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Permutation Methods: A Distance Function Approach
Permutation Methods: A Distance Function Approach
Date: 28 April 2011, 08:33

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Univariate and multivariate permutation methods are presented that provide exact probability values and approximate probability values based on resampling and moment techniques. Metric Euclidean distance functions are emphasized, in contrast to the nonmetric squared Euclidean distance functions common to statistical tests that rely on the assumption of normality. Permutation methods based on Euclidean distance yield powerful robust statistics for the detection of phenomena such as cyclic, autoregressive, and overly regular patterns, multiple clumping, and directional shifts of correlated data. The authors describe permutation methods associated with completely randomized and randomized block experimental designs. Applications of the distance function permutation approach include binary, and rank data. Type I error controlled regression analyses, including both prediction and linear models, are delineated. Because the regression analyses are based on a metric Euclidean distance function, special attention is paid to Least sum of Absolute Deviations (LAD) regression. Recently developed goodness-of-fit tests, measures of agreement, multidimensional contingency table tests, and multisample univariate permutation methods are discussed and compared.

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