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Correlation for circular data

circcorrvarname1 varname2[ifexp] [inrange]

Description

circcorrproduces a correlation coefficient appropriate for two circular variables taking on values between 0 and 360 degrees. The correlation is defined fornvalues of two such variablesxandyasSUM sin(

x[i] -x[j]) sin(y[i] -y[j])i<jr_T = ---------------------------------------------------- 2 2 ROOT [ SUM sin (x[i] -x[j]) SUM sin (y[i] -y[j]) ]i<ji<jand takes on values between -1 and 1.

The

P-value associated with r_T can be computed for large samples, sayn>= 25, but depends on the distribution ofxandy. If either has a mean resultant length (vector strength) of 0, thenn* r_T is double exponential. Otherwise, ROOT ofn* r_T has a Gaussian (normal) distribution. BothP-values are calculated. See Fisher (1993, pp.151-153) for details, but note that bothUterms in (6.40) on p.152 should be rooted.

Example

. circcorr wallasp axisasp

ReferenceFisher, N.I. 1993.

Statistical analysis of circular data.Cambridge: Cambridge University Press.

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

Also seeOn-line: help for circscatter, circlccorr