# watson.test: Watson's Test In circular: Circular Statistics

## Description

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

## Usage

 ```1 2 3``` ```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.

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

## Examples

 ```1 2 3 4 5 6``` ```# 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") ```

### Example output

```Attaching package: 'circular'

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

sd, var

Watson's Test for Circular Uniformity

Test Statistic: 0.142
P-value > 0.10

Watson's Test for the von Mises Distribution

Test Statistic: 0.0195
Level 0.05 Critical Value: 0.113
Do Not Reject Null Hypothesis
```

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