Test whether groups share the same circular distribution

Compares the angular distributions of two or more groups. Complements test_mean_directions (which tests only the mean direction) and test_concentration (which tests only the spread) by testing the distributions as a whole, or – for method = "rao" – the mean and the dispersion jointly.

Usage

test_distributions(
  hd,
  group_col,
  angle_col = "heading",
  method = c("watson_wheeler", "watson_two", "rao"),
  pairwise = FALSE,
  p_adjust = "none",
  axial = FALSE,
  p_method = c("table", "monte_carlo"),
  n_perm = 9999L
)

Arguments

hd

Data frame with heading and group columns.

group_col

Column identifying the groups to compare.

angle_col

Heading column in radians. Default "heading".

method

One of "watson_wheeler" (default), "watson_two", or "rao".

pairwise

Logical. FALSE (default) runs a single omnibus test across all groups ("watson_two" then requires exactly two groups). TRUE runs every pairwise comparison.

p_adjust

Multiple-comparison correction passed to p.adjust. Default "none". Applies only to the pairwise output, where a p_value_adj column is added; "BH" or "holm" are recommended. Meaningless for the tabled "watson_two" p-values.

axial

Logical. Treat the angles as axial (bidirectional, mod-pi) data: the test is run via the angle-doubling method. Default FALSE.

p_method

For method = "watson_two" only: "table" (default) reports the tabled significance band; "monte_carlo" instead returns a continuous permutation p-value from n_perm label shuffles. Ignored by the other methods (which already give continuous p-values).

n_perm

Number of label permutations for p_method = "monte_carlo". Default 9999. Set the RNG seed with set.seed for reproducible p-values.

Value

A tidy data frame. Omnibus output has columns method, component, statistic, df, p_value, n_groups, n. Pairwise output replaces n_groups with group1/group2 and adds p_value_adj when p_adjust != "none".

Details

"watson_wheeler" (default)

Mardia-Watson-Wheeler uniform-scores test: a non-parametric k-sample test that makes no von Mises assumption. Returns an exact (chi-squared) p-value.

"watson_two"

Watson's two-sample \(U^2\) test of homogeneity. Strictly two-sample: with more than two groups set pairwise = TRUE. The circular package returns only tabled critical values, so by default p_value is the upper edge of a tabled band (e.g. 0.05 means \(0.01 < p < 0.05\)) and is NA when \(p > 0.10\). Set p_method = "monte_carlo" for a continuous permutation p-value.

"rao"

Rao's test for homogeneity of both mean directions and dispersions across k groups; returns two rows per comparison, one for each component ("mean", "dispersion").

See also

test_mean_directions, test_concentration, test_uniformity