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Circular data in biology: advice for effectively implementing statistical procedures.

ABSTRACT: Circular data are common in biological studies. The most fundamental question that can be asked of a sample of circular data is whether it suggests that the underlying population is uniformly distributed around the circle, or whether it is concentrated around at least one preferred direction (e.g. a migratory goal or activity phase). We compared the statistical power of five commonly used tests (the Rayleigh test, the V-test, Watson's test, Kuiper's test and Rao's spacing test) across a range of different unimodal scenarios. The V-test showed higher power for symmetrical distributions, Rao's spacing performed worst for all explored unimodal distributions tested and the remaining three tests showed very similar performance. However, the V-test only applies if the hypothesis is restricted to one (pre-specified) direction of interest. In all other unimodal cases, we recommend using the Rayleigh test. Much less explored is the multimodal case with data concentrated around several directions. We performed power simulations for a variety of multimodal situations, testing the performance of the widely used Rayleigh, Rao's, Watson, and Kuiper's tests as well as the more recent Bogdan and Hermans-Rasson tests. Our analyses of alternative statistical methods show that the commonly used tests lack statistical power in many of multimodal cases. Transformation of the raw data (e.g. doubling the angles) can overcome some of the issues, but only in the case of perfect f-fold symmetry. However, the Hermans-Rasson method, which is not yet implemented in any software package, outcompetes the alternative tests (often by substantial margins) in most of the multimodal situations explored. We recommend the wider uptake of the powerful but hitherto neglected Hermans-Rasson method. In summary, we provide guidance for biologists helping them to make decisions when testing circular data for single or multiple departures from uniformity.

SUBMITTER: Landler L

PROVIDER: S-EPMC6060829 | biostudies-other | 2018

REPOSITORIES: biostudies-other

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Circular data in biology: advice for effectively implementing statistical procedures.

Landler Lukas L Ruxton Graeme D GD Malkemper E Pascal EP

Behavioral ecology and sociobiology 20180711 8

Circular data are common in biological studies. The most fundamental question that can be asked of a sample of circular data is whether it suggests that the underlying population is uniformly distributed around the circle, or whether it is concentrated around at least one preferred direction (e.g. a migratory goal or activity phase). We compared the statistical power of five commonly used tests (the Rayleigh test, the V-test, Watson's test, Kuiper's test and Rao's spacing test) across a range of ...[more]

PMID: 30100666

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Project description:AbstractThe 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.Significance statementCircular data are widespread across biological disciplines, e.g. in orientation studies or circadian rhythms. Often these data are rounded to the nearest 1-10 degrees. We have shown previously that this leads to an inflation of false-positive results when testing whether the data is significantly different from a random distribution using the Rao test. Here we present a modification that avoids this increase in false-positives for rounded data while retaining statistical power for a variety of tests. In sum, we provide comprehensive guidance on how best to test for departure from uniformity in non-continuous data.

Dataset Information

Circular data in biology: advice for effectively implementing statistical procedures.

Publications

Circular data in biology: advice for effectively implementing statistical procedures.

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