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Correlation for linear-circular data

circlccorrlinearvar circularvar[ifexp] [inrange]

Description

circlccorrproduces 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

nvalues of two such variables,xlinear and theta circular, as2 2 2 2 r = ( r + r - 2 r r r ) / ( 1 - r ), 12 13 12 13 23 23

where

r is correlation of

xand cos theta, 12 r is correlation ofxand sin theta, and 13 r is correlation of sin theta and cos theta. 23Batschelet (1981, p.193) suggested for a large-sample significance test that if

xand theta are independent, thenn*r-square is approximately distributed as chi-square with 2 degrees of freedom. Fisher (1993, p.145) recommends obtainingP-values by randomisation. Caveat emptor.

Example

. circlccorr ozone dir

ReferencesBatschelet, E. 1981.

Circular statistics in biology.London: Academic Press.Fisher, 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, circcorr