msw {mvnormalTest}

Shapiro-Wilk Type (SWT) Tests for Multivariate Normality

Description

The SWT-based tests for multivariate normality including Royston's H test and the test proposed by Villasenor-Alva and Gonzalez-Estrada (2009).

Usage

msw(X)

Arguments

X

an n*p numeric matrix or data frame, the number of n must be between 3 and 5000, n>p.

Value

Returns a list with two objects:

mv.test

a result table of multivariate normality tests, including the name of the test, test statistic, p-value, and multivariate normality summary (Yes, if p-value>0.05). Note that the test results of Royston will not be reported if n > 2000 or n < 3 and the test results of Villasenor-Alva and Gonzalez-Estrada (VAGE) will not be reported if n > 5000 or n < 12.

uv.shapiro

a dataframe with p rows detailing univariate Shapiro-Wilk tests. Columns in the dataframe contain test statistics W, p-value,and univariate normality summary (YES, if p-value>0.05).

If the number of variable is p=1, only univariate Shapiro-wilk's test result will be produced.

References

Shapiro, S. S., & Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52(3/4), 591-611.

Royston, J. P. (1982). An extension of Shapiro and Wilk's W test for normality to large samples. Journal of the Royal Statistical Society: Series C (Applied Statistics), 31(2), 115-124.

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

Lee, R., Qian, M., & Shao, Y. (2014). On rotational robustness of Shapiro-Wilk type tests for multivariate normality. Open Journal of Statistics, 4(11), 964.

See Also

power.mswR, power.mswV, mvnTest, faTest, msk, mardia, mhz, mvn, shapiro.test

Examples

set.seed(12345)

## Data from gamma distribution
X = matrix(rgamma(50*4,shape =  2),50)
msw(X)

## Data from normal distribution
X = matrix(rnorm(50*4,mean = 2 , sd = 1),50)
msw(X)

## load the ubiquitous multivariate iris data ##
## (first 50 observations of columns 1:4) ##
iris.df = iris[1:50, 1:4]
msw(iris.df)