Statistical power, conceptually, is the probability of detecting a treatment effect (or significant difference) given you actually have a treatment effect. Statistical power is a probability, and you need to go through a series of steps to find the probability (there is not just a short formula you use to calculate it).

A sample of 36 students are randomly selected from a normal population and are given Dr. Jain's scheduling app. We know that students in this population typically miss an average of 12 deadlines each year and the standard deviation is 4 (? = 12 and ? = 4). The students who are given the app are expected to have a decrease in the number of deadlines missed, specifically the treatment effect is predicted to decrease the mean from 12 to 10 (a 2 point effect). Assuming a two-tailed hypothesis test with ? = .05, what is the power associated with this test? Complete the following steps to calculate power.

a. Given an alpha = 0.05, what z-scores define the critical regions for the null hypothesis distribution?

b. Convert the z-scores that define the critical regions into raw scores (i.e., number of deadlines missed). What are those values? (be sure to use SEM for this calculation!)

Null Hypothesis Distribution

H = 12 deadlines 7 = 7 = lower cutoff raw score = upper cutoff raw score =\fHypothetical Treated Distribution Null Hypothesis Distribution M = 10 M = 12