R: Cronbach's alpha

cronbach.alpha {ltm}

R Documentation

Cronbach's alpha

Description

Computes Cronbach's alpha for a given data-set.

Usage


cronbach.alpha(data, standardized = FALSE, CI = FALSE, 
    probs = c(0.025, 0.975), B = 1000, na.rm = FALSE)

Arguments

`data`	a `matrix` or a `data.frame` containing the items as columns.
`standardized`	logical; if `TRUE` the standardized Cronbach's alpha is computed.
`CI`	logical; if `TRUE` a Bootstrap confidence interval for Cronbach's alpha is computed.
`probs`	a numeric vector of length two indicating which quantiles to use for the Bootstrap CI.
`B`	the number of Bootstrap samples to use.
`na.rm`	logical; what to do with `NA`'s.

Details

The Cronbach's alpha computed by cronbach.alpha() is defined as follows

\alpha = \frac{p}{p - 1}\left(1 - \frac{\sum_{i=1}^p \sigma_{y_i}^2}{\sigma_x^2}\right),

where p is the number of items \sigma_x^2 is the variance of the observed total test scores, and \sigma_{y_i}^2 is the variance of the ith item.

The standardized Cronbach's alpha computed by cronbach.alpha() is defined as follows

\alpha_s = \frac{p \cdot \bar{r}}{1 + (p - 1) \cdot \bar{r}},

where p is the number of items, and \bar{r} is the average of all (Pearson) correlation coefficients between the items. In this case if na.rm = TRUE, then the complete observations (i.e., rows) are used.

The Bootstrap confidence interval is calculated by simply taking B samples with replacement from data, calculating for each \alpha or \alpha_s, and computing the quantiles according to probs.

Value

cronbach.alpha() returns an object of class cronbachAlpha with components

`alpha`	the value of Cronbach's alpha.
`n`	the number of sample units.
`p`	the number of items.
`standardized`	a copy of the `standardized` argument.
`name`	the name of argument `data`.
`ci`	the confidence interval for alpha; returned if `CI = TRUE`.
`probs`	a copy of the `probs` argument; returned if `CI = TRUE`.
`B`	a copy of the `B` argument; returned if `CI = TRUE`.

Author(s)

Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl

References

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

Examples


# Cronbach's alpha for the LSAT data-set
# with a Bootstrap 95% CI
cronbach.alpha(LSAT, CI = TRUE, B = 500)

[Package ltm version 1.2-0 Index]