Introduction to circular data

In many diverse scientific fields, the measurements are directions. For instance, a biologist may be measuring the direction of flight of a bird or the orientation of an animal. A series of such observations is called”directional data”. Since a direction has no magnitude, these can be conveniently represented as points on the circumference of a unit circle centered at the origin or as unit vectors connecting the origin to these points. Because of this circular representation, such observations are also called circular data. In this paper, circular data will be introduced at first and then it is explained how to calculate the mean direction, dispersion and higher moments. The solutions to many directional data problems are often not obtainable in simple closed analytical forms. Therefore, computer softwares is essential to use these methods. At the end of this paper, the CircStat’s package has been used to analyze data sets in R and Matlab softwares.