Suppose the investigator referred to in Exercise 15.9 decided that instead of running one group and comparing it against μ₀ = 5.8, she would run two groups (one with and one without lesions).

She would still expect the same degree of difference, however.

a) How many subjects does she now need (overall) if she is to have power equal 0.60?

b) How many subjects does she now need (overall) if she is to have power equal 0.90?

Exercise 15.9

A neuroscience laboratory run by a friend of mine studied avoidance behavior in rabbits for many years and published numerous papers on the topic. It is clear from this research that, for animals that have not received any experimental treatment, the mean response latency on a particular task is 5.8 seconds with a standard deviation of two seconds (based on a very large number of rabbits). Now another investigator wants to create lesions in certain areas of the amygdala and demonstrate poorer avoidance conditioning in those animals. (The amygdala is associated with emotion, and if you reduce an emotional response you would be expected to reduce avoidance behavior.) She expects latencies to decrease by about one second (i.e., rabbits will repeat the punished response sooner), and she plans to run a one-sample t test (with H₀: μ₀ = 5.8).

a) How many subjects does she need in order to have at least a 50:50 chance of success?

b) How many subjects does she need in order to have at least an 80:20 chance of success?