Watson's Two-Sample Test of Homogeneity

Performs Watson's test for homogeneity on two samples of circular data. watson_two_test_perm() uses permutation to estimate p-values.

Usage

watson_two_test(x, y, alpha = NULL, axial = TRUE, quiet = FALSE)

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

Arguments

x, y

numeric vectors. Angles in degrees

alpha

Significance level of the test. Valid levels are 0.01, 0.05, and 0.1. This argument may be omitted (NULL, the default), in which case, a range for the p-value will be returned.

axial

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

quiet

logical. Prints the test's decision.

n_perm

integer. Number of permutations

Value

list

Details

Watson's two-sample test of homogeneity is performed, and the results are printed. If alpha is specified and non-zero, the test statistic is printed along with the critical value and decision. If alpha is omitted, the test statistic is printed and a range for the p-value of the test is given.

Critical values for the test statistic are obtained using the asymptotic distribution of the test statistic. It is recommended to use the obtained critical values and ranges for p-values only for combined sample sizes in excess of 17. Tables are available for smaller sample sizes and can be found in Mardia (1972) for instance.

See also

Other Tests: ar_test(), kuiper_test(), norm_chisq(), rayleigh-test, watson_test(), watson_wheeler_test_perm(), 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_two_test(x1, x2, axial = FALSE)
#> $statistic
#> [1] 0.1457431
#> 
#> $p.value
#> [1] "P-value > 0.10"
#> 
watson_two_test_perm(x1, x2, axial = FALSE)
#> $statistic
#> [1] 0.1457431
#> 
#> $p.value
#> [1] 0.1208791
#> 

data1 <- rvm(n=20, mean = 0, kappa=3)
data2 <- rvm(n=20, mean = 90, kappa=2)
watson_two_test(data1, data2, axial = FALSE)
#> $statistic
#> [1] 0.61775
#> 
#> $p.value
#> [1] "P-value < 0.001"
#> 
watson_two_test_perm(data1, data2, axial = FALSE)
#> $statistic
#> [1] 0.61775
#> 
#> $p.value
#> [1] 0.000999001
#> 


# San Andreas Fault Data:
data(san_andreas)
data("nuvel1")
PoR <- subset(nuvel1, nuvel1$plate.rot == "na")
sa.por <- PoR_shmax(san_andreas, PoR, "right")
watson_two_test(sa.por$azi, 135, alpha = 0.05)
#> Do not reject null hypothesis
#> $statistic
#> [1] 0.08340728
#> 
#> $p.value
#> [1] 0.187
#> 
watson_two_test_perm(sa.por$azi, rvm(100, 135, 10))
#> $statistic
#> [1] 0.201153
#> 
#> $p.value
#> [1] 0.02897103
#>