Skip to contents

Watson-Williams test for equal mean directions

Source: R/stats-circular.R
watsonWilliamsTest.Rd

The circular analogue of a one-way ANOVA: tests whether two or more groups of angles share a common mean direction (assuming von Mises data of similar concentration). Use it to compare, e.g., coupling angles between limbs, speeds or groups.

Usage

watsonWilliamsTest(angles, group = NULL, units = c("degrees", "radians"))

Arguments

angles

Numeric vector of angles, or a list of per-group angle vectors.

group

Grouping factor (length length(angles)); required when angles is a single vector, ignored when angles is a list.

units

"degrees" (default) or "radians".

Value

an htest: F statistic (concentration-corrected), df and p.value. Warns when the pooled concentration is low (rbar < 0.45), where the test is unreliable.

References

Watson GS, Williams EJ (1956); Zar JH (1999) eq. 27.9.

See also

rayleighTest()

Examples

set.seed(2)
g1 <- rnorm(25, 20, 10); g2 <- rnorm(25, 60, 10)
watsonWilliamsTest(list(g1, g2))$p.value              # differ -> small
#> [1] 9.183644e-15