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A set of techniques referred to as circular statistics has been developed for the analysis of directional and orientational data. The unit of measure for such data is angular (usually in either degrees or radians), and the statistical distributions underlying the techniques are characterised by their cyclic nature—for example, angles of 359.9° are considered close to angles of 0°. In this paper, we assert that such approaches can be easily adapted to analyse time-of-day and time-of-week data, and in particular daily cycles in the numbers of incidents reported to the police. We begin the paper by describing circular statistics. We then discuss how these may be modified, and demonstrate the approach with some examples for reported incidents in the Cardiff area of Wales.