Test a circular distribution for reflective symmetry

Pewsey's (2002) omnibus test of reflective symmetry about an unspecified mean direction, based on the standardised second central sine moment. The null hypothesis is that the distribution is symmetric about its mean direction; a small p-value indicates skewness (asymmetry). Useful as a precondition check before applying methods that assume symmetry, such as a von Mises fit or the Watson-Williams test.

Usage

test_symmetry(
  hd,
  group_col = NULL,
  angle_col = "heading",
  p_adjust = "none",
  axial = FALSE
)

Arguments

hd: Data frame with a heading column in radians.
group_col: Column to group by. NULL (default) tests the whole data frame as one group.
angle_col: Heading column name. Default "heading".
p_adjust: Multiple-comparison correction method passed to p.adjust. Default "none". Applies only when group_col is supplied; a p_value_adj column is added.
axial: Logical. Treat the angles as axial (bidirectional, mod-pi) data: symmetry is tested via the angle-doubling method. Default FALSE.

Value

Tidy data frame with columns group_col (if supplied), statistic (the standardised \(|\bar b_2|\)), p_value, n, test, and p_value_adj (when p_adjust != "none"). Groups with fewer than four finite angles yield NA statistics.

Details

The test uses a large-sample normal approximation and can be liberal at small \(n\) or low concentration; treat borderline results at small samples with caution.

References

Pewsey, A. (2002). Testing circular symmetry. Canadian Journal of Statistics 30(4), 591–600. doi:10.2307/3316098 .