circular (version 0.3-1)

equal.kappa.test: Equal Kappa Test

Description

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

Usage

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.

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
  match.call()

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.

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

x <- c(rvonmises(50, 0, 1), rvonmises(100, pi/3, 10))
group <- c(rep(0, 50), rep(1, 100)) 

equal.kappa.test(x, group)