circ.cor {CircStats} 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

```circ.cor(alpha, beta, test=FALSE)
```

### Arguments

 `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.

### 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 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.

### 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.
data1 <- rvm(50, 0, 3)
data2 <- data1 + pi + rvm(50, 0, 10)
circ.cor(data1, data2, test=TRUE)
```

[Package CircStats version 0.2-6 Index]