HyLown Power and Sample Size Calculators

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PowerAndSampleSize.com.

For either a non-inferiority (when $\delta>0$) or a superiority test(when $\delta<0$), where

$H_0:p_1-p_0\le\delta$ versus $H_1:p_1-p_0>\delta$

and $\delta$ is the superiority or non-inferiority margin.

Sample Size

Power

X-axis

min

max

This sample size calculator uses the following formula: $$n=p_1(1-p_1)\left(\frac{\Phi^{-1}(\alpha)+\Phi^{-1}(\beta)}{p_1-p_0-\delta}\right)^2$$ where

  • $n$ is sample size
  • $p_1$ is the rate, proportion, or probability to be tested
  • $p_0$ is the comparison value
  • $\Phi^{-1}$ is the standard Normal quantile function
  • $\alpha$ is Type I error
  • $\beta$ is Type II error, meaning $1-\beta$ is power
  • $\delta$ is the testing margin

R code to implement this function:

p0=0.3
p1=0.5
delta=-0.1
alpha=0.05
beta=0.20
(n=ceiling(p1*(1-p1)*((qnorm(alpha)+qnorm(beta))/(p1-p0-delta))^2)) # 18

Reference: Chow, page 86