{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}