HyLown Power and Sample Size Calculators

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This is the description for the calculator for the 1-sample normal test.

Sample Size

Power

X-axis

min

max

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

  • $n$ is sample size
  • $\sigma$ 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

R code to implement this function:

diff=5
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 230