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I need to calculate the sample size needed. The outcome variable is binary (0 if no, 1 if yes). I have three groups (e.g., group A, group B, group C). What I know (or assume) is that the proportions of "yes" for group A, group B and group C are 15%, 25% and 45%, respectively.

If I have two groups (two proportions), I would simply use the function "power.prop.test" in R (Power Calculations for Two-Sample Test for Proportions).

However, in this case, I have three groups and, accordingly, three proportions. Under this circumstance, which method/technique should I use to calculate the sample size to achieve 80% power and significance level of 0.5?

I can use R and Stata. Many thanks!

  • You can use simulation to do this, but you will need to be specific about the hypotheses you want to test. – dimitriy Apr 07 '21 at 01:08
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    There is a nice example in R [here](https://stats.stackexchange.com/a/468000/7071). – dimitriy Apr 07 '21 at 01:16
  • @DimitriyV.Masterov Hi Dimitriy! Thanks for the comment. I tried three different ways based on the link that you suggested. I noticed that the number of participants needed is varying somewhat greatly depending on the methods. Is it normal? If so, what will be the reason? – rudgus51998 Apr 07 '21 at 14:02
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    Without seeing exactly what you did, it is hard to answer precisely. However, I think they are different tests and hypotheses, so that you would expect different sample sizes. – dimitriy Apr 10 '21 at 00:38

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