If the researchers conducted a one-sided two-sample proportion z-test to evaluate the prediction (insomnia response % > no insomnia response %) with an alpha value of .05, it would be able to detect a proportion difference of .22 with 80% statistical power (power analysis conducted with G*Power, http://www.gpower.hhu.de/en.html). This corresponds to a Cohen h effect size of .45, which is "small" bordering on "medium" in size by convention. Considering the placebo response rate was 30%, while there is no consensus on what represents a clinically meaningful subgroup effect, the researchers would consider a subgroup response rate encompassing an additional 22% to be clinically meaningful and worthy of reporting (especially in an area of medicine where response rates are typically < 50%). Furthermore, the researchers would have adequate statistical power to detect an effect size that is neither overly large nor trivial in size (i.e., within the small-to-medium range) and thus the test is appropriately powered.