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help for circcorr
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Correlation for circular data

circcorr varname1 varname2 [if exp] [in range]

Description

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.

Example

. circcorr wallasp axisasp

Reference

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

Author

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

Also see

On-line: help for circscatter, circlccorr

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