MVN (version 4.0)

# mardiaTest: Mardia's Multivariate Normality Test

## Description

This function performs Mardia's Multivariate Normality Test.

## Usage

`mardiaTest(data, cov = TRUE, qqplot = FALSE)`

## Arguments

data
a numeric matrix or data frame
cov
if `TRUE` covariance matrix is normalized by `n`, if `FALSE` it is normalized by `n-1`
qqplot
if `TRUE` it creates a chi-square Q-Q plot

## Value

g1p
Mardia's multivariate skewness statistic
chi.skew
Chi-square value of the skewness statistic
p.value.skew
`p-value` of the skewness statistic
g2p
Mardia's multivariate kurtosis statistic
z.kurtosis
z value of the kurtosis statistic
p.value.kurt
`p-value` of kurtosis statistic
chi.small.skew
Chi-square value of the small sample skewness statistic
p.value.small
`p-value` of small sample skew statistic

## Details

This function calculate the Mardia's multivariate skewness and kurtosis coefficients as well as their corresponding statistical significance. It can also calculate corrected version of skewness coefficient for small sample size (n< 20).

For multivariate normality, both p-values of skewness and kurtosis statistics should be greater than `0.05`.

If sample size less than 20 then `p.value.small` should be used as significance value of skewness instead of `p.value.skew`.

## References

Trujillo-Ortiz, A. and R. Hernandez-Walls. (2003). Mskekur: Mardia's multivariate skewness and kurtosis coefficients and its hypotheses testing. A MATLAB file. URL http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=3519

Mardia, K. V. (1970), Measures of multivariate skewnees and kurtosis with applications. Biometrika, 57(3):519-530. Mardia, K. V. (1974), Applications of some measures of multivariate skewness and kurtosis for testing normality and robustness studies. Sankhy A, 36:115-128.

Stevens, J. (1992), Applied Multivariate Statistics for Social Sciences. 2nd. ed. New-Jersey:Lawrance Erlbaum Associates Publishers. pp. 247-248.

`roystonTest` `hzTest` `mvnPlot` `mvOutlier` `uniPlot` `uniNorm`

## Examples

Run this code
```setosa = iris[1:50, 1:4] # Iris data only for setosa and four variables
result = mardiaTest(setosa, qqplot = TRUE)
result
```

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