Abstract
Circular data is data that is measured on a circle in degrees or radians. It is fundamentally different from linear data due to its periodic nature (0° = 360°). Circular data arises in a large variety of research fields. Among others in ecology, the medical sciences, personality measurement, educational science, sociology, and political science circular data is collected. The most direct examples of circular data within the social sciences arise in cognitive and experimental psychology. However, despite numerous examples of circular data being collected in different areas of cognitive and experimental psychology, the knowledge of this type of data is not well-spread and literature in which these types of data are analyzed using methods for circular data is relatively scarce. This paper therefore aims to give a tutorial in working with and analyzing circular data to researchers in cognitive psychology and the social sciences in general. It will do so by focusing on data inspection, model fit, estimation and hypothesis testing for two specific models for circular data using packages from the statistical programming language R.
Highlights
Circular data arises in almost all fields of research, from ecology where data on the movement direction of animals is investigated (Rivest et al, 2015) to the medical sciences where protein structure (Mardia et al, 2006) or neuronal activity (Rutishauser et al, 2010) is investigated using periodic and circular measurements
Note that the Watson-Williams test falls within a different approach to modeling circular data, the intrinsic approach. In this approach we directly model the circular data instead of making use of a mathematical trick that allows us to model the data in bivaraite space and translate the results back to the circle
In this paper we have given a tutorial for researchers in cognitive psychology on how to analyse circular data using the package bpnreg
Summary
Circular data arises in almost all fields of research, from ecology where data on the movement direction of animals is investigated (Rivest et al, 2015) to the medical sciences where protein structure (Mardia et al, 2006) or neuronal activity (Rutishauser et al, 2010) is investigated using periodic and circular measurements. The most direct examples of circular data within the social sciences arise in cognitive and experimental psychology. Measurements at 0◦ and 360◦ represent the same direction whereas on a linear scale they would be located at opposite ends of a scale For this reason circular data require specific analysis methods. Some less technical textbooks on analysis methods for circular data have been written (Batschelet, 1981; Fisher, 1995; Pewsey et al, 2013). These works are not part of the “standard” texts on statistical analysis
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