# cor.circular: Correlation Coefficient for Angular Variables In circular: Circular Statistics

## Description

Computes a circular version of the Pearson's product moment correlation, and performs a significance test if requested.

## Usage

 `1` ```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

 ```1 2 3 4``` ```# 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) ```

### Example output

```Attaching package: 'circular'

The following objects are masked from 'package:stats':

sd, var

\$cor
[1] 0.9338005

\$statistic
[1] 5.03145

\$p.value
[1] 4.867846e-07
```

circular documentation built on May 1, 2019, 7:57 p.m.