cronbach.alpha | R Documentation |
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 |
standardized |
logical; if |
CI |
logical; if |
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 |
The Cronbach's alpha computed by cronbach.alpha()
is defined as follows
alpha = (p / (p - 1)) (1 - (∑_{i=1}^p sigma_{y_i}^2/ sigma_x^2)),
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 = (p r) / (1 + (p - 1) r),
where p is the
number of items, and 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.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 |
name |
the name of argument |
ci |
the confidence interval for alpha; returned if |
probs |
a copy of the |
B |
a copy of the |
Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl
Cronbach, L. J. (1951) Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297–334.
# Cronbach's alpha for the LSAT data-set # with a Bootstrap 95% CI cronbach.alpha(LSAT, CI = TRUE, B = 500)
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