| Type: | Package |
| Title: | Cronbach's Alpha |
| Version: | 0.3 |
| Date: | 2025-07-21 |
| Author: | Michail Tsagris [aut, cre], Constantinos Frangos [aut], Christos Frangos [ctb] |
| Maintainer: | Michail Tsagris <mtsagris@uoc.gr> |
| Depends: | R (≥ 3.6.0) |
| Imports: | boot, Rfast, Rfast2, stats |
| Description: | Cronbach's alpha and various formulas for confidence intervals. The relevant paper is Tsagris M., Frangos C.C. and Frangos C.C. (2013). "Confidence intervals for Cronbach's reliability coefficient". Recent Techniques in Educational Science, 14-16 May, Athens, Greece. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| NeedsCompilation: | no |
| Packaged: | 2025-07-21 11:41:49 UTC; mtsag |
| Repository: | CRAN |
| Date/Publication: | 2025-07-21 12:10:09 UTC |
Cronbach's Alpha
Description
Cronbach's alpha and various formulas for confidence intervals.
Details
| Package: | fsn |
| Type: | Package |
| Version: | 0.3 |
| Date: | 2025-07-21 |
| License: | GPL-2 |
Maintainers
Michail Tsagris <mtsagris@uoc.gr>
Note
Acknowledgments:
Michai Tsagris would like to express his gratitude to Linus Banse for spotting a bug in the function cronfree.ci() when type is "whalen" which has now been fixed.
Author(s)
Michail Tsagris mtsagris@uoc.gr, Constantinos Frangos kfragkos@outlook.com and Christos Frangos cfragos@teiath.gr.
References
Cronbach L. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3): 297–334.
Tsagris M., Frangos C.C. and Frangos C.C. (2013). Confidence intervals for Cronbach's reliability coefficient. Recent Techniques in Educational Science, 14-16 May, Athens, Greece. http://www.academia.edu/download/32613010/Cronbachs_alpha.pdf
Confidence intervals for Cronbach's alpha
Description
Confidence intervals for Cronbach's alpha.
Usage
cron.ci(x, conf = 0.95, type = "logit", B = 1000)
Arguments
x |
A numerical matrix with the data. |
conf |
The confidence level of the interval |
type |
The type of the confidence interval, "logit", "zyl", "boot", "bca.boot", or "cheap.boot. See details for more information. |
B |
This relevant only for the bootstrap based confidence interval. It is the number of bootstrap samples to generate. |
Details
This function contains some confidence intervals for Cronbach's alpha as described in Tsagris, Frangos and Frangos (2013). In particular, the type "zyl" refers to estimating the variance of alpha as suggested by van Zyl J., Neudecker H. and Nel D. (2000) and then constructing the classical confidence interval. The type "logit" computes the logit transformation and then approximates the variance based on the Delta method. This makes use of the variance as computed by van Zyl J., Neudecker H. and Nel D. (2000). The type "boot" computes the classical percentile type of bootstrap, whereas the "bca.boot" computes BCa confidence intervals. Finally, the "cheap.boot" option computes the cheap bootstrap confidence intervals proposed by Lam (2022). In this case, the B needs not be more than 100, even 50 should be enough.
Value
A confidence interval for the true value of alpha.
Author(s)
Michail Tsagris, Christos Frangos and Constantinos Frangos.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr, Christos Frangos cfragos@teiath.gr and Constantinos Frangos kfragkos@outlook.com.
References
Tsagris M., Frangos C.C. and Frangos C.C. (2013). Confidence intervals for Cronbach's reliability coefficient. Recent Techniques in Educational Science, 14-16 May, Athens, Greece. http://www.academia.edu/download/32613010/Cronbachs_alpha.pdf
van Zyl J., Neudecker H. and Nel D. (2000). On the distribution of the maximum likelihood estimator of Cronbach's alpha. Psychometrika, 65(3): 271–280
Efron B. and Tibshirani, R.J. (1993). An introduction to the bootstrap. Chapman & Hall CRC.
Cronbach L. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3): 297–334.
Lam H. (2022). A cheap bootstrap method for fast inference. arXiv preprint.
See Also
Examples
## silly example
x <- as.matrix( iris[1:50, 1:4] )
Cronbach::cron.ci(x)
Confidence intervals for Cronbach's alpha without the data
Description
Confidence intervals for Cronbach's alpha without the data.
Usage
cronfree.ci(a, p, n, conf = 0.95, type = "kf")
Arguments
a |
The Cronbach's alpha. |
p |
The number of items or variables. |
n |
The sample size of the data. |
conf |
The confidence level of the interval |
type |
The type of confidence interval to compute, "kf" or "whalen". See details for more information. |
Details
This function contains some confidence intervals for Cronbach's alpha. The "kf" was described in Tsagris, Frangos and Frangos (2013) and stands for the method of Koning A. and Franses H. P. (2006). The "whalen" stands for the method of Rodriguez and Maeda (2006). The difference with the confidence intervals produced by cron.ci is that with these methods the data are not necessary.
Value
A confidence interval for the true value of alpha.
Author(s)
Michail Tsagris, Christos Frangos and Constantinos Frangos.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr, Christos Frangos cfragos@teiath.gr and Constantinos Frangos kfragkos@outlook.com.
References
Tsagris M., Frangos C.C. and Frangos C.C. (2013). Confidence intervals for Cronbach's reliability coefficient. Recent Techniques in Educational Science, 14-16 May, Athens, Greece. http://www.academia.edu/download/32613010/Cronbachs_alpha.pdf
Rodriguez M. C. and Maeda Y. (2006). Meta-analysis of coefficient alpha. Psychological methods, 11(3): 306–322.
Koning A. and Franses H. P. (2006). Confidence intervals for Cronbach's coefficient alpha values. Technical report, Erasmus Research Institute of Management-ERIM.
Cronbach L. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3): 297–334.
See Also
Examples
## silly example
x <- as.matrix( iris[1:50, 1:4] )
a <- Cronbach::cronbach(x)
Cronbach::cronfree.ci(a, 4, 150)
Cronbach's alpha
Description
Cronbach's alpha.
Usage
cronbach(x)
Arguments
x |
A numerical matrix with the data. |
Details
This function computes Cronbach's alpha internal reliability coefficient.
Value
The Cronbach's alpha.
Author(s)
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
References
Cronbach L. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3): 297–334.
See Also
Examples
## silly example
x <- as.matrix( iris[1:50, 1:4] )
Cronbach::cronbach(x)