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I want to calculate sample size for a classic multiple testing problem of multiple doses in clinical trials. I have 3 groups: "high dose", "low dose" and "placebo", and I wish to test if at least one of the doses is significantly different than the placebo. Let's assume equal variances and normality, for simplicity. I wish to use a multiple testing method such as the Hochberg method (could be also Holm, but let's stick to Hochberg). I want to ask if there is a formula for calculating sample size and power, and if not, I'll need a simulation. In this case, what are the steps I need to do ? I know how to make a simulation for a t-test: I take N random samples with the means and standard deviations of interest, I run the t-test for each sample and count in how many samples the P value was rejected, this is the power for the specific sample size. How should I do it for my problem here ? I couldn't find a good solution online. I prefer writing in SAS, but R will do as well.

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If you are willing to assume normality, you don't have to run simulations to perform power calculations. One easy-to-use and flexible tool is provided by a Java applet available from Russ Lenth's power and sample-size page. From your description, it seems that the "Balanced ANOVA" analysis is what you need.

Note that if all you care about is whether "at least one of the doses is significantly different than the placebo" then the simple F-test from the ANOVA might be adequate. A significant F-test means that there are significant differences among the three groups, so if the placebo result is either less than or greater than both of the test groups you are done.

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