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)a matrix or a data.frame containing the items as columns.
logical; if TRUE the standardized Cronbach's alpha is computed.
logical; if TRUE a Bootstrap confidence interval for Cronbach's alpha is computed.
a numeric vector of length two indicating which quantiles to use for the Bootstrap CI.
the number of Bootstrap samples to use.
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)
# }
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