watson_test: Watson's U^2 Test of Circular Uniformity

In tectonicr: Analyzing the Orientation of Maximum Horizontal Stress

Watson's U^2 Test of Circular Uniformity

Description

Watson's test statistic is a rotation-invariant Cramer - von Mises test

Usage

watson_test(
  x,
  alpha = 0,
  dist = c("uniform", "vonmises"),
  axial = TRUE,
  mu = NULL,
  quiet = FALSE
)

Arguments

x	numeric vector. Values 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.
dist	Distribution to test for. The default, "uniform", is the uniform distribution. "vonmises" tests the von Mises distribution.
axial	logical. Whether the data are axial, i.e. \pi-periodical (TRUE, the default) or circular, i.e. 2 \pi-periodical (FALSE).
mu	(optional) The specified mean direction (in degrees) in alternative hypothesis
quiet	logical. Prints the test's decision.

Details

If statistic > p.value, the null hypothesis is rejected. If not, randomness (uniform distribution) cannot be excluded.

Value

list containing the test statistic statistic and the significance level p.value.

References

Mardia and Jupp (1999). Directional Statistics. John Wiley and Sons.

Examples

# Example data from Mardia and Jupp (1999), pp. 93
pidgeon_homing <- c(55, 60, 65, 95, 100, 110, 260, 275, 285, 295)
watson_test(pidgeon_homing, alpha = .05)

# San Andreas Fault Data:
data(san_andreas)
data("nuvel1")
PoR <- subset(nuvel1, nuvel1$plate.rot == "na")
sa.por <- PoR_shmax(san_andreas, PoR, "right")
watson_test(sa.por$azi.PoR, alpha = .05)
watson_test(sa.por$azi.PoR, alpha = .05, dist = "vonmises")

tectonicr documentation built on June 8, 2025, 11:33 a.m.