faTest: Rotational Robust Shapiro-Wilk Type (SWT) Test for... In mvnormalTest: Powerful Tests for Multivariate Normality

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

 `1` ```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 Shapiroâ€“Wilk's test for multivariate normality. Communications in Statisticsâ€”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.

`power.faTest`, `mvnTest`, `msk`, `mardia`, `msw`, `mhz`
 ``` 1 2 3 4 5 6 7 8 9 10``` ```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) ```