help for cirlccorr

Correlation for linear-circular data

circlccorr linearvar circularvar [if exp] [in range]


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.

The square of the correlation is defined for n values of two such variables, 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


r is correlation of x and cos theta, 12 r is correlation of x and sin theta, and 13 r is correlation of sin theta and cos theta. 23

Batschelet (1981, p.193) suggested for a large-sample significance test that if x and theta are independent, then n * r-square is approximately distributed as chi-square with 2 degrees of freedom. Fisher (1993, p.145) recommends obtaining P-values by randomisation. Caveat emptor.


. circlccorr ozone dir


Batschelet, E. 1981. Circular statistics in biology. London: Academic Press.

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, circcorr