Grouped circular data in biology: advice for effectively implementing statistical procedures

Lukas Landler, Graeme D. Ruxton, E. Pascal Malkemper*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


The most common statistical procedure with a sample of circular data is to test the null hypothesis that points are spread uniformly around the circle without a preferred direction. An array of tests for this has been developed. However, these tests were designed for continuously distributed data, whereas often (e.g. due to limited precision of measurement techniques) collected data is aggregated into a set of discrete values (e.g. rounded to the nearest degree). This disparity can cause an uncontrolled increase in type I error rate, an effect that is particularly problematic for tests that are based on the distribution of arc lengths between adjacent points (such as the Rao spacing test). Here, we demonstrate that an easy-to-apply modification can correct this problem, and we recommend this modification when using any test, other than the Rayleigh test, of circular uniformity on aggregated data. We provide R functions for this modification for several commonly used tests. In addition, we tested the power of a recently proposed test, the Gini test. However, we concluded that it lacks sufficient increase in power to replace any of the tests already in common use. In conclusion, using any of the standard circular tests (except the Rayleigh test) without modifications on rounded/aggregated data, especially with larger sample sizes, will increase the proportion of false-positive results—but we demonstrate that a simple and general modification avoids this problem.
Original languageEnglish
Article number100
Number of pages8
JournalBehavioral Ecology and Sociobiology
Issue number8
Publication statusPublished - 20 Jul 2020


  • Gini test
  • Hermans-Rasson test
  • Rao’s spacing test
  • Rayleigh test
  • Rounding error
  • Type I error


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