tectonicr (version 0.4.10)

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(samples, method = NULL, alpha = 0.05, axial = TRUE)

Value

A list with class "htest"

Arguments

samples

list of samples of orientations

method

character. One of

"f"

(default for two samples): \(F = ((n_1 - R_1) / \nu_1) / ((n_2 - R_2) / \nu_2)\), two-sided, \(F(\nu_1, \nu_2)\) (Mardia and Jupp, 2000 eq. 10.5.3; Watson, 1956).

"bartlett"

(default for more samples): Bartlett's test of the dispersions \((n_i - R_i) / \nu_i\), chi-square with \(q - 1\) degrees of freedom (Mardia and Jupp, 2000 eq. 10.6.21; McFadden & Lowes, 1981, eq. 64-66).

alpha

Significance level of the test ranging between 0 and 1. For dist = "vonmises" it must be one of 0.1, 0.05, 0.01 or 0 (only the tabulated p-value range is returned).

axial

logical. Whether the data are axial, i.e. \(\pi\)-periodical (TRUE, the default) or directional, i.e. \(2 \pi\)-periodical (FALSE). In case of axial data, the angles will be doubled for the test.

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 \(\kappa\).

For concentrated data \(2 \kappa (n_i - R_i)\) is approximately chi-square with \(\nu_i = n_i - 1\) degrees of freedom on the circle, where \(R_i\) is the resultant length of sample \(i\).

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.

See Also

Other Two-Sample-Tests: ar_test(), uniform_scores_test(), walraff_test(), watson_two_sample, watson_wheeler_test_perm(), watson_williams_test()

Examples

set.seed(20250411)
x1 <- c(35, 45, 50, 55, 60, 70, 85, 95, 105, 120)
x2 <- c(75, 80, 90, 100, 110, 130, 135, 140, 150, 160, 165)
equal_kappa_test(list(x1, x2))

x1 <- rvm(100, mean = 90, kappa = 20)
x2 <- rvm(100, mean = 90, kappa = 10)
x3 <- rvm(100, mean = 90, kappa = 1)
equal_kappa_test(list(x1, x2, x3))

# San Andreas Fault Data:
data(san_andreas)
data("nuvel1")
PoR <- subset(nuvel1, nuvel1$plate.rot == "na")
sa.por <- PoR_shmax(san_andreas, PoR, "right")
equal_kappa_test(list(sa.por$azi.PoR, rvm(100, 135, 10)))