# equal.kappa.test: Equal Kappa Test In circular: Circular Statistics

## Description

This function tests for the homogeneity of concentration parameters for multiple samples of directional data.

## Usage

 ```1 2 3``` ```equal.kappa.test(x, group) ## S3 method for class 'equal.kappa.test' print(x, digits = max(3, getOption("digits") - 3), ...) ```

## Arguments

 `x` a vector of class `circular`. `group` a vector identifying the groups or samples. `digits` the number of digits to be printed. `...` additional arguments.

## Details

The samples are assumed to have been drawn from von Mises populations. The null hypothesis tested is that all populations sampled have the same concentration parameter, kappa.

When the pooled data has high concentration, sample mean resultant length above 0.70, Bartlett's test is used. For less concentrated pooled data, variance-stabilizing transformations are used to improve normal approximations needed to arrive at an approximate chi-squared test statistic (see references below). For pooled sample mean resultant length below 0.45, it is possible that individually a sample may in fact have quite a large sample mean resultant length. In this case, it is possible that the variance-stabilizing transformation involving the inverse sine function is passed a value outside of -1,1. If this occurs, the function will automatically use Bartlett's test and issue a warning to that effect.

## Value

An object of class `equal.kappa.test` with the following components:

 `kappa` concentration parameter for each sample. `kappa.all` concentration parameter of all samples combined. `rho` mean resultant length for each sample. `rho.all` mean resultant length of all samples combined. `df` degrees of freedom for chi-squared distribution. `statistic` the value of the chi-squared test statistic. `p.value` the p.value of the test statistic. `call` the `match.call` result.

## Author(s)

Claudio Agostinelli and Ulric Lund

## References

Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, Section 5.3, World Scientific Press, Singapore.

Mardia, K. and Jupp, P. (1999). Directional Statistics, Section 7.4, John Wiley and Sons, England.

## Examples

 ```1 2 3 4``` ```x <- c(rvonmises(50, circular(0), 1), rvonmises(100, circular(pi/3), 10)) group <- c(rep(0, 50), rep(1, 100)) equal.kappa.test(x, group) ```

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