R: Watson's Test

watson {CircStats} | R Documentation

## Watson's Test

### Description

Performs a Watson's goodness of fit test for the von Mises or circular uniform distribution.

### Usage

    watson(x, alpha=0, dist='uniform')

### Arguments

`x` | vector of angular measurements in radians.
`alpha` | significance level of the test. Valid levels are 0.01, 0.05, 0.1. This argument may be ommited, in which case, a range for the p-value will be returned.
`dist` | distribution to test for. The default is the uniform distribution. To test for the von Mises distribution, set dist = 'vm'.

### Value

NULL

### Note

If dist = 'uniform', Watson's one-sample test for the circular uniform distribution 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 dist = 'vm', estimates of the population parameters are used to evaluate the von Mises distribution function at all data points, thereby arriving at a sample of approximately uniformly distributed data, if the original observations have a von Mises distribution. The one-sample Watson test is then applied to the transformed data as above.

### References

Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, Section 7.2, World Scientific Press, Singapore.

Stephens, M. (1970). Use of the Kolmogorov-Smirnov, Cramer-von Mises and related statistics without extensive tables. Journal of the Royal Statistical Society, B32, 115-122.

### See Also

circ.range, kuiper, rao.spacing, r.test, v0.test

### Examples

    # Generate data from the uniform distribution on the circle.
    data <- runif(100, 0, 2*pi)
    watson(data)
    # Generate data from a von Mises distribution.
    data <- rvm(50, 0, 4)
    watson(data, 0.05, dist='vm')

[Package CircStats version 0.2-4 Index]