cocron (version 1.0-1)

cocron.n.coefficients: Statistical comparisons of n alpha coefficients

Description

Performs a test of significance for the difference between $n$ alpha coefficients (Cronbach, 1951). The function expects alpha coefficients as input.

Usage

cocron.n.coefficients(alpha, n, items = NULL, dep = FALSE, r = NULL, los = 0.05, conf.level = 0.95)

Arguments

alpha

A numeric vector containing the alpha coefficients.

n

A numeric vector containing the number of individuals who provided the data for the test for which alpha coefficients were determined.

items

A numeric vector containing the number of items the alpha coefficients are based on.

dep

A logical indicating whether the alpha coefficients are based on dependent groups of individuals (default is FALSE).

r

A matrix that contains in the upper triangle all correlations between the scores the alpha coefficients are based on (see examples). Only required if the alpha coefficients are computed for dependent groups of individuals (dep = TRUE).

los

A number indicating the level of significance (default is .05).

conf.level

A number defining the level of confidence for the confidence intervals of the alpha coefficients (default is $.95$; see cronbach.alpha.CI). The confidence intervals serve as additional information only, they are not used for the test of significance.

Value

Returns an object of the class "cocron.n.coefficients" with the following slots:

alpha

Input parameter

n

Input parameter

items

Input parameter

dep

Input parameter

r

Input parameter

los

Input parameter

conf.level

Input parameter

statistic

The value of the test statistic

distribution

The distribution of the test statistic

df

The degrees of freedom of the distribution of the test statistic

p.value

The p-value of the test

conf.int

The confidence intervals of the alpha coefficients

Details

To compare $n$ dependent or independent alpha coefficients (Cronbach, 1951), the methods by Feldt, Woodruff, and Salih (1987) are implemented.

References

Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334.

Feldt, L. S., Woodruff, D. J., & Salih, F. A. (1987). Statistical inference for coefficient alpha. Applied Psychological Measurement, 11, 93-103.

See Also

cocron, cocron.two.coefficients

Examples

# independent alpha coefficients
cocron.n.coefficients(alpha=c(.784,.875,.936), items=c(5,5,5), n=c(51,101,151),
dep=FALSE)

# dependent alpha coefficients
r <- rbind(
 c(1,.8,.6,.75),
 c(NA,1,.65,.7),
 c(NA,NA,1,.55),
 c(NA,NA,NA,1)
)
cocron.n.coefficients(alpha=c(.857,.875,.800,.833), items=c(50,40,35,25), n=100,
dep=TRUE, r=r)