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help for ^circ2sam^
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Two-sample tests for circular data
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    ^circ2sam^ varname [^if^ exp] [^in^ range] ^, by(^groupvar^)^

Description
-----------

^circ2sam^ carries out two-sample tests for circular variables with
scales between 0 and 360 degrees due to Watson (1962) and Kuiper (1960).
The values of varname are grouped according to the precisely two
distinct values defined by groupvar together with any restrictions
imposed by ^if^ or ^in^. The hypothesis under test is that the distributions
so defined are identical. The test statistics are based on the empirical
distribution functions of the two samples.


Option
------

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


Example
-------

        . ^circ2sam dir , by(group)^


Note on P-values and statistical tables
---------------------------------------

For the Watson U-square statistic, critical values are given here for a
few examples of sample sizes n_1 and n_2 and significance level P. For
many problems with large or moderate samples, the values for infinite
sizes will serve as adequate approximations.

n_1 n_2   P = 0.5      0.2      0.1      0.05     0.01     0.005    0.001
  5   5       0.089    0.161    0.225    0.225
  7   7       0.079    0.135    0.158    0.199    0.304    0.304
  9   9       0.077    0.125    0.155    0.187    0.266    0.286    0.384
 12  12       0.075    0.122    0.153    0.186    0.256    0.284    0.344
 20  20       0.069    0.117    0.151    0.185    0.261    0.293    0.367
 40  40       0.069    0.117    0.152    0.186    0.264    0.298    0.374
100 100       0.069    0.117    0.152    0.187    0.267    0.300    0.378
infinite      0.071    0.117    0.152    0.187    0.268    0.304    0.385

Fuller tables can be found in Mardia (1972, p.314), Batschelet (1981,
p.348) and Zar (1999, Table B.38), the last being the most extensive of
these.

For the Kuiper statistics, tables can be found in Batschelet (1981,
pp.341, 346-7) and in Upton and Fingleton (1989, pp.393, 395). So long as
at least one sample is more than 12, k* may be compared with the
following critical values (see discussion in Upton and Fingleton,
p.279):

    P = 0.1      0.05      0.01      0.005      0.001
        1.62     1.75      2.00      2.10       2.30


Saved values
------------

     S_1   smaller sample size
     S_2   larger sample size
     S_3   Watson U-square statistic
     S_4   Kuiper V statistic
     S_5   Kuiper k statistic
     S_6   Kuiper k* statistic


References
----------

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

Mardia, K.V. 1972. Statistics of directional data. London: Academic
Press.

Upton, G.J.G. and Fingleton, B. 1989. Spatial data analysis by example.
Volume 2: Categorical and directional data. Chichester: John Wiley.

Zar, J.H. 1999. Biostatistical analysis. Upper Saddle River, NJ:
Prentice-Hall.


Author
------

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


Also see
--------

On-line:  help for @circwwm@
