Omnibus Test for Univariate and Multivariate Normality ------------------------------------------------------
^omninorm^ varlist [^if^ exp] [^in^ range]
varlist may contain time-series operators; see help @varlist@.
Description -----------
^omninorm^ performs an omnibus test for normality on one or several variables proposed by Doornik and Hansen (1994), based on a test by Shenton and Bowman (1977). In its small-sample form, the test statistic uses transformed skewness and kurtosis measures to generate empirical moments that are much closer to standard normal. The test may be readily applied to a set of variables, such as the residuals from a multivariate regression. Doornik and Hansen conduct simulations that illustrate that this test will generally have better size and power than several proposed in the literature, including the multivariate Shapiro-Wilk of Royston (1983). They find that their omnibus test "is both simple, has coorect size and good power properties." (p.6)
Under the null hypothesis of normality of the specified k variables, the test statistic is distributed Chi-squared with 2 k degrees of freedom. An asymptotic form of the test is also provided; it is essentially a multivariate equivalent of the Bowman and Shenton (1975) test, which those authors consider "unsuitable except in very large samples." (p.2)
Users of Stata 9.0+ should use ^omninorm^.
Examples --------
. ^use http://fmwww.bc.edu/ec-p/data/micro/iris,clear^ . ^omninorm7 set_sepl set_sepw set_petw ^ . ^omninorm7 set_sepl set_sepw set_petw set_petl ver_sepl ver_sepw^
Acknowledgements ----------------
The code for this routine draws heavily from Jurgen Doornik's implementation of normtest.ox in the Ox programming language. Nick Cox' matmap is required for this routine.
References ----------
Bowman, K.O. and Shenton, L.R. 1975. Omnibus test contours for departures from normality based on root-b1 and b2. Biometrika, 62:243-250.
Doornik, Jurgen A. and Hansen, Henrik. 1994. An Omnibus Test for Univariate and Multivariate Normality. Unpublished working paper, Nuffield College, Oxford University. http://ideas.uqam.ca/ideas/data/Papers/wuknucowp9604.html
Royston, J.P. 1983. Some techniques for assessing multivariate normality based on the Shapiro-Wilk W. Applied Statistics, 32, 121-133.
Shenton, L.R. and Bowman, K.O. 1977. A Bivariate Model for the Distribution of root-b1 and b2. Journal of the American Statistical Association, 72:206-211.
Author ------
Christopher F Baum, Boston College, USA baum@@bc.edu
Also see --------
Manual: ^[R] sktest, swilk^ On-line: help for @sktest@, @swilk@