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 1-Sample Z Test 1.0 Sample Size 80 -90 ー-100 110 120 な 0.6 Assumptions 0.01 1.2 StDev Alternative 0.4 0.2 0.0 0.50 0.25 0.00 0.25 0.50 Difference

Power curve for varying sample size

Power Curve for 1-Sample Z Test 1.0 Sample Size 100 0.8 Assumptions 0.01 1.2 StDev Alternative 0.6 0.4 0.2 0.0 0.50 0.25 0.00 0.25 0.50 0.75 1.00 Difference

Graph for effect size unity.

Power Curve for 1-Sample Z Test 1.0 Sample Size 100 0.8 Assumptions 0.05 1.2 StDev Alternative 0.6 0.4 0.2 0.0 0.50 0.25 0.00 0.25 Difference 0.50 0.75 1.00

Power curve for alpha=.05