Institute of Zoology, University of Natural Resources and Life Sciences (BOKU), Gregor-Mendel-Straße 33/I, 1180, Vienna, Austria.
School of Biology, University of St Andrews, St Andrews, KY16 9TH, UK.
Sci Rep. 2021 Oct 13;11(1):20337. doi: 10.1038/s41598-021-99299-5.
Many biological variables are recorded on a circular scale and therefore need different statistical treatment. A common question that is asked of such circular data involves comparison between two groups: Are the populations from which the two samples are drawn differently distributed around the circle? We compared 18 tests for such situations (by simulation) in terms of both abilities to control Type-I error rate near the nominal value, and statistical power. We found that only eight tests offered good control of Type-I error in all our simulated situations. Of these eight, we were able to identify the Watson's U test and a MANOVA approach, based on trigonometric functions of the data, as offering the best power in the overwhelming majority of our test circumstances. There was often little to choose between these tests in terms of power, and no situation where either of the remaining six tests offered substantially better power than either of these. Hence, we recommend the routine use of either Watson's U test or MANOVA approach when comparing two samples of circular data.
许多生物学变量都是在圆形刻度上记录的，因此需要不同的统计处理。对于这样的循环数据，人们经常会问一个问题，即两个组之间的比较：从两个样本中抽取的两个群体在圆周围的分布是否不同？我们通过模拟比较了 18 种用于这种情况的检验方法（根据模拟），包括控制第一类错误率接近名义值的能力和统计功效。我们发现，只有 8 种检验方法在我们所有模拟的情况下都能很好地控制第一类错误。在这 8 种检验方法中，我们发现基于数据三角函数的 Watson U 检验和多元方差分析（MANOVA）方法在绝大多数情况下都具有最佳的功效。这两种检验方法在功效方面往往没有太大区别，而且在没有一种检验方法的功效明显优于另外两种检验方法的情况下。因此，当比较两组循环数据时，我们建议常规使用 Watson U 检验或 MANOVA 方法。
