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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