R: Watson-Williams Test of Homogeneity of Means

watson.wheeler.test {circular} | R Documentation

## Watson-Williams Test of Homogeneity of Means

### Description

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

### Usage

    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

    # 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))

[Package circular version 0.4-93 Index]