Beware the F test (or, how to compare variances)
Beware the F test (or, how to compare variances)
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DOI：
10.1016/j.anbehav.2017.12.014
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发表时间：
2018-02-01
期刊：
影响因子：
2.5
通讯作者：
Hodgson, D. J.
中科院分区：
文献类型：
--
作者：
Hosken, D. J.;Buss, D. L.;Hodgson, D. J.
生物学家通常比较样本之间的方差，以测试潜在的种群是否具有相等的传播。然而，尽管有统计学家的警告，不正确的测试仍然很普遍。在这里，我们表明，最常用的这些测试，F检验，是非常敏感的偏离正态性。当基础分布是重尾分布时，F检验的假阳性错误大大增加，这是一种很难使用标准正态性检验检测到的分布特征。我们强调和评估的选择参数，折刀和排列测试，考虑他们的表现方面的假阳性，并在它存在时检测信号的功率，然后显示正确的方法来比较样本之间的变化措施。基于这些评估，我们建议使用Levene检验、Box-Anderson检验、折刀检验或排列检验来比较正态性有疑问时的方差。Levene检验和Box-Anderson检验在小样本量下是最有效的，但Box-Anderson检验可能无法控制极端重尾分布的I型错误。如前所述，不要使用F检验来比较方差。(c)2018动物行为研究协会。由爱思唯尔有限公司出版。保留所有权利。
Biologists commonly compare variances among samples, to test whether underlying populations have equal spread. However, despite warnings from statisticians, incorrect testing is rife. Here we show that one of the most commonly employed of these tests, the F test, is extremely sensitive to deviations from normality. The F test suffers greatly elevated false positive errors when the underlying distributions are heavy tailed, a distribution feature that is very hard to detect using standard normality tests. We highlight and assess a selection of parametric, jackknife and permutation tests, consider their performance in terms of false positives, and power to detect signal when it exists, then show correct methods to compare measures of variation among samples. Based on these assessments, we recommend using Levene's test, Box-Anderson test, jackknifing or permutation tests to compare variances when normality is in doubt. Levene's and Box-Anderson tests are the most powerful at small sample sizes, but the Box-Anderson test may not control type I error for extremely heavy-tailed distributions. As noted previously, do not use F tests to compare variances. (c) 2018 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.