.-
help for ^circlcco^
.-

Correlation for linear-circular data
------------------------------------

    ^circlcco^ linearvar circvar [^if^ exp] [^in^ range]

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

^circlcco^ produces a correlation coefficient appropriate for a linear
variable and a circular variable taking on values between 0 and 360
degrees. The first-named variable is taken to be linear and the
second-named variable is taken to be circular.

The square of the correlation is defined for n values of two such
variables, x linear and theta circular, as

      2     2     2                           2
     r = ( r   + r   - 2 r  r  r   ) / ( 1 - r   ),
            12    13      12 13 23            23

where

    r   is correlation of x and cos theta
     12

    r   is correlation of x and sin theta
     13

    r   is correlation of sin theta and cos theta.
     23

Batschelet (1981, p.193) suggested for a large-sample significance test
that if x and theta are independent, then n * r-square is approximately
distributed as chi-square with 2 degrees of freedom. Fisher (1993,
p.145) recommends obtaining P-values by randomisation. Caveat emptor.


Example
-------

        . ^circlcco ozone dir^


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

     S_1  number of observations
     S_2  correlation squared
     S_3  large sample P-value


References
----------

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

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


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


Also see
--------

On-line: help for @circplot@, @circcorr@

