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help for ^circwwm^
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Wheeler-Watson-Mardia test for circular data
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    ^circwwm^ varname [^if^ exp] [^in^ range] ^, by(^groupvar^)^

Description
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^circwwm^ carries out a homogeneity test for circular variables with
scales between 0 and 360 degrees due to Wheeler and Watson (1964) and
Mardia (1972). The values of varname are grouped according to the r (2
or more) distinct values of groupvar. 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, ^circwwm^ 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. The tabulation of group
frequencies should help here.


Option
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^by(^groupvar^)^ is in fact not optional.


Example
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        . ^circwwm wallasp, by(grading)^


Saved values
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     S_1  Wheeler-Watson-Mardia statistic
     S_2  degrees of freedom
     S_3  P-value


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


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


Also see
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On-line:  help for @circ2sam@