First we analyse the ANOVA dataset using a method for circular GLM and give interpretation guidelines for this model. After that we will continue with an analysis of the example datasets. Then we introduce the ANOVA example after which descriptive methods for circular data are explained through a section on data inspection for this example. First however, we give a short introduction to circular data in general. One is an example for an ANOVA model and the other for a mixed-effects model. The structure of the tutorial is such that the reader is guided by two examples throughout the paper. The reader does not need to be familiar with circular data. Note that for an optimal understanding of the paper, the reader should ideally have some knowledge on R ( R Core Team, 2017) and on GLM and mixed-effects models in the linear setting. We do so for the flexibility of this approach and the resulting variety in types of models that have already been outlined in the literature on circular data for this approach. In this tutorial we decide to mainly focus on one particular approach to the analysis of circular data, the embedding approach.
We will discuss data inspection, model fit, estimation and hypothesis testing in general linear models (GLM) and mixed-effects models.
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The main goal of this tutorial is to explain how to inspect and analyse your data when the outcome variable is circular. Therefore, this paper aims at giving a tutorial in working with and analysing circular data to researchers in cognitive psychology and the social sciences in general.
However, these works are not part of the “standard” texts on statistical analysis in psychology or the social sciences in general nor are they very well known amongst social scientific researchers. Some less technical textbooks on analysis methods for circular data have been written ( Batschelet, 1981 Fisher, 1995 Pewsey et al., 2013). For this reason circular data require specific analysis methods. On the circle, measurements at 0° and 360° represent the same direction whereas on a linear scale they would be located at opposite ends of a scale.
Circular data is fundamentally different from linear data due to its periodic nature. However, despite the fact that circular data is being collected in different areas of cognitive and experimental psychology, the knowledge of this type of data is not well-spread. Other examples include the visual perception of space ( Matsushima et al., 2014), visual working memory ( Heyes et al., 2016) and sensorimotor synchronization in music making ( Kirschner and Tomasello, 2009). The closer the participants' pointing or walking direction was to the actual north or target object, the better their sense of direction. For example, in experiments on cognitive maps the human sense of direction is investigated through asking participants in a study to point north ( Brunyé et al., 2015) or to walk to a target object ( Warren et al., 2017). The most direct examples of circular data within the social sciences arise in cognitive and experimental psychology. 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.Ĭircular 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 thus circular measurements. 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. 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. Among others in ecology, the medical sciences, personality measurement, educational science, sociology, and political science circular data is collected. Circular data arises in a large variety of research fields. It is fundamentally different from linear data due to its periodic nature (0° = 360°). Department of Methodology and Statistics, Faculty of Social and Behavioural Sciences, Utrecht University, Utrecht, NetherlandsĬircular data is data that is measured on a circle in degrees or radians.
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