X^2 the variance of the total test score for a sample of individuals that completed the test.

The standardized Cronbach's alpha is defined as

α_s = (k\overline{r})/(1 + (k - 1)\overline{r})

where k is the number of items and \overline{r} the mean correlation between the items.

Cases that have missing values on any of the items are excluded.

Value

Returns Cronbach's alpha as a numeric object.

References

Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334.

See Also

cocron, cocron.n.coefficients, cocron.two.coefficients

Examples

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