Applying Circular Statistics to the Analysis of Monitoring Data

Abstract

Abstract. Patterns of psychological variables in time have been of interest to research from the beginning. This is particularly true for ambulatory monitoring research, where large (cross-sectional) time-series datasets are often the matter of investigation. Common methods for identifying cyclic variations include spectral analyses of time-series data or time-domain based strategies, which also allow for modeling cyclic components. Though the prerequisites of these sophisticated procedures, such as interval-scaled time-series variables, are seldom met, their usage is common. In contrast to the time-series approach, methods from a different field of statistics, directional or circular statistics, offer another opportunity for the detection of patterns in time, where fewer prerequisites have to be met. These approaches are commonly used in biology or geostatistics. They offer a wide range of analytical strategies to examine “circular data,” i.e., data where period of measurement is rotationally invariant (e.g., directions on the compass or daily hours ranging from 0 to 24, 24 being the same as 0). In psychology, however, circular statistics are hardly known at all. In the present paper, we intend to give a succinct introduction into the rationale of circular statistics and describe how this approach can be used for the detection of patterns in time, contrasting it with time-series analysis. We report data from a monitoring study, where mood and social interactions were assessed for 4 weeks in order to illustrate the use of circular statistics. Both the results of periodogram analyses and circular statistics-based results are reported. Advantages and possible pitfalls of the circular statistics approach are highlighted concluding that ambulatory assessment research can benefit from strategies borrowed from circular statistics.