## HyLown Power and Sample Size Calculators

Good News! These calculators have earned their own website! We'll leave these calculators here for now, but for our latest calculators please visit

PowerAndSampleSize.com.

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