HyLown Power and Sample Size Calculators

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When you have $k$ treatment levels or $k$ comparison groups, there are a total of $K=k(k-1)/2$ possible pairwise comparisons that could be made. Suppose you wish to make $\tau\le K$ pairwise equality-comparisons between two group means. That is, we have $\tau$ hypotheses of the form

$H_0:\mu_A=\mu_B$ versus $H_1:\mu_A\ne\mu_B$

where $\mu_A$ and $\mu_B$ represent the means of two of the $k$ groups, groups 'A' and 'B'.

Sample Size

Power

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This sample size calculator uses the following formula: $$n=\left(p_0(1-p_0)+p_1(1-p_1)\right)\left(\frac{\Phi^{-1}(\alpha/(2\tau))+\Phi^{-1}(\beta)}{p_0-p_1}\right)^2$$ 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
• $\tau$ is the number of comparisons to be made
• $\beta$ is Type II error, meaning $1-\beta$ is power

R code to implement this function:

p0=0.2
p1=0.4
tau=2
alpha=0.05
beta=0.20
(n=ceiling((p0*(1-p0)+p1*(1-p1))*((qnorm(alpha/2/tau)+qnorm(beta))/(p0-p1))^2)) # 96

Reference: Chow, page 100