HyLown Power and Sample Size Calculators

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PowerAndSampleSize.com.

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

X-axis

min

max

This sample size calculator uses the following formula: $$n=\left(\sigma\frac{\Phi^{-1}(\alpha/(2\tau))+\Phi^{-1}(\beta)}{\mu_1-\mu_0}\right)^2$$ where

  • $n$ is sample size
  • $\sigma$ is standard deviation
  • $\Phi^{-1}$ 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:

mu0=1.5
mu1=2
sd=1
tau=1
alpha=0.05
beta=0.20
(n=ceiling((sd*(qnorm(alpha/2/tau)+qnorm(beta))/(mu1-mu0))^2)) # 32

Reference: Chow, page 71