## Sample size for multiple exact binomial tests

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# Sample size for multiple exact binomial tests

Hello everyone,

I need to understand how to calculate sample size in following scenario:

There are two possible responses of a variable: D(detected) and ND(not detected). There are two treatment conditions, let say B(before) and A(after). There are three variables, let say Y1, Y2 and Y3.

I want to test whether difference between percentage detected (%D) from two treatment condition(Before and After) should not be more than 5% (0.05) at 5% level of significance and with at least 80% power. For decision making, I am looking at the lower bound of one-sided 95% confidence interval.

The issue here is the multiplicity effect from three simultaneous variables. I need sample size at 80% power to detect significant difference.

It is kind of interesting that how should we plan the study and obtain the sample size with at least 80% power which is able to detect 5% difference between %detected from two treatments over three variables.

If anyone feels it is confusing please let me know, I will try to explain bit more of this. We want to control FWER(Family Wise Error Rate) no more than 5%.

DJ
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