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.
faTest(X, B = 1000)
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.
number of Monte Carlo simulations for null distribution, default is 1000 (increase B to increase the precision of p-value).
Returns a list with two objects:
results of the FA test for multivariate normality, i.e., test statistic, p-value, and multivariate normality summary (YES, if p-value>0.05).
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).
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.
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