Omnibus Test for Univariate and Multivariate Normality ------------------------------------------------------
^omninorm^ varlist [^if^ exp] [^in^ range]
varlist may contain time-series operators; see help @varlist@.
^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^.
. ^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^
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.
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 Unpublished working paper, Nuffield College, Oxford University.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.
Christopher F Baum, Boston College, USA baum@@bc.edu
Also see --------
Manual: ^[R] sktest, swilk^ On-line: help for @sktest@, @swilk@