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I need to do a Wilcoxon rank sum statistic for some data with a permuted-block with 2 blocks of size 6. However, I'm confused how we deal with the permuted-block randomization.

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.

(and that subsequently they may not be correct). 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. It however doesn't say how it accounts for it. I assume we must also account for it in the Wilcoxon test?

Here are the Data:

Participant 1   2   3   4   5   6   7   8   9   10  11  12
Assignment  1   2   1   2   1   2   1   2   1   2   1   2
Rank        12  1   11  2   10  3   9   4   8   5   6   7
Response    3.7 1.16    3.57    1.65    3.50    1.89    3.04    2.34    2.86    2.37    2.54    2.74
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