cor.circular: Correlation Coefficient for Angular Variables
Description
Computes a circular version of the Pearson's product moment correlation, and performs a significance test if requested.
Usage
cor.circular(x, y=NULL, test=FALSE)
Value
Returns a vector or a matrix of a circular version of the Pearson's
product moment correlation, if test == TRUE then a list is
reported with statistic and p.value, the test statistic and p-value respectively, for testing significance of the correlation coefficient.
Arguments
x
vector or matrix of circular data.
y
vector or matrix of circular data.
test
if test == TRUE, then a significance test for the correlation coefficient is computed.
Author
Claudio Agostinelli and Ulric Lund
Details
The correlation coefficient is computed like Pearson's product moment correlation for two linear variables X and Y. In the computational formula, however, (xi - xbar) and (yi - ybar) are replaced by sin(xi - xbar) and sin(yi - ybar), where xbar and ybar in the second two expressions are the mean directions of the samples.
References
Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, Section 8.2, World Scientific Press, Singapore.
Jammalamadaka, S. and Sarma, Y. (1988). A correlation coefficient for angular variables. Statistical Theory and Data Analysis 2. North Holland: New York.
# Generate two circular data sets, and compute their correlation.x <- rvonmises(n=50, mu=circular(0), kappa=3)
y <- x + rvonmises(n=50, mu=circular(pi), kappa=10)
cor.circular(x, y, test=TRUE)