Abstract
Synchronized permutation tests have been introduced to test for main effects and interaction in two-way ANOVA problems (Pesarin, 2001, Salmaso, 2003, Basso et al., 2007). The permutation space is restricted in order the test statistic for each factor or interaction to depend only on the true effects (if any) under testing and on exchangeable errors. The proposed test statistics can be viewed as a direct combination (i.e. the sum) of partial statistics to perform all pair-wise comparisons between the effects of a main factor. Note that the tests for each comparison are dependent. Constrained synchronized permutations allow to test all pair-wise comparisons between pairs of effects of a main factor. Simultaneous and individual confidence intervals for each comparison can be provided through CSP tests.
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