Just a pre-announcement because I have a nice graph.

I am looking into tests for binomial proportions, especially equivalence (TOST) and non-inferiority tests.

SAS provides a good overview over the available methods and power for it

Power and significance levels in testing for proportions have a saw tooth pattern because the observed proportions are discrete, see for example this SAS page

Unfortunately for my unit testing, I have not found any equivalence tests for proportions in R. Currently, I'm just trying to match some examples that I found on the internet.

And here is the plot for my power function. It shows the power as a function of the sample size, for either the normal approximation or the binomial distribution, of the test for equivalence, TOST two one-sided tests. The TOST test itself is based on the normal approximation.

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