cronbach.alpha {cocron}

Cronbach's Alpha

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

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

\alpha = \frac{k}{k - 1}\left(1 - \frac{\sum_{i=1}^{k}{\sigma_Y}_i^2}{\sigma_X^2}\right)

with X = Y_1 + Y_2 + ... + Y_k. {\sigma_Y}_i^2 is the variance of item i, and \sigma_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

\alpha_s = \frac{k\overline{r}}{\left(1 + (k - 1)\overline{r}\right)}

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

data("knowledge")

cronbach.alpha(knowledge$test1)
cronbach.alpha(knowledge$test2)