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This is the description for the calculator for the 1-sample binomial test.
This sample size calculator uses the following formula: $$n=2$$ where
R code to implement this function:
diff=5 # but change sd=23 alpha=0.05 beta=0.90 (n=ceiling(2*(sd*(qnorm(1-alpha)+qnorm(1-beta/2))/diff)^2)) # 458
Reference: Rosner, page 250