An R
package for doing inference with coefficient alpha
(Cronbach, 1951) and standardized alpha (Falk & Savalei, 2011). Many
methods are supported, with special emphasis on small samples and
nonnormality.
The package is not available on CRAN
yet, so use the
following command from inside R
:
# install.packages("remotes")
::install_github("JonasMoss/alphaci") remotes
Call the library
function and load some data:
library("alphaci")
library("psychTools")
< bfi[, 1:5]
x 1] < 7  x[, 1] # Reversecoded item.
x[, head(x)
#> A1 A2 A3 A4 A5
#> 61617 5 4 3 4 4
#> 61618 5 4 5 2 5
#> 61620 2 4 5 4 4
#> 61621 3 4 6 5 5
#> 61622 5 3 3 4 5
#> 61623 1 6 5 6 5
Then calculate an asymptotically distributionfree confidence interval for
alphaci(x)
#> Call: alphaci(x = x)
#>
#> 95% confidence interval (n = 2709).
#> 0.025 0.975
#> 0.6828923 0.7246195
#>
#> Sample estimates.
#> alpha sd
#> 0.7037559 0.5536964
You can also calculate confidence intervals for standardized alpha
alphaci_std(x)
#> Call: alphaci_std(x = x)
#>
#> 95% confidence interval (n = 2709).
#> 0.025 0.975
#> 0.6828923 0.7246195
#>
#> Sample estimates.
#> alpha sd
#> 0.7037559 0.5536964
alphaci
supports three basic asymptotic confidence
interval constructios. The asymptotically distributionfree interval of
MaydeuOlivares et al. 2007, the pseudoelliptical construction of Yuan
& Bentler (2002), and the normal method of van Zyl et al.,
(1999).
Method  Description 

adf 
The asymptotic distribution free method (MaydeuOlivares et al. 2007). The method is asymptotically correct, but has poor smallsample performance. 
elliptical 
The elliptical or pseudoelliptical kurtosis correction (Yuan &
Bentler, 2002). Uses the unbiased sample estimator of the common
kurtosis (Joanes, 1998). Has better smallsample performance than
adf and normal if the kurtosis is large and

normal 
Assumes normality of 
Standardized alpha, computed with alpha_std
, support the
same type
arguments. Their formulas can be derived using
the methods of Hayashi and Kamata (2005) and Neudecker (2007).
In addition, you may transform the intervals using one of four transforms:
The option bootstrap
does studentized bootstrapping
Efron, B. (1987) with n_reps
repetitions. If
bootstrap = FALSE
, an ordinary normal approximation will be
used. The studentized bootstrap intervals are is a secondorder correct,
so its confidence intervals will be better than the normal approximation
when
Finally, the option parallel = TRUE
can be used, which
is suitable if covariance matrix
where
There are several R
packages that make confidence
intervals for coefficient alpha, but not much support for standardized
alpha. Most packages use some sort of normality assumption.
The alpha
and alpha.ci
functions of psych
calculates confidence intervals for coefficient alpha following normal
theory. semTools
calculates numerous reliability coefficients with its
reliability
function. The Cronbach
package provides confidence intervals based on normal theory, as does
the alpha.CI
function of psychometric
.
Confidence intervals for both alphas can, in principle, be calculated
using structural equation modeling together with the delta method.
Packages such as lavaan
can be used for this purpose, but this is seldom done.
If you encounter a bug, have a feature request or need some help, open a Github issue. Create a pull requests to contribute.