Stratified Cronbach's Alpha

This function computes the stratified Cronbach's Alpha for composite scales (Cronbach, Schoenemann & McKie, 1965; He, 2010; 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. doi:10.1177/001316446502500201

He, Q. (2010). Estimating the reliability of composite scores. Ofqual/10/4703. Coventry: The Office of Qualifications and Examinations Regulation.

Meyer, P. (2010). Reliability. Cambridge: Oxford University Press.

Examples

#############################################################################
# EXAMPLE 1: data.read
#############################################################################

data(data.read, package="sirt")
dat <- data.read
I <- ncol(dat)

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

# define item strata
itemstrata <- cbind( colnames(dat), substring( colnames(dat), 1,1 ) )
sirt::stratified.cronbach.alpha( dat, 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

if (FALSE) {
#**************************
# reliability analysis in psych package
library(psych)
# Cronbach's alpha and item discriminations
psych::alpha(dat)
# McDonald's omega
psych::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.
psych::omega(dat, nfactors=2)     # 2 factors
  ##   Omega Total            0.72
psych::omega(dat, nfactors=3)     # 3 factors
  ##   Omega Total            0.74
}