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Watson-Williams Test of Homogeneity of Means

Source: R/stat_tests.R
watson_williams_test.Rd

Performs the Watson-Williams test for homogeneity of means between several samples of circular data.

Usage

watson_williams_test(samples, alpha = 0.05, axial = TRUE)

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 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.

Value

A list with class "htest"

Details

The Watson-Williams test for the homogeneity of means between two or more groups is performed and the results are printed. The null hypothesis is that means are equal across groups.

The assumptions are that: (1) the samples are drawn from populations with a von Mises distribution; (2) the parameter of concentration has the same value in all populations; (3) this parameter is sufficiently large (i.e. > 2 for two samples, > 1 for more samples). Assumptions 2 and 3 are checked and a warning is issued if they are not met.

See also

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

Examples

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_williams_test(list(x1, x2), axial = FALSE)
#> 
#> 	Watson-Williams test for homogeneity of mean directions
#> 
#> data:  1 and 2
#> F = 13.935, df1 = 1, df2 = 19, p-value = 0.00141
#> sample estimates:
#> mean direction 1 mean direction 2 
#>         71.60242        121.56169 
#> 

data1 <- rvm(n=20, mean = 0, kappa=3)
data2 <- rvm(n=20, mean = 90, kappa=2)
watson_williams_test(list(data1, data2), axial = FALSE)
#> 
#> 	Watson-Williams test for homogeneity of mean directions
#> 
#> data:  1 and 2
#> F = 46.167, df1 = 1, df2 = 38, p-value = 4.669e-08
#> sample estimates:
#> mean direction 1 mean direction 2 
#>         6.351635        87.388648 
#> 

# San Andreas Fault Data:
data(san_andreas)
data("nuvel1")
PoR <- subset(nuvel1, nuvel1$plate.rot == "na")
sa.por <- PoR_shmax(san_andreas, PoR, "right")
watson_williams_test(list(sa.por$azi.PoR, rvm(100, 135, 10)))
#> Warning: Concentrations (1.76, 2.77) differ between samples (p = 0.00458); the test might not be applicable
#> 
#> 	Watson-Williams test for homogeneity of mean axes
#> 
#> data:  1 and 2
#> F = 13.208, df1 = 1, df2 = 1224, p-value = 0.0002903
#> sample estimates:
#> mean direction 1 mean direction 2 
#>         140.8778         132.5831 
#>