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

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

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.

`cronbach.alpha()`

returns an object of class `cronbachAlpha`

with components

the value of Cronbach's alpha.

the number of sample units.

the number of items.

a copy of the `standardized`

argument.

the name of argument `data`

.

the confidence interval for alpha; returned if `CI = TRUE`

.

a copy of the `probs`

argument; returned if `CI = TRUE`

.

a copy of the `B`

argument; returned if `CI = TRUE`

.

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`

.

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

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

Run the code above in your browser using DataLab