Landler Lukas, Ruxton Graeme D, Malkemper E Pascal
Institute of Zoology, University of Natural Resources and Life Sciences (BOKU), Gregor-Mendel-Straße 33, 1180, Vienna, Austria.
School of Biology, University of St Andrews, St Andrews, KY16 9TH, UK.
Mov Ecol. 2022 Apr 27;10(1):21. doi: 10.1186/s40462-022-00323-8.
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.
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.
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.
The herein presented MANOVA approach offers a substantial broadening of the scientific questions that can be addressed statistically using circular data.
广泛的科学研究涉及在圆形而非线性尺度上进行测量（通常是与时间或方向相关的变量）。对于线性测量，有一套基于线性建模的成熟统计工具包，用于探索该焦点变量与潜在的多个解释因素和协变量之间的关联。相比之下，圆形数据的统计检验要简单得多，通常涉及检验焦点测量值的变化是否偏离圆形均匀性，或者是否支持具有两个水平的单个解释因素。
我们使用模拟和示例数据集来研究多变量方差分析（MANOVA）方法对圆形数据的有用性，并与常用统计检验进行比较。
我们在此证明，基于圆形数据的正弦和余弦的多变量方差分析方法在检验偏离均匀分布时与最常用的检验一样有效，同时还提供了传统圆形统计检验所没有的多因素建模扩展。
本文提出的多变量方差分析方法极大地拓宽了可以使用圆形数据进行统计处理的科学问题范围。
