On the Gini Mean Difference Test for Circular Data

Tung, David D.; Jammalamadaka, S. Rao

doi:10.1080/03610926.2011.601947

Cited by 5 publications

(7 citation statements)

References 10 publications

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“…Finally, we tested a real-life example dataset of homing pigeon vanishing bearings explored by Tung and Jammalamadaka ( 2013 ). The application of the seven tests provided the following p values for standard (and, if available, TB) versions of the tests: Rayleigh 0.555, Watson p > 0.1 (0.138), Kuiper p > 0.15 (0.162), Rao 0.1 > p > 0.05 (0.0685), Gini 0.044 (0.048), HR 0.0034 (0.0039) and chi-squared 0.046.…”

Section: Resultsmentioning

confidence: 99%

“…The Gini and HR tests are carried out in the same fashion, only the test statistics differ. For the Gini test, the test statistic is given in Tung and Jammalamadaka ( 2013 ) as …”

Section: Methodsmentioning

confidence: 99%

“…We also applied the original and TB versions of all tests to an example dataset explored by Tung and Jammalamadaka ( 2013 ). This consists of the directions taken by 13 released homing pigeons.…”

Section: Methodsmentioning

confidence: 99%

“…Here we consider how that test functions when applied to grouped data. Finally, Tung and Jammalamadaka ( 2013 ) introduced a test based on the Gini mean difference in arc lengths between adjacent points in a sample that they argue is asymptotically more powerful than the Rao spacing test. Here we explore whether this test also suffers from the same lack of control of type I error that we observed in the Rao test and whether this control can be regained by the same modification.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Resultsmentioning

confidence: 99%

“…The Gini and HR tests are carried out in the same fashion, only the test statistics differ. For the Gini test, the test statistic is given in Tung and Jammalamadaka ( 2013 ) as …”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Landler

Ruxton

Malkemper

2020

Behav Ecol Sociobiol

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“…Recent non-Sobolev tests for circular uniformity include the four-point Cramérvon Mises test of Feltz and Goldin ( 2001), the likelihood-ratio test against a mixture with symmetric wrapped stable and circular uniform components of SenGupta and Pal ( 2001), the spacings-based Gini mean difference test of Tung and Jammalamadaka (2013), and the Bayesian tests of Mulder and Klugkist (2021) against the vM distribution and the kernel density estimator (18). Tests for uniformity on S d include that of Faÿ et al (2013), based on needlets (see Sect.…”

Section: Uniformitymentioning

confidence: 99%

Recent advances in directional statistics

Pewsey

García‐Portugués

2021

TEST

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Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere, and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper, we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (Wiley 1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, space situational awareness, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. AnWe are most grateful to three anonymous referees and, in alphabetical order, to

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U-statistic based on overlapping sample spacings

Singh

Misra

2023

Journal of Statistical Planning and Inference

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On the Gini Mean Difference Test for Circular Data

Cited by 5 publications

References 10 publications

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

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

Recent advances in directional statistics

U-statistic based on overlapping sample spacings

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