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help for ^omninorm^        (Statalist distribution 26 Mar 2001)
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Omnibus Test for Univariate and Multivariate Normality
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^omninorm^ varlist  [^if^ exp] [^in^ range]

varlist may contain time-series operators; see help @varlist@.

Description
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^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
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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 Unpublished working paper, Nuffield College, Oxford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
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Manual:  ^[R] sktest, swilk^
On-line:  help for @sktest@, @swilk@
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