ltm (version 1.1-1)

# cronbach.alpha: 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.

## 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.

## 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 $$i$$th 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.

## References

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

## Examples

# NOT RUN {
# Cronbach's alpha for the LSAT data-set
# with a Bootstrap 95% CI
cronbach.alpha(LSAT, CI = TRUE, B = 500)

# }