faTest {mvnormalTest}

Rotational Robust Shapiro-Wilk Type (SWT) Test for Multivariate Normality (FA Test of Fattorini)

Description

It computes FA Test proposed by Fattorini (1986). This test would be more rotationally robust than other SWT tests such as Royston (1982) H test and the test proposed by Villasenor-Alva and Gonzalez-Estrada (2009). The p-value of the test statistic is computed based on a simulated null distribution of the statistic.

Usage

faTest(X, B = 1000)

Arguments

X

an n*p data matrix or data frame, where n is number of rows (observations) and p is number of columns (variables) and n>p.

B

number of Monte Carlo simulations for null distribution, default is 1000 (increase B to increase the precision of p-value).

Value

Returns a list with two objects:

mv.test

results of the FA test for multivariate normality, i.e., test statistic, p-value, and multivariate normality summary (YES, if p-value>0.05).

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).

References

Fattorini, L. (1986). Remarks on the use of Shapiro-Wilk statistic for testing multivariate normality. Statistica, 46(2), 209-217.

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.

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.

Zhou, M., & Shao, Y. (2014). A powerful test for multivariate normality. Journal of applied statistics, 41(2), 351-363.

See Also

power.faTest, mvnTest, msk, mardia, msw, mhz

Examples

set.seed(12345)

## Data from gamma distribution ##
X = matrix(rgamma(50*4,shape =  2),50)
faTest(X, B=100)

## load the ubiquitous multivariate iris data ##
## (first 50 observations of columns 1:4) ##
iris.df = iris[1:50, 1:4]
faTest(iris.df, B=100)