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help for circwwmardia
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Wheeler-Watson-Mardia test for circular data

        circwwmardia varlist [if exp] [in range] , by(byvar)


Description 

    circwwmardia carries out a homogeneity test due to Wheeler and Watson
    (1964) and Mardia (1972) for circular variables in varlist with scales
    between 0 and 360 degrees. The values of each varname are grouped
    according to the r (2 or more) distinct values of byvar. The hypothesis
    under test is that the distributions so defined are identical. The test
    statistic is based on the circular ranks of the data, 2 * pi * rank / n,
    where rank varies from 1 to the number of values n.

    The W_r statistic can be compared with a chi-square distribution with 2r
    - 2 degrees of freedom so long as there are 10 or more values in each
    group. Randomisation is recommended otherwise to get an estimate of the
    P-value. However, circwwmardia carries out the chi-square calculation
    regardless and the onus is on the user to identify examples with small
    group sizes and take appropriate action. A tabulation of group
    frequencies should help here.

    Note that allowing a varlist is a convenience to allow many tests from a
    single command: the tests are separate and users searching for
    significant results are urged to consider carefully what they are doing.


Remarks 

    This test is called the Mardia-Watson-Wheeler test by Batschelet (1981)
    and Kanji (1999).


Options

    by() indicating grouping is a required option.


Example 

    . circwwmardia wallasp, by(grade)


Reference 

    Batschelet, E. 1981. Circular statistics in biology.  London: Academic
        Press.

    Fisher, N.I. 1993. Statistical analysis of circular data.  Cambridge:
        Cambridge University Press.

    Kanji, G.K. 1999. 100 statistical tests. London: Sage.

    Mardia, K.V. 1972. A multi-sample uniform scores test on a circle and its
        parametric competitor.  Journal, Royal Statistical Society Series B
        34: 102-113.

    Wheeler, S. and Watson, G.S. 1964. A distribution-free two-sample test on
        a circle. Biometrika 51: 256-257.


Author

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


Acknowledgments

    Leora Vegosen found a bug.


Also see