tectonicr (version 0.4.10)

ar_test: Angular Randomisation Test of Homogeneity

Description

Performs Angular Randomisation Test for homogeneity on two samples of circular data after Ruxton et al. (2023). Test whether samples of directions share the mean direction P-values are estimated using permutation.

Usage

ar_test(x, y, n_perm = 1000L, axial = FALSE, alpha = NULL)

Value

A list with class "htest" containing the following components:

statistic

the value of the G statistic

parameter

the number of data in x and y, and the number of permutations

p.value

the p-value for the test

alternative

a character string describing the alternative hypothesis.

method

a character string indicating what type of test was performed.

alpha

the significance level

reject

logical. whether to reject the null-hypothesis based on the significance level.

data.name

a character string giving the name(s) of the data.

Arguments

x, y

numeric vectors. Angles in degrees

n_perm

integer. Number of permutations

axial

logical. Whether the data are axial, i.e. \(\pi\)-periodical (TRUE) or directional, i.e. \(2 \pi\)-periodical (FALSE, the default).

alpha

(optional) numeric. Significance level of the test (values between 0 and 1).

Details

Null Hypothesis (\(H_0\)): The two circular samples share an identical underlying probability distribution.

Alternative Hypothesis (\(H_{1}\)): The two samples come from different distributions.

Interpretation

• Small p-value (\(p < \alpha\), e.g., <0.05): Reject the null hypothesis. This indicates strong evidence that the two samples come from different circular distributions (differing in central tendency/mean direction or shape).

• Large p-value (\(p \ge \alpha\)): Fail to reject the null hypothesis; there is insufficient evidence to claim the two circular samples differ.

References

Ruxton, G.D., Malkemper, E.P. & Landler, L. Evaluating the power of a recent method for comparing two circular distributions: an alternative to the Watson U2 test. Sci Rep 13, 10007 (2023). https://doi.org/10.1038/s41598-023-36960-1

See Also

Other Two-Sample-Tests: equal_kappa_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)
ar_test(x1, x2)

# San Andreas Fault Data:
data(san_andreas)
data("nuvel1")
PoR <- subset(nuvel1, nuvel1$plate.rot == "na")
sa.por <- PoR_shmax(san_andreas, PoR, "right")
ar_test(sa.por$azi.PoR, rvm(100, 135, 10), axial = TRUE, alpha = 0.05)