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

Description Usage Arguments Details Value Author(s) References See Also Examples

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

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

`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.

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.

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.

Claudio Agostinelli and Ulric Lund

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

# 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")

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