Date: Sun, 30 Apr 2006 14:18:56 -0700 David L Cassell "SAS(r) Discussion" David L Cassell Re: How to get two-sided p value of permutation test <200604302041.k3UAkPXW027943@mailgw.cc.uga.edu> text/plain; format=flowed

mufannnn@YAHOO.COM wrote: >Hello, everybody: > >I have two questions about permutation tests (Fisher's randomization >tests). > >I used permutation test to analyze the difference between two unbalanced >groups. One group has 3 observations, the other has 5. The procedure is as >following: > >1. calculate the sum of group 1 as observed value--obs; >2. recompute the sum of group 1 for each permutation (totally 56 >permutations) >3. Of these 56 combinations, I calculate the number N of group 1 sum >greater >than or equal to obs(original sum). >4. get one sided p-value using: N/56. > >My questions are: > >1.Is it the right procedure for unbalanced comparison? >2.How to get two-sided p-value? especially when one-sided p-value>0.5?

[1] No. The 'unbalanced' part is not the problem. The problems are the sample size and the method used.

There's no reason why 'unbalanced' means you cannot use ordinary statistical approaches. But there's no way around the fact that you have ridiculously small groups. You are not going to get any sort of power (probability of finding a significant difference when there really is one) that you can live with.

Now why do you have 8 observations? How did the study work? How did you categorize into two groups? A permutation test makes assumptions about the nature of the data and the meta-data. Your data may not meet those specs. I would like you to write back to SAS-L and explain more about your study. If you cannot afford more than 8 observations, then perhaps you should give up on the 'statistical inference' part of the study.

And finally, I do not see that you are using an appropriate approach. What are you trying to test? Why is the sum of group 1 meaningful? How can the mere sum be attributed as meaning something about your study if you do not compare against group 2, and you do not think about the variability involved within and across groups? It seems from way over here that your method -before you evne get to a randomization test - is flawed.

[2] I don't think there's any point in talking about 1-sided and 2-sided tests until you get part #1 fixed first.

I think you would benefit from writing back to SAS-L and discussing your problem in a lot more depth. What are you data? Where do they come from? What do they mean? What do you want to achieve with these data? What is your hypothesis that you want to test? (Write the null and alternative hypotheses as explicitly as possible, putting them into mathematical formulas if you can.) What will you do once you make a 'significant difference'/'no significant difference' evaluation?

HTH, David -- David L. Cassell mathematical statistician Design Pathways 3115 NW Norwood Pl. Corvallis OR 97330

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