# 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

 1 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.

 1 2 3 4 data("knowledge") cronbach.alpha(knowledge$test1) cronbach.alpha(knowledge$test2)