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Is it technically possible to calculate the statistical power for a test where the two groups don't have by design the same size. I'm thinking to a 90%-10% split of the population.

Namely, is there a specific method for calculating the power with this experimental design?

Alternatively can I reasonably assume the required sample size is the size needed on the smaller of the two groups?

I'm quite dubious about this last approach because the variance on the two groups might differ significantly.

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  • $\begingroup$ If you have two samples that between them contain 100% of the population as you state, the power for any amount of falsity in the null should be 100%. $\endgroup$
    – Glen_b
    Sep 17, 2014 at 15:42
  • $\begingroup$ Assuming you don't mean the whole population, my question is why? Yes, it is technically possible. How to interpret depends on the software setup or formulation you use. But for the same total sample size, the power for comparing the groups is way smaller with a 90-10 allocation than with a 50-50 allocation. So I'd say you need a really good reason to require such an unbalanced split. $\endgroup$
    – Russ Lenth
    Sep 17, 2014 at 23:25
  • $\begingroup$ @rvl: The reason why you might want to try a 90-10 allocation is due to business. You might want to test the effectiveness of a certain solution using a hold out group a little as possible without affecting statistical power. $\endgroup$
    – Gianluca
    Sep 20, 2014 at 19:12

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