Watson-Wheeler Test of Homogeneity of Means

Performs the Watson-Wheeler test for homogeneity on two or more samples of circular data.

Usage

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

Arguments

x, y

numeric vectors. Angles in degrees

axial

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

n_perm

integer. Number of permutations

Value

list

Details

The Watson-Wheeler (or Mardia-Watson-Wheeler, or uniform score) test is a non-parametric test to compare two or several samples. The difference between the samples can be in either the mean or the variance.

The p-value is estimated by assuming that the test statistic follows a chi-squared distribution. For this approximation to be valid, all groups must have at least 10 elements.

See also

Other Tests: ar_test(), kuiper_test(), norm_chisq(), rayleigh-test, watson_test(), watson_two_sample, weighted-rayleigh-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)
#> $statistic
#> [1] 3.67827
#> 
#> $p.value
#> [1] 0.1688312
#> 

data1 <- rvm(n=20, mean = 0, kappa=3)
data2 <- rvm(n=20, mean = 90, kappa=2)
watson_wheeler_test_perm(data1, data2, axial = FALSE)
#> $statistic
#> [1] 15.96367
#> 
#> $p.value
#> [1] 0.000999001
#> 

# 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))
#> $statistic
#> [1] 2.934737
#> 
#> $p.value
#> [1] 0.2547453
#>