R: Correlation Coefficient for Angular Variables

cor.circular {circular} | R Documentation

## 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)

### 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.

### 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.

### 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.

### Author(s)

Claudio Agostinelli and Ulric Lund

### 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.

### Examples

    # 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)

[Package circular version 0.4-93 Index]