cronbach.alpha(data, standardized = FALSE, CI = FALSE,
probs = c(0.025, 0.975), B = 1000, na.rm = FALSE)matrix or a data.frame containing the items as columns.TRUE the standardized Cronbach's alpha is computed.TRUE a Bootstrap confidence interval for Cronbach's alpha is computed.NA's.cronbach.alpha() returns an object of class cronbachAlpha with componentsstandardized argument.data.CI = TRUE.probs argument; returned if CI = TRUE.B argument; returned if CI = TRUE.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'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