Bootstrap confidence interval for a between-condition concentration contrast

Contrasts the concentration of two (or more) groups via a stratified nonparametric bootstrap: angles are resampled with replacement within each group independently, and the contrast is recomputed on every resample. For a pair of groups it reports the difference in von Mises concentration (\(\Delta\kappa\)), the concentration ratio (\(\kappa_1/\kappa_2\)), and the difference in mean resultant length (\(\Delta R\)), each with a percentile confidence interval, plus a two-sided bootstrap p-value for \(\Delta\kappa = 0\). It is the assumption-light, estimation-focused companion to test_concentration (parametric equal.kappa / non-parametric Wallraff).

Usage

boot_kappa_contrast(
  hd,
  group_col,
  angle_col = "heading",
  conf = 0.95,
  R = 999L,
  axial = FALSE
)

Arguments

hd

Data frame containing headings in radians.

group_col

Grouping column. Required; must have at least two distinct values. With exactly two groups a single contrast row is returned; with more than two, every unordered pair is returned.

angle_col

Name of the heading column. Default "heading".

conf

Confidence level. Default 0.95.

R

Number of bootstrap resamples. Default 999. Set the RNG seed with set.seed for reproducible intervals.

axial

Logical; when TRUE, treat the angles as axial and estimate concentration in the doubled-angle frame (see boot_kappa_ci). Default FALSE.

Value

Data frame with one row per group pair: group1, group2, delta_kappa, delta_kappa_ci_lo/delta_kappa_ci_hi, kappa_ratio, kappa_ratio_ci_lo/kappa_ratio_ci_hi, delta_R, delta_R_ci_lo/delta_R_ci_hi, p_value (two-sided bootstrap p for \(\Delta\kappa = 0\)), n1, n2.

Details

The concentration ratio is skewed and can be unstable or non-finite when the denominator concentration is near zero; \(\Delta\kappa\) is the more robust default in the low-concentration regime.

See also

boot_kappa_ci, test_concentration