sirt (version 0.36-30)

stratified.cronbach.alpha: Stratified Cronbach's Alpha

Description

This function computes the stratified Cronbach's Alpha for composite scales (Cronbach, Schoenemann & McKie, 1965; Meyer, 2010).

Usage

stratified.cronbach.alpha(data, itemstrata=NULL)

Arguments

data

An $N \times I$ data frame

itemstrata

A matrix with two columns defining the item stratification. The first column contains the item names, the second column the item stratification label (these can be integers). The default $NULL$ does only compute Cronbach's Alpha for the whole scale.

References

Cronbach, L.J., Schoenemann, P., & McKie, D. (1965). Alpha coefficient for stratified-parallel tests. Educational and Psychological Measurement, 25, 291-312. Meyer, P. (2010). Reliability. Cambridge: Oxford University Press.

Examples

data( data.read )
dat <- data.read
I <- ncol(dat)

# apply function without defining item strata
stratified.cronbach.alpha( data.read  )

# define item strata
itemstrata <- cbind( colnames(dat) , substring( colnames(dat) , 1 ,1 ) )
stratified.cronbach.alpha( data.read , itemstrata=itemstrata )
##   scale  I alpha mean.tot var.tot alpha.stratified
## 1 total 12 0.677    8.680   5.668            0.703
## 2     A  4 0.545    2.616   1.381               NA
## 3     B  4 0.381    2.811   1.059               NA
## 4     C  4 0.640    3.253   1.107               NA

#**************************
# reliability analysis in psych package
library(psych)
# Cromnbach's alpha and item discriminations
alpha( dat )
# McDonald's omega
omega(dat , nfactors=1)     # 1 factor
##   Alpha:                 0.69 
##   Omega Total            0.69 
##  => Note that alpha in this function is the standardized Cronbach's
##     alpha, i.e. alpha computed for standardized variables.
omega(dat , nfactors=2)     # 2 factors
##   Omega Total            0.72 
omega(dat , nfactors=3)     # 3 factors  
##   Omega Total            0.74