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In the design of experiments, blocking refers to grouping similar experimental units together in groups ("blocks"). Comparing treatments based on within-block differences reduces the influence of extraneous variables, thus increasing power.

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Permuted block design Wilcoxon sum rank test

My book says When permuted-block randomization is used the permutation test should take the blocking into account. If blocking is ignored there is no randomization basis for tests. … It goes on to say that for a t-test if you do not account for the blocking it means it is not necessarily going to have a t distribution but if it is it will. …
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