Circular Statistics
Circular Distribution
Von Mises Distribution = normal distribution for
where
How spread is the distribution?
Resultant Vector Length (R)
- It describes how spread is the distrbution around the mean.
- range [0, 1]
Circular Variance
- Circular Variance = 1 - R
Info
Note that it does not describe the "expected deviation from the mean" as in normal linear statistics
Whether the distribution is uniform?
- If the distribution is von Mises
=> Parametric test for uniformity = Rayleigh test- The tested distribution must be von Mises
- Null hypothesis: the data are from a unifrom distribution
- If the distribution is not von Mises (e.g. bimodal)
=> Non-Parametric test (for linear data see Non-parametric methods):- Omnibus test
- Rao's test
Test for significance of the mean/median
| Circular | Similar tests for linear data | Prerequisites |
|---|---|---|
| circular version of t-test | student t-test | from a von Mises distribution |
| parametric paired-tests" Watson-Williams Test | paired-t test | from a von Mises distribution |
| non-parametric paired-test (on median!!!) | Kruskal-Wallis testNon-parametric methods#Non-parametric methods | no prerequisites for the distribution |
In non-parametric tests, median is always more important and better estimated, because it is more resilient to the outlier is more robust (e.g. considering when you have a outlier group far away from the 'main' distibution)