DH.test {asbio} | R Documentation |

## Doornik-Hansen test for multivariate normality.

### Description

The Doornik-Hansen test for multivariate normality is a powerful alternative to the Shapiro-Wilk test.

### Usage

```
DH.test(Y, Y.names = NULL)
```

### Arguments

`Y` |
An |

`Y.names` |
Names of |

### Details

An assumption of multivariate normality is exceedingly difficult to verify. Hypothesis
tests tend to be too stringent, and multivariate diagnostic plots only allow viewing
of two variables at a time. Univariate normality of course can be verified using normal
probability plots. However while marginal non-normality indicates multivariate non-normality,
marginal normality does not insure that *Y* variables collectively follow a multivariate normal
distribution.

The Doornik-Hansen test for multivariate normality (Doornik and Hansen 2008) is based on the
skewness and kurtosis of multivariate data that is transformed to insure independence.
The DH test is more powerful than the Shapiro-Wilk test for most tested multivariate
distributions (Doornik and Hansen 2008). The function `DH.test`

also runs the Doornik-Hansen
test for both multivariate and univariate normality. The later test follows
directly from the work of Bowman and Shenton (1975), Shenton and Bowman (1977) and D'Agostino (1970).

### Value

Returns a list with two objects.

`multi` |
A dataframe containing multivariate results, i.e. the test statistic, |

`comp2` |
A dataframe with |

### Note

As with all inferential normality tests our null hypothesis is that the underlying population is normal, in this case multivariate normal.

### Author(s)

Ken Aho

### References

D'Agostino, R. B. (1970). Transformation to normality of the null distribution of g1, *Biometrika*
57: 679-681.

Doornik, J.A. and Hansen, H. (2008). An Omnibus test for univariate and multivariate
normality. *Oxford Bulletin of Economics and Statistics* 70, 927-939.

Shenton, L. R. and Bowman, K. O. (1977). A bivariate model for the distribution of b1 and b2,
*Journal of the American Statistical Association* 72: 206.211.

### See Also

### Examples

```
data(iris)#The ubiquitous multivariate iris data.
DH.test(iris[,1:4],Y.names=names(iris[,1:4]))
```

*asbio*version 1.9-7 Index]