Permutation tests for univariate or multivariate analysis of variance and regression
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Abstract
The most appropriate strategy to be used to create a permutation distribution for tests of individual terms in complex experimental designs is currently unclear. There are often many possibilities, including restricted permutation or permutation of some form of residuals. This paper provides a summary of recent empirical and theoretical results concerning available methods and gives recommendations for their use in univariate and multivariate applications. The focus of the paper is on complex designs in analysis of variance and multiple regression (i.e., linear models). The assumption of exchangeability required for a permutation test is assured by random allocation of treatments to units in experimental work. For observational data, exchangeability is tantamount to the assumption of independent and identically distributed errors under a null hypothesis. For partial regression, the method of permutation of residuals under a reduced model has been shown to provide the best test. For analysis of variance, one must first identify exchangeable units by considering expected mean squares. Then, one may generally produce either (i) an exact test by restricting permutations or (ii) an approximate test by permuting raw data or some form of residuals. The latter can provide a more powerful test in many situations.
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The record
- Venue
- Canadian Journal of Fisheries and Aquatic Sciences
- Topic
- Optimal Experimental Design Methods
- Field
- Decision Sciences
- Canadian institutions
- —
- Funders
- —
- Keywords
- Permutation (music)UnivariateResamplingMathematicsMultivariate statisticsStatisticsIndependent and identically distributed random variablesNull distributionVariance (accounting)Omnibus testRegression analysisRandom permutationLinear regressionStatistical hypothesis testingEconometricsTest statisticRandom variableCombinatorics
- Has abstract in OpenAlex
- yes