Watson-Williams Test

The Watson-Williams test compares mean directions of two or more groups of circular data, analogous to one-way ANOVA, assuming von Mises distributions with a common concentration.

왓슨-윌리엄스 검정은 둘 이상의 집단의 원형 자료 평균방향이 같은지를 검정하는 원형 분산분석으로, 같은 집중도를 가진 폰 미제스 분포를 가정합니다.

Do the groups differ in their average direction or average time of day?

집단마다 평균 방향이나 평균 발생 시각이 다른지 비교하고 싶어요.

The Watson-Williams test compares the sum of within-group resultant lengths with the overall resultant length, giving an F statistic with k − 1 and N − k degrees of freedom. A correction factor based on the pooled concentration (Stephens) improves the approximation, and a small p value means at least one group has a different mean direction.

When to use Watson-Williams Test

• You compare mean angles or clock times across two or more groups
• Each group is reasonably concentrated (pooled mean resultant length above about 0.45)
• Group concentrations are similar

When to use something else

• Data are widely dispersed or concentrations differ markedly; use a nonparametric common-median test for circular data
• The variable is linear; use one-way ANOVA

Assumptions and requirements

• Each group follows a von Mises distribution
• Groups share a common concentration parameter
• Observations are independent

What the analysis reports

• F statistic with degrees of freedom
• p value
• Group mean directions and mean resultant lengths
• Pooled concentration and Stephens correction factor

How to report it

A Watson-Williams test indicated a difference in mean direction among the [value] groups, F([value], [value]) = [value], p = [value].

Related methods

• Rayleigh Test of Uniformity
• One way ANOVA
• Circular Descriptive Statistics

Run Watson-Williams Test on Quorant