A new method for non-parametric multivariate analysis of variance
A new method for non-parametric multivariate analysis of variance
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DOI：
10.1111/j.1442-9993.2001.01070.pp.x
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发表时间：
2001-02-01
期刊：
影响因子：
1.5
通讯作者：
Anderson, MJ
中科院分区：
文献类型：
--
作者：
Anderson, MJ
多变量数据的假设检验方法需要对实验中因子的影响及其相互作用做出严格的概率陈述。方差分析对于单变量数据的分析特别强大。然而，传统的多元模拟，在大多数生态多元数据集的假设过于严格。最好采用基于排列检验的非参数方法。本文继McArdle和安德森（出版中）之后，提出了一种新的非参数多元方差分析方法。它在这里给出，在生态学中的几个应用，提供一个替代的，也许更直观的制定方差分析（基于平方距离的总和），以补充由麦卡德尔和安德森（在出版）提供的描述，用于分析任何线性模型。它是对以前的非参数方法的改进，因为它允许对复杂模型的变化进行直接的加法分割。它这样做，同时保持灵活性和缺乏其他非参数方法的正式假设。检验统计量是Fisher F比的多变量模拟，并直接从任何对称距离或相异度矩阵计算。然后使用排列获得P值。该方法的一些例子给出了测试涉及几个因素，包括析因和层次（嵌套）设计和测试的相互作用。
Hypothesis-testing methods for multivariate data are needed to make rigorous probability statements about the effects of factors and their interactions in experiments. Analysis of variance is particularly powerful for the analysis of univariate data. The traditional multivariate analogues, however, are too stringent in their assumptions for most ecological multivariate data sets. Non-parametric methods, based on permutation tests, are preferable. This paper describes a new non-parametric method for multivariate analysis of variance, after McArdle and Anderson (in press). It is given here, with several applications in ecology, to provide an alternative and perhaps more intuitive formulation for ANOVA (based on sums of squared distances) to complement the description provided by McArdle and Anderson (in press) for the analysis of any linear model. It is an improvement on previous non-parametric methods because it allows a direct additive partitioning of variation for complex models. It does this while maintaining the flexibility and lack of formal assumptions of other non-parametric methods. The test-statistic is a multivariate analogue to Fisher's F-ratio and is calculated directly from any symmetric distance or dissimilarity matrix. P-values are then obtained using permutations. Some examples of the method are given for tests involving several factors, including factorial and hierarchical (nested) designs and tests of interactions.