watson.two {CircStats} R Documentation

## Watson's Two-Sample Test of Homogeneity

### Description

Performs Watson's test for homogeneity on two samples of circular data.

### Usage

```watson.two(x, y, alpha=0, plot=FALSE)
```

### Arguments

 `x` vector of circular data measured in radians. `y` vector of circular data measured in radians. `alpha` significance level of the test. Valid levels are 0.001, 0.01, 0.05, 0.1. This argument may be ommited, in which case, a range for the p-value will be returned. `plot` logical value. If TRUE, an overlayed plot of both empirical distribution functions will be sent to the current graphics device. The default value if FALSE.

### Details

Critical values for the test statistic are obtained using the asymptotic distribution of the test statistic. It is recommended to use the obtained critical values and ranges for p-values only for combined sample sizes in excess of 17. Tables are available for smaller sample sizes and can be found in Mardia (1972) for instance.

NULL

### Note

Watson's two-sample test of homogeneity is performed, and the results are printed to the screen. If alpha is specified and non-zero, the test statistic is printed along with the critical value and decision. If alpha is omitted, the test statistic is printed and a range for the p-value of the test is given. If plot=TRUE, an overlayed plot of both empirical distribution functions will be sent to the current graphics device.

### References

Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, Section 7.5, World Scientific Press, Singapore.

### Examples

```# Perform a two-sample test of homogeneity on two
# simulated data sets.
data1 <- rvm(20, 0, 3)
data2 <- rvm(20, pi, 2)
watson.two(data1, data2, alpha=0.05, plot=TRUE)
watson.two(data1, data2)
```

[Package CircStats version 0.2-6 Index]