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.

See Also

roystonTest hzTest mvnPlot mvOutlier uniPlot uniNorm

Examples

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