Question

In 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, using the same scale, you wish to compare attitudes in a single neighborhood, using a single sample of people who respond both before and 3 months after a state election. You would like to be able to detect a change of 0.2 scale units. Previous research using the scale has reported correlations between pre-test and posttest attitudes in the range .72 to .89. Consider power and make recommendations.

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: