## HyLown Power and Sample Size Calculators

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PowerAndSampleSize.com.

For testing equivalence to a gold standard:

$H_0:|\mu-\mu_0|\ge\delta$ versus $H_1:|\mu-\mu_0|<\delta$

where $\delta$ is the superiority or non-inferiority margin and the ratio between the sample sizes of the two groups is
$$\kappa=\frac{n_1}{n_2}$$

Sample Size

Power

X-axis

min

max

This sample size calculator uses the following formula: $$n_1=\kappa n_2 \;\text{ and }\; n_2=\left(1+\frac{1}{\kappa}\right) \left(\sigma\frac{\Phi^{-1}(\alpha)+\Phi^{-1}(\beta/2)}{|\mu_1-\mu_0|-\delta}\right)^2$$ where

• $n$ is sample size
• $\kappa=n_1/n_2$ is the matching ratio
• $\sigma$ is standard deviation
• $\Phi^{-1}$ 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:

mu0=5
mu1=4
delta=5
kappa=1
sd=10
alpha=0.05
beta=0.20
(n=ceiling((1+1/kappa)*(sd*(qnorm(alpha)+qnorm(beta/2))/(abs(mu1-mu0)-delta))^2)) # 108

Reference: Chow, page 62