{smcl}
{* 21apr2004}{...}
{hline}
help for {hi:cirlccorr}
{hline}
{title:Correlation for linear-circular data}
{p 8 17 2}
{cmd:circlccorr}
{it:linearvar circularvar}
[{cmd:if} {it:exp}]
[{cmd:in} {it:range}]
{title:Description}
{p 4 4 2}
{cmd:circlccorr} 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.
{p 4 4 2}
The square of the correlation is defined for {it:n} values of two such
variables, {it: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
{p 4 4 2}where
r is correlation of {it:x} and cos theta,
12
r is correlation of {it:x} and sin theta, and
13
r is correlation of sin theta and cos theta.
23
{p 4 4 2}
Batschelet (1981, p.193) suggested for a large-sample significance test
that if {it:x} and theta are independent, then {it:n} * {it:r}-square is
approximately distributed as chi-square with 2 degrees of freedom. Fisher (1993,
p.145) recommends obtaining {it:P}-values by randomisation. Caveat emptor.
{title:Example}
{p 4 8 2}{cmd:. circlccorr ozone dir}
{title:References}
{p 4 8 2}Batschelet, E. 1981. {it:Circular statistics in biology.} London:
Academic Press.
{p 4 8 2}Fisher, N.I. 1993. {it:Statistical analysis of circular data.}
Cambridge: Cambridge University Press.
{title:Author}
{p 4 4 2}Nicholas J. Cox, University of Durham, U.K.{break}
n.j.cox@durham.ac.uk
{title:Also see}
On-line: help for {help circscatter}, {help circcorr}