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Rao Spacing Test

Source: R/stat_tests.R
rao_spacing_test.Rd

Rao's spacing test of uniformity on the circle

Usage

rao_spacing_test(x, alpha = 0.05, n_perm = 9999L, axial = TRUE)

Arguments

x

numeric vector. Values in degrees

alpha

Significance level of the test ranging between 0 and 1.

n_perm

integer. Number of simulated uniform samples.

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" containing the following components:

statistic

the value of the L statistic

parameter

the number of data and the number of simulations

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.

data.name

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

Details

Test statistic is $$L = 1/2 \sum(|T_i - 360 / n|)$$ in degrees, with the spacings \(T_i\) between consecutive angles (Mardia & Jupp 2000, eq. 6.3.45). The p-value is the proportion of n_perm simulated uniform samples with a larger \(L\)

See also

Other One-Sample-Tests: hodges_ajne_test(), kuiper_test(), norm_chisq(), rayleigh-test, watson_test(), weighted-rayleigh-test

Examples

set.seed(20250411)
rao_spacing_test(rvm(100, mean = 0, kappa = 10))
#> 
#> 	Rao's spacing test of uniformity with simulated p-value (based on 9999
#> 	replicates)
#> 
#> data:  rvm(100, mean = 0, kappa = 10)
#> L = 230.53, n = 100, n_perm = 9999, p-value = 1e-04
#> alternative hypothesis: non-uniform distribution
#> 

# San Andreas Fault Data:
data(san_andreas)
data("nuvel1")
PoR <- subset(nuvel1, nuvel1$plate.rot == "na")
sa.por <- PoR_shmax(san_andreas, PoR, "right")
rao_spacing_test(sa.por$azi.PoR, alpha = .05)
#> 
#> 	Rao's spacing test of uniformity with simulated p-value (based on 9999
#> 	replicates)
#> 
#> data:  sa.por$azi.PoR
#> L = 202.73, n = 1126, n_perm = 9999, p-value = 1e-04
#> alternative hypothesis: non-uniform distribution
#>