Suppose you are evaluating a grant proposal. The proposer seeks $250,000 to conduct a series of experiments on patients with a rare kind of brain lesion. Let's say the proposer will measure the ability to remember lists of words in the experiment. A very interesting and provocative theory, described clearly in the proposal, predicts that the brain-damaged people should actually remember slightly better than the control group, and so the investigator proposes an experiment to test this prediction. A pilot study shows that among normals, the mean number of words remembered (from a list of 20words) is 12.2, and the standard deviation is 3.1. (assume that the SD is the same for the lesion group) The investigator explains that a pool of 24 subjects with brain lesions is already available from a local clinic for the brain-damaged group. Suppose that you, as a reviewer of the proposal, want a power of .80 in proposed experiments.

a) What effect size would be required to generate this power of .80? (Assume a Type I error rate, i.e. alpha, of 0.05.) (hint: find the expected mean difference, based on sample size, alpha, beta, and SD)

b) Suppose that the effect size is actually 0.2 (small, as predicted by the proposed theory). What sample size would be needed to achieve a power of .80? Should you fund the proposal?