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help for omninorm
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Omnibus test for univariate or multivariate normality

omninorm varlist [if exp] [in range] [, allobs by(byvar) missing
marginals ]

by ... : may also be used with omninorm: see help on by. varlist may
contain time-series operators; see help on varlist.

Description

omninorm performs an omnibus test for normality on one or several
variables proposed by Doornik and Hansen (1994, 2008), itself based on a
test by Shenton and Bowman (1977). The test statistic is based on
transformations of skewness and kurtosis that are much closer to standard
normal than the raw moment measures. The test may be applied to a set of
variables, such as the residuals from a multivariate regression. Doornik
and Hansen conducted simulations that illustrate that this test will
generally have better size and power than several proposed in the
literature, including the multivariate Shapiro-Wilk test of Royston
(1983). They find that their omnibus test "is simple, has correct size
and good power properties" (Doornik and Hansen 2008, p.936).

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, which is essentially a
multivariate equivalent of the Bowman and Shenton (1975) test, which
those authors consider "unsuitable, except in very large samples"
(Doornik and Hansen 2008, p.928).

Options

allobs specifies use of the maximum possible number of observations for
each variable. The default is to use only those observations for
which all variables in varlist are not missing.  This option bites
only if marginals is also specified.

by() specifies a variable defining distinct groups for which statistics
should be calculated. by() is allowed only with a single byvar. The
choice between by: and by() is partly one of precisely what kind of
output display is required. The display with by: is clearly
structured by groups while that with by() is more compact. To show
statistics for the marginal distributions of several variables and
several groups with a single call to omninorm, the display with by:
is essential.

marginals specifies that whenever several variables are specified,
univariate (i.e. marginal) tests are to be carried out for each.

missing specifies that with the by() option observations with missing
values of byvar should be included in calculations. The default is to
exclude them.

Examples

. use http://fmwww.bc.edu/ec-p/data/micro/iris,clear
. omninorm set_sepl set_sepw set_petw set_petl
. omninorm set_sepl set_sepw set_petw set_petl, marginals

Citation of omninorm

omninorm is not an official Stata command.  It is a free contribution to
the research community, like a paper. Please cite it as such:

Baum, C.F., Cox, N.J. 2007.  omninorm: Stata module to calculate omnibus
test for univariate/multivariate normality.
http://ideas.repec.org/c/boc/bocode/s417501.html

Acknowledgments

We are grateful to William Gould for assistance with Mata programming.

Authors

Christopher F. Baum, Boston College, USA
baum@bc.edu

Nicholas J. Cox, Durham University, U.K.
n.j.cox@durham.ac.uk

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.  Working Paper, Nuffield
College, University of Oxford. See
http://ideas.repec.org/p/nuf/econwp/9604.html or
http://www.doornik.com/research/normal2.pdf

Doornik, Jurgen A. and Hansen, Henrik.  2008.  An omnibus test for
univariate and multivariate normality.  Oxford Bulletin of Economics
and Statistics 70: 927-939.

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.

Saved results

(for last-named variable or group only)

r(df)        degrees of freedom of test
r(k)         number of variables in test
r(dhansen)   Doornik-Hansen test statistic
r(p_dhansen) P-value of above
r(asy)       asymptotic test statistic
r(p_asy)     P-value of above

Also see

Online: sktest, swilk

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