Using circular statistics to analyse spatial flow and temporal data

Circular statistics is a specialized branch of statistics that is focused on the visualization and analysis of directional data. Directional data can be classified into two broad categories: · those arising from a direction – for example, data describing movement over space, such as the daily journey-to-work (JTW); or · some unit of time · for example, data describing the time that calls are received by the emergency services. The data from both of these sources can be considered cyclic and as such can be plotted on a circle, either as a direction (in which the circle would represent a compass) or some unit of time (in which the circle would represent a clock). The early roots of circular statistics can be traced to the mid-eighteenth century (Bernoulli, 1734) where circular measures were first used to show that the orbital planes of the planets in the solar system could not be aligned by chance (see Mardia, 1972), and Florence Nightingale (Nightingale, 1858) developed the rose diagram to illustrate the efficacy of improved sanitation in hospitals during the Crimean War. Since these early beginnings, circular statistics have developed as a set of techniques that largely remains the domain of non-human-related research, having been applied in a number of disciplines including the physical, ecological and biological sciences