R: Watson's Test

watson.test {circular} | R Documentation

## Watson's Test

### Description

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

### Usage

    watson.test(x, alpha=0, dist=c("uniform", "vonmises"))
    ## S3 method for class 'watson.test'
    print(x, digits = 4, ...)

### Arguments

`x` | a vector. The object is coerced to class `circular`.
`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` to "vonmises".
`digits` | integer indicating the precision to be used.
`...` | further arguments passed to or from other methods.

### Details

If `dist` = "uniform", Watson's one-sample test for the circular uniform distribution is performed, and the results are printed. 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` = "vonmises", 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.

### Value

a list with the statistic, alpha, the number of observations, the distribution and 'row' which is used by `print.watson.test` to evaluate the p-value.

### Author(s)

Claudio Agostinelli and Ulric Lund

### 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

`range.circular`, `kuiper.test`, `rao.spacing.test` and `rayleigh.test`

### Examples

    # Generate data from the uniform distribution on the circle.
    x <- circular(runif(100, 0, 2*pi))
    watson.test(x)
    # Generate data from a von Mises distribution.
    x <- rvonmises(n=50, mu=circular(0), kappa=4)
    watson.test(x, alpha=0.05, dist="vonmises")

[Package circular version 0.4-93 Index]