By Beau Lucas
Today will be a brief introduction in to circular statistics (sometimes referred to as directional statistics). Circular statistics is an interesting subdivision of statistics involving observations taken as vectors around a unit circle. As an example, imagine measuring birth times at a hospital over a 24-hour cycle, or the directional dispersion of a group of migratory animals. This type of data is involved in a variety fields, such as ecology, climatology, and biochemistry. The nature of measuring observations around a unit circle necessitates a different approach to hypothesis testing. Distributions need to be “wrapped” around the circle to be of use, and conventional estimators such as the sample mean or sample variance hold no water.
In this post, we will conduct Rao’s Spacing Test to assess the uniformity of a circular dataset. This is a basic procedure and should be thought of as an introduction to handling circular data.
Getting started
We are going to conduct a hypothesis test on turtles, a small dataset consisting of the arrival angles of 10 green sea turtles to their nesting island. Our goal is to determine where the arrival angles show signs of directionality or are more indicative of a random scatter.
First, install the circular package and attach the turtles dataset.
install.packages("circular")
require(circular)
attach(turtles)
Plotting the data
The circular package contains its own plotting function, plot.circular. Let’s observe the arrival angles of the turtles.
plot.circular(arrival)
Here is the plot:
Given the eye test, the observations appear to be uniform around the circle. If we want to run a hypothesis test to determine if the data is truly uniform, we will need to develop a test statistic that works with angular data.
What is a good parameter for us to utilize? Taking the sample mean doesn’t tell us much about the direction of the data (180 degrees is not a useful mean of 2 degrees and …read more
Source:: r-bloggers.com