Question

You are planning a study of attitudes to the length of jail sentences for homicide, using a scale running from –4 to +4, where 0 indicates a judgment that current sentences are about right. Previous research suggests that the population SD for the scale is 1.2. You plan to use a single sample and would like to be able to detect a true effect of 0.5 scale units, using α = .01. If you use N = 100, what is the power? Explore power for various other choices of effect size, α, and N.

Answer 1

We assume normality with known population SD.

Then we find the power for a two sided test with α = 0.01 as 0.944177.

Power curve for varying sample size

Graph for effect size unity.

Power curve for alpha=.05