Testing uniformity on the circle using spacings when data are rounded

Testing for uniformity for any given data set on the circle is an important first step before any further inference. One important class of tests are those based on spacings, which assume that the data are measured on a continuous scale. In practice however, the observed data may come grouped, or the recorded observations may be rounded values. Ignoring this fact can result in incorrect Type I error probabilities and inference, especially if the degree of rounding is severe or if the sample size is large. In this article, we propose a simple modification to such rounded data, which then allows us to continue to use the Rao’s spacing test and its exact critical values, without affecting the probability of Type I error. We provide theoretical justification for the suggested modification, as well as simulation studies that demonstrate its strong and robust performance.