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Source: http://www.lock5stat.com/StatKey/randomization_1_quant_1_cat/randomization_1_quant_1_cat.html

There are three randomization methods for conducting the permutation test which is a non-parametric hypothesis test via simulation. The three randomization methods are

  1. reallocate groups
  2. shift groups
  3. combine groups.

I heard you choose which one to use depending on whether you have randomized assignment of treatments or depending on the experimental design.

So Duke University made this powerpoint discussing how to decide but it's incomplete

https://www2.stat.duke.edu/courses/Fall12/sta101.002/Sec4-45.pdf

This would be a quick into incase you don't know what I'm talking about and learn quickly.

How do I pick which of the three to use? I'm looking for an answer that's a flow chart.

  • In the lock5stat link, method 1 appears to be shuffling the treatment assignments, method 3 appears to be bootstrapping the sample, and method 2 appears to be effectively bootstrapping the residuals of the model of a simple difference in means. There is not a simple flowchart on when to pick one approach over the other. It depends on what you want the method to provide and what assumptions you can justify / live with. Here is a nice post discussing those assumptions. https://stats.stackexchange.com/questions/129485/what-are-the-assumptions-of-permutation-test – Robert Alan Greevy Jr PhD Aug 16 '19 at 18:57
  • Why bootstrap the sample? That's not a permutation test. A permutation test isn't bootstrapping. –  Aug 17 '19 at 15:23
  • Nor is the bootstrap being used a randomization test, which is the title of the web app you linked to. It's a fun app, but at this time, it's doubtful you should be using that webpage to base decisions on how to analyze your data. – Robert Alan Greevy Jr PhD Aug 18 '19 at 17:58

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