cronbach.alpha {cocron} | R Documentation |
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.
cronbach.alpha(x, standardized = FALSE)
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). |
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.
Returns Cronbach's alpha as a numeric object.
Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334.
cocron, cocron.n.coefficients, cocron.two.coefficients
data("knowledge")
cronbach.alpha(knowledge$test1)
cronbach.alpha(knowledge$test2)