asbio (version 1.5-5)

Kullback: Kullback test for equal covariance matrices.

Description

Provides Kullback's (1959) test for multivariate homoscedasticity.

Usage

Kullback(Y, X)

Arguments

Y

An n x p matrix of quantitative variables

X

An n x 1 vector of categorical assignments (e.g. factor levels)

Value

Returns a dataframe with the test statistic (which follows a chi-square distribution if H\(_0\) is true), the chi-square degrees of freedom, and the calculated p-value. Invisible objects include the within group dispersion matrix.

Details

Multivariate general linear models assume equal covariance matrices for all factor levels or factor level combinations. Legendre and Legendre (1998) recommend this test for verifying homoscedasticity. P-values concern a null hypothesis of equal population covariance matrices. P-values from the test are conservative with respect to type I error.

References

Kullback, S. (1959) Information Theory and Statistics. John Wiley and Sons.

Legendre, P, and Legendre, L. (1998) Numerical Ecology, 2nd English edition. Elsevier, Amsterdam, The Netherlands.

Examples

# NOT RUN {
Y1<-rnorm(100,10,2)
Y2<-rnorm(100,15,2)
Y3<-rnorm(100,20,2)
Y<-cbind(Y1,Y2,Y3)
X<-factor(c(rep(1,50),rep(2,50)))
Kullback(Y,X)
# }