Permutation Test with Stratified Data and Repeated Measurements

April 21, 2011
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This is an example for a permutation test on stratified samples with repeated measurements. Samples are interdependent firstly because they come from several sites and secondly because the sampling was repeated a second time. That is samples of the same sites are dependent and sample t1 and sample t2, taken from the very same places are dependent. 

What I want to test is whether there is a difference between timepoint one (t1) and two (t2) or not. A hypothesis could be: the average difference t1-t2 is sign. larger than zero (a one-sided test). Another hypothesis could be: the average difference is sign. different from zero, either larger or smaller (a two-sided test).

If you deal with a distribution of your data that ordinary Linear Mixed Models (LMMs) or Generalized LMMs (GLMMs) can handle you should vote for this option – but sometimes you deal with awkard data and permutation tests may the only thing to bail you out…

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