Consequences of grouped data for testing for departure from circular uniformity

Humphreys, Rosalind K.; Ruxton, Graeme D.

doi:10.1007/s00265-017-2393-2

Cited by 13 publications

(10 citation statements)

References 37 publications

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“…Our paper provides up-to-date and comprehensive comparisons of available tests, with clear guidelines which approach to use in which situation. We note, however, that we have considered only continuously distributed data, and for aggregated (grouped) circular data, we recommend Humphreys and Ruxton (2017) as a useful starting point.…”

Section: Resultsmentioning

confidence: 99%

Circular data in biology: advice for effectively implementing statistical procedures

Landler

Ruxton

Malkemper

2018

Behav Ecol Sociobiol

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134

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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.Electronic supplementary materialThe online version of this article (10.1007/s00265-018-2538-y) contains supplementary material, which is available to authorized users.

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Section: Resultsmentioning

confidence: 99%

Circular data in biology: advice for effectively implementing statistical procedures

Landler

Ruxton

Malkemper

2018

Behav Ecol Sociobiol

Self Cite

134

120

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“…This means that, instead of being continuously distributed, the possible recorded values are restricted to a finite number m of values equally spaced around the circle. A recent survey by Humphreys and Ruxton ( 2017 ) found that commonly experienced values of m are 4, 8, 12 and 36; with 12 and 36 being particularly common (Freedman 1979 ). These values suggest that the assumption of a continuous distribution is often strongly violated.…”

Section: Introductionmentioning

confidence: 99%

“…We have recently offered some guidance on how to overcome this mismatch between the assumptions of the statistical tests and commonly collected real-life data. The most commonly used circular test is the Rayleigh test, and Humphreys and Ruxton ( 2017 ) argued that this test could be used on samples of grouped data. However, that study only investigated sample sizes up to 50; in the current analysis, we extend that to larger sample sizes.…”

Section: Introductionmentioning

confidence: 99%

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

Landler

Ruxton

Malkemper

2020

Behav Ecol Sociobiol

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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. Significance statement Circular 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.

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“…Further, this test also can be demonstrated numerically to perform very reliably when deviations are of other unimodal forms [8] or if data is discrete (e.g. as might be produced by a measuring instrument with finite precision; [6]). However, this test is known to be less reliable when the deviation from uniformity is multi-modal, specifically its power to reject the null hypothesis when the deviation from uniformity involves more than one mode can be concerningly low even for substantial sample sizes [1, 17].…”

Section: Introductionmentioning

confidence: 99%

The Hermans–Rasson test as a powerful alternative to the Rayleigh test for circular statistics in biology

2019

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Background Circular data are gathered in diverse fields of science where measured traits are cyclical in nature: such as compass directions or times of day. The most common statistical question asked of a sample of circular data is whether the data seems to be drawn from a uniform distribution or one that is concentrated around one or more preferred directions. The overwhelmingly most-popular test of the null hypothesis of uniformity is the Rayleigh test, even though this test is known to have very low power in some circumstances. Here we present simulation studies evaluating the performance of tests developed as alternatives to the Rayleigh test. Results The results of our simulations demonstrate that a single test, the Hermans and Rasson test is almost as powerful as the Rayleigh test in unimodal situations (when the Rayleigh test does well) but substantially outperforms the Rayleigh test in multimodal situations. Conclusion We recommend researchers switch to routine use of the new Hermans and Rasson test. We also demonstrate that all available tests have low power to detect departures from uniformity involving more than two concentrated regions: we recommend that where researchers suspect such complex departures that they collect substantially-sized samples and apply another recent test due to Pycke that was designed specifically for such complex cases. We provide clear textual descriptions of how to implement each of these recommended tests and encode them in R functions that we provide. Electronic supplementary material The online version of this article (10.1186/s12898-019-0246-8) contains supplementary material, which is available to authorized users.

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Consequences of grouped data for testing for departure from circular uniformity

Cited by 13 publications

References 37 publications

Circular data in biology: advice for effectively implementing statistical procedures

Circular data in biology: advice for effectively implementing statistical procedures

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

The Hermans–Rasson test as a powerful alternative to the Rayleigh test for circular statistics in biology

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