q-sample uniform-scores test tests the equality of given distributions, i.e., whether samples of directions share the mean direction. The test is the distribution-free test of Mardia, Watson & Wheeler on the uniform scores \(2 \pi r_i / n\) of the ranks in the pooled sample.
Arguments
- samples
list of samples of orientations
- alpha
Significance level of the test ranging between 0 and 1. For
dist = "vonmises"it must be one of0.1,0.05,0.01or0(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
$$W = 2 \sum_{i=1}^q R_i^2 / n_i$$ with \(2(q - 1)\) degrees of freedom, \(R^* = 2 (n - 1) R_1^2 / (n_1 n_2)\) for two samples. Ties within a sample get consecutive ranks, ties between samples the average rank.
See also
Other Two-Sample-Tests:
ar_test(),
equal_kappa_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)
uniform_scores_test(list(x1, x2))
#>
#> Uniform scores test
#>
#> data: 1 and 2
#> W = 3.6783, df = 2, p-value = 0.159
#> alternative hypothesis: Samples come from different distributions
#>
# San Andreas Fault Data:
data(san_andreas)
data("nuvel1")
PoR <- subset(nuvel1, nuvel1$plate.rot == "na")
sa.por <- PoR_shmax(san_andreas, PoR, "right")
uniform_scores_test(list(sa.por$azi.PoR, rvm(100, 135, 10)))
#>
#> Uniform scores test
#>
#> data: 1 and 2
#> W = 0.9193, df = 2, p-value = 0.6315
#> alternative hypothesis: Samples come from different distributions
#>