{smcl} {* 31mar2004}{...} {hline} help for {hi:circcorr} {hline} {title:Correlation for circular data} {p 8 17 2} {cmd:circcorr} {it:varname1 varname2} [{cmd:if} {it:exp}] [{cmd:in} {it:range}] {title:Description} {p 4 4 2} {cmd:circcorr} produces a correlation coefficient appropriate for two circular variables taking on values between 0 and 360 degrees. The correlation is defined for {it:n} values of two such variables {it:x} and {it:y} as SUM sin({it:x}[{it:i}] - {it:x}[{it:j}]) sin({it:y}[{it:i}] - {it:y}[{it:j}]) {it:i}<{it:j} r_T = {hline 52} 2 2 ROOT [ SUM sin ({it:x}[{it:i}] - {it:x}[{it:j}]) SUM sin ({it:y}[{it:i}] - {it:y}[{it:j}]) ] {it:i}<{it:j} {it:i}<{it:j} {p 4 4 2}and takes on values between -1 and 1. {p 4 4 2} The {it:P}-value associated with r_T can be computed for large samples, say {it:n} >= 25, but depends on the distribution of {it:x} and {it:y}. If either has a mean resultant length (vector strength) of 0, then {it:n} * r_T is double exponential. Otherwise, ROOT of {it:n} * r_T has a Gaussian (normal) distribution. Both {it:P}-values are calculated. See Fisher (1993, pp.151-153) for details, but note that both {it:U} terms in (6.40) on p.152 should be rooted. {title:Example} {p 4 8 2}{cmd:. circcorr wallasp axisasp} {title:Reference} {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 circlccorr}