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Test a circular distribution for reflective symmetry

Source: R/circular_statistics.R
test_symmetry.Rd

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 .

See also

test_uniformity, vonmises_fit

Examples

hd <- derive_headings(cpunctatus, rule = "distal", carry = "arc")
test_symmetry(hd, group_col = "arc")
#>   arc  statistic   p_value  n                test
#> 1  10 1.56321945 0.1180010 29 reflective_symmetry
#> 2  15 0.88419396 0.3765915 30 reflective_symmetry
#> 3  20 0.29553248 0.7675871 27 reflective_symmetry
#> 4  30 0.08177353 0.9348268 37 reflective_symmetry
#> 5  40 0.07846124 0.9374612 20 reflective_symmetry
#> 6  50 0.20542215 0.8372423 26 reflective_symmetry
#> 7   5 0.01789729 0.9857208 31 reflective_symmetry
#> 8   0 0.69364399 0.4879055 35 reflective_symmetry