psych (version 1.0-17)

alpha.scale: Cronbach alpha for a scale

Description

Find Cronbach's coefficient alpha given a scale and a data.frame of the items in the scale. For X, a total score composed of items in the data.frame Y, find Cronbach's alpha.

Usage

alpha.scale(x, y)

Arguments

x

A scale made by summing items

y

A data frame of items

Value

• Coefficient alpha

Details

Alpha is one of several estimates of the internal consistency reliability of a test. Perhaps because it is so easy to calculate, it is without doubt the most frequently reported measure of internal consistency reliability. Alpha is the mean of all possible spit half reliabilities (corrected for test length). For a unifactorial test, it is a reasonable estimate of the first factor saturation, although if the test has any microstructure (i.e., if it is "lumpy") coefficients beta and omega are more appropriate estimates of the general factor saturation.

Alpha is a positive function of the number of items in a test as well as the average intercorrelation of the items in the test. When calculated from the item variances and total test variance, as is done here, alpha is sensitive to differences in the item variances. Alternative functions score.items and cluster.cor will also score multiple scales and report more useful statistics. "Standardized" alpha is calculated from the inter-item covariances and will differ from raw alpha. Standardized alpha can be found by using cluster.cor.

References

http://personality-project.org/revelle/syllabi/405.syllabus.html

See Also

score.items, cluster.cor, ICLUST, omega, describe,pairs.panels, alpha in psychometrics

Examples

y <- attitude     #from the datasets package
x <- rowSums(y)   #find the sum of the seven attitudes
alpha.scale(x,y)
#[1] 0.8431428
#compare with standardized alpha:
st.alpha <- cluster.cor(rep(1,7),cor(attitude),digits=4)
st.alpha 
#compare with score.items
si <- score.items(rep(1,7), attitude,digits=3)
si$alpha


## The function is currently defined as
function (x,y)   #find coefficient alpha given a scale and 
#a data.frame of the items in the scale
	{
		n=length(y)          #number of variables
		Vi=sum(diag(var(y,na.rm=TRUE)))     #sum of item variance
		Vt=var(x,na.rm=TRUE)                #total test variance
		((Vt-Vi)/Vt)*(n/(n-1))}              #alpha