Estimating Power (2 of 4)
Estimating the effect size includes estimating the population variance as well as the population means. In the SAT example, the experimenter would have to estimate the variance of the SAT (it is about 10,000) before the calculations could be done.
Frequently it is easiest to specify the effect size in terms of the number of standard deviations separating the population means. Thus, one might find it easier to estimate that the population mean for the experimental group is 0.5 standard deviations above the population mean for the control group than to estimate the two population means and the population variance. Fortunately, the power for any experiment in which the difference between population means is the same number of population standard deviations apart is the same. The power for an experiment in which µ1 = 10, µ2 = 20, and σ = 20 is the same as the power for an experiment in which µ1 = 5, µ2 = 7, and σ = 4. In both cases, the means are 0.5 standard deviations apart.