tectonicr (version 0.4.9)

watson_test: Watson's \(U^2\) Test for Goodness-of-Fit against known Distribution

Description

A non-parametric statistical test used for circular data to determine whether a sample fits a specified theoretical distribution

Usage

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

Value

list containing the test statistic statistic, the significance level p.value, the critical value critical.value, whether to reject the null hypothesis, the significance level alpha, the tested distribution dist, and the number of data n

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 circular uniform distribution. "vonmises" tests the von Mises distribution.

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.

quiet

logical. Prints the test's decision.

Details

Hypotheses

Null Hypothesis (\(H_0\)): The circular sample comes from a specified theoretical distribution (such as a uniform distribution or a specific von Mises distribution).

Alternative Hypothesis (\(H_1\)): The circular sample does not follow the specified theoretical distribution.

Interpretation

To interpret the output of Watson's \(U^2\) test, compare your calculated \(U^2\) test statistic to the critical value from Watson's goodness-of-fit/homogeneity tables at your chosen significance level (\(\alpha\), commonly set to 0.05), or check the resulting p-value:

• If \(U^2_{\text{calculated}} > U^2_{\text{critical}}\) (or p < \(\alpha\)): Reject the null hypothesis (\(H_0\)). Conclude that the data significantly deviates from the theoretical distribution.

• If \(U^2_{\text{calculated}} \le U^2_{\text{critical}}\) (or \(p \ge \alpha\)): Fail to reject the null hypothesis (\(H_0\)). There is not enough evidence to claim the data deviates from the expected model.

References

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

See Also

vonmises and cunif

Other Tests: ar_test(), kuiper_test(), norm_chisq(), rayleigh-test, watson_two_sample, watson_wheeler_test_perm(), weighted-rayleigh-test

Examples

# Example data from Mardia and Jupp (1999), pp. 93
watson_test(homing, axial = FALSE, 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$azi.PoR, alpha = .05, dist = "vonmises")
watson_test(sa.por$azi.PoR, alpha = .05, dist = "vonmises")