Correlation Coefficient for Angular Variables
Computes a circular version of the Pearson's product moment correlation, and performs a significance test if requested.
circ.cor(alpha, beta, test=FALSE)
alpha |
vector of circular data measured in radians. |
beta |
vector of circular data measured in radians. |
test |
if test = TRUE, then a significance test for the correlation coefficient is computed. |
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.
Returns a data frame with variables r, a circular version of the Pearson's product moment correlation, test.stat and p.value, the test statistic and p-value respectively, for testing significance of the correlation coefficient. test.stat and p.value are by default not produced, but are given when test=TRUE is specified in the function call.
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. data1 <- rvm(50, 0, 3) data2 <- data1 + pi + rvm(50, 0, 10) circ.cor(data1, data2, test=TRUE)
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