tectonicr (version 0.4.6)

watson_test: 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
)

Value

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

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.

References

Mardia and Jupp (2000). Directional Statistics. John Wiley and Sons.

Examples

# Example data from Mardia and Jupp (2001), 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")