If s 5 15, n 5 25, and we are testing versus , what value of the mean under would result in power being equal to the probability of a Type II error? (Hint: Try sketching the two distributions; which areas are you trying to equate?)
Prentice and Miller (1992) presented an interesting argument that suggested that, while most studies do their best to increase the effect size of whatever they are studying (e.g., by maximizing the differences between groups), some research focuses on minimizing the effect and still finding a difference. (For example, although it is well known that people favor members of their own group, it has been shown that even if you create groups on the basis of random assignment, the effect is still there.) Prentice and Miller then state, “In the studies we have described, investigators have minimized the power of an operationalization and, in so doing, have succeeded in demonstrating the power of the underlying process.”
a. Does this seem to you to be a fair statement of the situation? In other words, do you agree that experimenters have run experiments with minimal power?
b. Does this approach seem reasonable for most studies in psychology?
c. Is it always important to find large effects? When would it be important to find even quite small effects?