# watson.wheeler.test: Watson-Williams Test of Homogeneity of Means In circular: Circular Statistics

## Description

Performs the Watson-Wheeler test for homogeneity on two or more samples of circular data.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10``` ```watson.wheeler.test(x, ...) ## Default S3 method: watson.wheeler.test(x, group, ...) ## S3 method for class 'list' watson.wheeler.test(x, ...) ## S3 method for class 'formula' watson.wheeler.test(formula, data, ...) ```

## Arguments

 `x` a vector of angles (coerced to class `circular`) or a list of such angles. `group` a vector or factor object giving the groups for the corresponding elements of `x`. Ignored if `x` is a list `formula` a formula of the form `lhs ~ rhs` where `lhs` is a vector of angles and `rhs` a vector or factor giving the corresponding groups. `data` an optional data.frame containing the variables in the formula `formula`. `...` further arguments passed to or from other methods.

## Details

The Watson-Wheeler (or Mardia-Watson-Wheeler, or uniform score) test is a non-parametric test to compare two or several samples. The difference between the samples can be in either the mean or the variance.

The p-value is estimated by assuming that the test statistic follows a chi-squared distribution. For this approximation to be valid, all groups must have at least 10 elements.

In the default method, `x` is a vector of angles and `group` must be a vector or factor object of the same length as `x` giving the group for the corresponding elements of `x`.

If `x` is a list, its elements are taken as the samples to be compared.

In the `formula` method, the angles and grouping elements are identified as the left and right hand side of the formula respectively.

All angles should be of class `circular` and will be coerced as such if they are not.

## Value

A list with class `"htest"` containing the following components:

 `statistic` W, the statistic of the test, which is approximately distributed as a chi-squared. `parameter` the degrees of freedom for the chi-squared approximation of the statistic. `p.value` the p-value for the test. `method` a character string containing the name of the test. `data.name` a character string giving the name(s) of the data.

## Author(s)

Jean-Olivier Irisson

## References

Batschelet, E (1981). Circular Statistics in Biology. chap 6.3, p. 104

Zar, J H (1999). Biostatistical analysis. section 27.5, p. 640

## Examples

 ```1 2 3 4 5 6 7``` ```# Example used in Zar (1999) x1 <- circular(c(35, 45, 50, 55, 60, 70, 85, 95, 105, 120), units="degrees", template="geographics") x2 <- circular(c(75, 80, 90, 100, 110, 130, 135, 140, 150, 160, 165), units="degrees", template="geographics") watson.wheeler.test(list(x1,x2)) ```

circular documentation built on July 4, 2017, 9:03 a.m.