Watson's \(U^2\) Test of Circular Uniformity — watson

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.

Value

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

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)
#> Do Not Reject Null Hypothesis
#> $statistic
#> [1] 0.1153633
#> 
#> $p.value
#> [1] 0.187
#> 

# 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)
#> Reject Null Hypothesis
#> $statistic
#> [1] 52.14744
#> 
#> $p.value
#> [1] 0.187
#> 
watson_test(sa.por$azi.PoR, alpha = .05, dist = "vonmises")
#> Reject Null Hypothesis
#> $statistic
#> [1] 5.386914
#> 
#> $p.value
#> [1] 0.113
#>