help for circcorr

Correlation for circular data

circcorr varname1 varname2 [if exp] [in range]


circcorr produces a correlation coefficient appropriate for two circular variables taking on values between 0 and 360 degrees. The correlation is defined for n values of two such variables x and y as

SUM sin(x[i] - x[j]) sin(y[i] - y[j]) i<j r_T = ---------------------------------------------------- 2 2 ROOT [ SUM sin (x[i] - x[j]) SUM sin (y[i] - y[j]) ] i<j i<j

and takes on values between -1 and 1.

The P-value associated with r_T can be computed for large samples, say n >= 25, but depends on the distribution of x and y. If either has a mean resultant length (vector strength) of 0, then n * r_T is double exponential. Otherwise, ROOT of n * r_T has a Gaussian (normal) distribution. Both P-values are calculated. See Fisher (1993, pp.151-153) for details, but note that both U terms in (6.40) on p.152 should be rooted.


. circcorr wallasp axisasp


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


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

Also see

On-line: help for circscatter, circlccorr