Kullback {asbio} | R Documentation |

## Kullback test for equal covariance matrices.

### Description

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

### Usage

```
Kullback(Y, X)
```

### Arguments

`Y` |
An |

`X` |
An |

### 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.

### 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.

### Author(s)

Pierre Legendre is the author of the most recent version of this function asbio ver >= 1.0. Stephen Ousley discovered an error in the original code. Ken Aho was the author of the original function

### 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

```
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)
```

*asbio*version 1.9-7 Index]