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help for circtwosample 
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Two-sample tests for circular data 

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


Description 

    circtwosample carries out two-sample tests due to Watson (1962) and
    Kuiper (1960) for circular variables in varlist with scales between 0 and
    360 degrees.  The values of each variable are grouped according to the
    precisely two distinct non-missing values defined by byvar 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.

    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 

    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), Kanji (1999, p.210), Zar (1999, Table B.38) and Mardia and Jupp
    (2000, p.377); that of Zar is 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, 1989,
    p.279):

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


Options 

    by() indicating grouping is a required option.


Example 

    . circtwosample dir, by(group)


References 

    Batschelet, E. 1981. Circular statistics in biology.  London: Academic
        Press. (Edward Batschelet, 1914-1979)

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

    Kuiper, N.H. 1960. Tests concerning random points on a circle.
        Proceedings, Koninklijke Nederlandse Akademie van Wetenschappen
        Series A 68: 38-47. (Nicolaas Hendrik Kuiper, 1920-1994)

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

    Mardia, K.V. and Jupp, P.E. 2000. Directional statistics.  Chichester:
        John Wiley.

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

    Watson, G.S. 1962. Goodness-of-fit tests on a circle. II.  Biometrika 49:
        57-63. (Geoffrey Stuart Watson, 1921-1998)

    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