mvShapiro.Test {mvShapiroTest}

Generalized Shapiro-Wilk test for multivariate normality

Description

Given a d-dimensional random sample of size n, this function computes the test statistic and p-value of the Shapiro-Wilk test for multivariate normality proposed by Villasenor-Alva and Gonzalez-Estrada (2009).

Usage

mvShapiro.Test(X)

Arguments

X

Numeric data matrix with d columns (vector dimension) and n rows (sample size).

Details

n must be larger than d.

When d=1, mvShapiro.Test(X) produces the same results as shapiro.test(X).

Value

A list with class "htest" containing the following components.

statistic

the value of the generalized Shapiro-Wilk statistic for testing multivariate normality.

p.value

the p-value of the test.

method

the character string "Generalized Shapiro-Wilk test for multivariate normality".

data.name

a character string giving the name of the data set.

Author(s)

Elizabeth Gonzalez-Estrada [e-mail], Jose A. Villasenor-Alva

References

Villasenor-Alva, J.A. and Gonzalez-Estrada, E. (2009). A generalization of Shapiro-Wilk's test for multivariate normality. Communications in Statistics: Theory and Methods,38 11,1870-1883.

See Also

shapiro.test

Examples

X <-  matrix(rnorm(40),ncol=2)    # Generating a two dimensional random sample of size 20
mvShapiro.Test(X)                 # Testing multivariate normality on X

#-----------------------------------------------------------------------------------
# iris.virginica contains a set of measurements corresponding to 
# Iris virginica of the famous  iris dataset.

iris.virginica <- as.matrix(iris[iris$Species == "virginica",1:4],ncol=4) 
mvShapiro.Test(iris.virginica)    # Testing multivariate normality on iris.virginica