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An exact permutation method for testing any effect in balanced and unbalanced fixed effect ANOVA

机译：一种精确的置换方法，用于测试平衡和不平衡固定效应方差分析中的任何效应

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摘要

The ANOVA method and permutation tests, two heritages of Fisher, have been extensively studied. Several permutation strategies have been proposed by others to obtain a distribution-free test for factors in a fixed effect ANOVA (i.e., single error term ANOVA). The resulting tests are either approximate or exact. However, there exists no universal exact permutation test which can be applied to an arbitrary design to test a desired factor An exact permutation strategy applicable to fixed effect analysis of variance is presented. The proposed method can be used to test any factor, even in the presence of higher-order Interactions In addition, the method has the advantage of being applicable in unbalanced designs (all-cell-filled), which is a very common situation in practice, and it is the first method with this capability. Simulation studies show that the proposed method has an actual level which stays remarkably close to the nominal level, and its power is always competitive This is the case even with very small datasets, strongly unbalanced designs and non-Gaussian errors No other competitor show such an enviable behavior .
机译：方差分析方法和排列检验是费舍尔的两个遗产，已经得到了广泛的研究。其他人提出了几种置换策略，以获取固定效应方差分析（即单误差项方差分析）中因素的无分布检验。结果测试是近似的或精确的。但是，不存在可以应用于任意设计以测试所需因子的通用精确置换测试。提出了适用于方差固定效应分析的精确置换策略。所提出的方法即使在存在高阶相互作用的情况下也可以用于测试任何因素。此外，该方法具有适用于不平衡设计（全单元填充）的优点，这在实践中是非常普遍的情况，这是具有此功能的第一种方法。仿真研究表明，所提出的方法的实际水平非常接近标称水平，并且其功能始终具有竞争力。即使在数据集非常小，设计极不平衡且存在非高斯误差的情况下，情况也是如此。令人羡慕的行为。

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