Consequences of grouped data for testing for departure from circular uniformity

Limits to the precision of circular data often cause grouping of data points into discrete categories; but the effects of grouping on tests for circular uniformity have been little explored. The Rayleigh test is often applied to grouped circular data, despite it being designed for continuous data and the statistical literature recommending a suite of alternative tests specifically designed for grouped data. Here we investigated the performance of the Rayleigh test relative to four alternatives for testing the null hypothesis of uniformity in grouped circular data. We employed simulations grouping data into a discrete number of same-sized categories, and with samples drawn from a range of different distributions. We found that grouping had little effect on the type I error rate or the power of the Rayleigh test, and that the power of the Rayleigh test was very similar to that of the previously-recommended alternative tests designed specifically for grouped circular data. It may thus be appropriate to apply the Rayleigh test to grouped data, providing the situation is one in which the test has substantial statistical power.