The multivariate analysis of variance as a powerful approach for circular data

Lukas Landler; Graeme D. Ruxton; E. Pascal Malkemper

doi:10.1186/s40462-022-00323-8

The multivariate analysis of variance as a powerful approach for circular data

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Background
A broad range of scientific studies involve taking measurements on a circular, rather than linear, scale (often variables related to times or orientations). For linear measures there is a well-established statistical toolkit based on linear modelling to explore the associations between this focal variable and potentially several explanatory factors and covariates. In contrast, statistical testing of circular data is much simpler, often involving either testing whether variation in the focal measurements departs from circular uniformity, or whether a single explanatory factor with two levels is supported.

Methods
We use simulations and example data sets to investigate the usefulness of a MANOVA approach for circular data in comparison to commonly used statistical tests.

Results
Here we demonstrate that a MANOVA approach based on the sines and cosines of the circular data is as powerful as the most-commonly used tests when testing deviation from a uniform distribution, while additionally offering extension to multi-factorial modelling that these conventional circular statistical tests do not.

Conclusions
The herein presented MANOVA approach offers a substantial broadening of the scientific questions that can be addressed statistically using circular data.

Original language	English
Article number	21
Number of pages	10
Journal	Movement Ecology
Volume	10
DOIs	https://doi.org/10.1186/s40462-022-00323-8
Publication status	Published - 27 Apr 2022

Keywords

MANOVA
Rayleigh test
Directional data
Orientation
Periodicity

Access to Document

10.1186/s40462-022-00323-8Licence: CC BY

Landler_2022_ME_MANOVA-for-circular-data_CC
Copyright © The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Final published version, 2.65 MBLicence: CC BY

Additional file 1 of The multivariate analysis of variance as a powerful approach for circular data
Landler, L. (Creator), Ruxton, G. D. (Creator) & Malkemper, E. P. (Creator), Figshare, 2022
DOI: 10.6084/m9.figshare.19670032.v1
Dataset

Cite this

@article{56d08e94ea1a43c3819fc1c971aaeef9,

title = "The multivariate analysis of variance as a powerful approach for circular data",

abstract = "BackgroundA broad range of scientific studies involve taking measurements on a circular, rather than linear, scale (often variables related to times or orientations). For linear measures there is a well-established statistical toolkit based on linear modelling to explore the associations between this focal variable and potentially several explanatory factors and covariates. In contrast, statistical testing of circular data is much simpler, often involving either testing whether variation in the focal measurements departs from circular uniformity, or whether a single explanatory factor with two levels is supported.MethodsWe use simulations and example data sets to investigate the usefulness of a MANOVA approach for circular data in comparison to commonly used statistical tests.ResultsHere we demonstrate that a MANOVA approach based on the sines and cosines of the circular data is as powerful as the most-commonly used tests when testing deviation from a uniform distribution, while additionally offering extension to multi-factorial modelling that these conventional circular statistical tests do not.ConclusionsThe herein presented MANOVA approach offers a substantial broadening of the scientific questions that can be addressed statistically using circular data.",

keywords = "MANOVA, Rayleigh test, Directional data, Orientation, Periodicity",

author = "Lukas Landler and Ruxton, {Graeme D.} and Malkemper, {E. Pascal}",

note = "LL is supported by the Austrian Science Fund (FWF, Grant Number: P32586). EPM receives funding from the European Research Council (ERC) under the European Union{\textquoteright}s Horizon 2020 research and innovation program (Grant Agreement No. 948728).",

year = "2022",

month = apr,

day = "27",

doi = "10.1186/s40462-022-00323-8",

language = "English",

volume = "10",

journal = "Movement Ecology",

issn = "2051-3933",

publisher = "BioMed Central",

}

TY - JOUR

T1 - The multivariate analysis of variance as a powerful approach for circular data

AU - Landler, Lukas

AU - Ruxton, Graeme D.

AU - Malkemper, E. Pascal

N1 - LL is supported by the Austrian Science Fund (FWF, Grant Number: P32586). EPM receives funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 948728).

PY - 2022/4/27

Y1 - 2022/4/27

N2 - BackgroundA broad range of scientific studies involve taking measurements on a circular, rather than linear, scale (often variables related to times or orientations). For linear measures there is a well-established statistical toolkit based on linear modelling to explore the associations between this focal variable and potentially several explanatory factors and covariates. In contrast, statistical testing of circular data is much simpler, often involving either testing whether variation in the focal measurements departs from circular uniformity, or whether a single explanatory factor with two levels is supported.MethodsWe use simulations and example data sets to investigate the usefulness of a MANOVA approach for circular data in comparison to commonly used statistical tests.ResultsHere we demonstrate that a MANOVA approach based on the sines and cosines of the circular data is as powerful as the most-commonly used tests when testing deviation from a uniform distribution, while additionally offering extension to multi-factorial modelling that these conventional circular statistical tests do not.ConclusionsThe herein presented MANOVA approach offers a substantial broadening of the scientific questions that can be addressed statistically using circular data.

AB - BackgroundA broad range of scientific studies involve taking measurements on a circular, rather than linear, scale (often variables related to times or orientations). For linear measures there is a well-established statistical toolkit based on linear modelling to explore the associations between this focal variable and potentially several explanatory factors and covariates. In contrast, statistical testing of circular data is much simpler, often involving either testing whether variation in the focal measurements departs from circular uniformity, or whether a single explanatory factor with two levels is supported.MethodsWe use simulations and example data sets to investigate the usefulness of a MANOVA approach for circular data in comparison to commonly used statistical tests.ResultsHere we demonstrate that a MANOVA approach based on the sines and cosines of the circular data is as powerful as the most-commonly used tests when testing deviation from a uniform distribution, while additionally offering extension to multi-factorial modelling that these conventional circular statistical tests do not.ConclusionsThe herein presented MANOVA approach offers a substantial broadening of the scientific questions that can be addressed statistically using circular data.

KW - MANOVA

KW - Rayleigh test

KW - Directional data

KW - Orientation

KW - Periodicity

U2 - 10.1186/s40462-022-00323-8

DO - 10.1186/s40462-022-00323-8

M3 - Article

SN - 2051-3933

VL - 10

JO - Movement Ecology

JF - Movement Ecology

M1 - 21

ER -

The multivariate analysis of variance as a powerful approach for circular data

Abstract

Keywords

Access to Document

Fingerprint

Datasets

Additional file 1 of The multivariate analysis of variance as a powerful approach for circular data

Cite this