tectonicr (version 0.4.10)

watson_wheeler_test_perm: Watson-Wheeler Test of Homogeneity

Description

A non-parametric statistical test used to determine whether two independent samples of circular data (angles, directions, or periodic times) come from the same underlying population distribution. The difference between the samples can be in either the mean direction or the dispersion. P-values are estimated using permutation.

Usage

watson_wheeler_test_perm(x, y, axial = TRUE, n_perm = 1000L, alpha = NULL)

Value

A list with class "htest"

Arguments

x, y

numeric vectors. Angles in degrees

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.

n_perm

integer. Number of permutations

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).

Details

The statistic is \(R^* = 2 (n - 1) (C_1^2 + S_1^2) / (n_1 n_2)\) on the uniform scores \(2 \pi r_i / n\) of the ranks \(r_i\) in the pooled sample (Mardia & Jupp, 2000, eq. 8.3.4). Tied values get their average rank.

Hypotheses

Null Hypothesis (\(H_0\)) The samples come from identical populations (meaning both the mean direction and the dispersion/variance are homogeneous across groups).

Alternative Hypothesis (\(H_1\)): The samples come from different population distributions, which can be due to a difference in the mean direction, a difference in variance/concentration, or both.

Interpretation

Test Statistic: Higher values indicate larger discrepancies between the angular distributions of your groups.

• If the p-value is less than your significance level (commonly \(\alpha\) = 0.05), you reject the null hypothesis. This means you have strong evidence that the groups differ significantly in their central direction or spread around the circle.

• If the p-value is greater than 0.05, you fail to reject the null hypothesis, meaning there is no statistically significant evidence of difference among the groups.

See Also

Other Two-Sample-Tests: ar_test(), equal_kappa_test(), uniform_scores_test(), walraff_test(), watson_two_sample, 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)
watson_wheeler_test_perm(x1, x2, axial = FALSE)

data1 <- rvm(n=20, mean = 0, kappa=3)
data2 <- rvm(n=20, mean = 90, kappa=2)
watson_wheeler_test_perm(data1, data2, axial = FALSE)

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