242 Chapter 8 Power
8.4 A second investigator thinks that she can show that a quite different manipulation can raise
the mean influence score from 520 to 550.
a. What is the effect size in question?
b. What is the value of dif the size of her sample is 100?
c. What is the power of the test?
8.5 Diagram the situation described in Exercise 8.4 along the lines of Figure 8.1.
8.6 Assume that a third investigator ran both conditions described in Exercises 8.1 and 8.4, and
wanted to know the power of the combined experiment to find a difference between the two
experimental manipulations.
a. What is the effect size in question?
b. What is the value of dif the size of his sample is 50 for both groups?
c. What is the power of the test?
8.7 A physiological psychology laboratory has been studying avoidance behavior in rabbits for
several years and has published numerous papers on the topic. It is clear from this research
that the mean response latency for a particular task is 5.8 seconds with a standard deviation
of 2 seconds (based on many hundreds of rabbits). Now the investigators wish to induce le-
sions in certain areas in the rabbits’ amygdalae and then demonstrate poorer avoidance con-
ditioning in these animals (i.e., show that the rabbits will repeat a punished response
sooner). They expect latencies to decrease by about 1 second, and they plan to run a one-
sample t test (of ).
a. How many subjects do they need to have at least a 50:50 chance of success?
b. How many subjects do they need to have at least an 80:20 chance of success?
8.8 Suppose that the laboratory referred to in Exercise 8.7 decided not to run one group and
compare it against , but instead to run two groups (one with and one without le-
sions). They still expect the same degree of difference.
a. How many subjects do they need (overall) if they are to have power 5 .60?
b. How many subjects do they need (overall) if they are to have power 5 .90?
8.9 A research assistant ran the experiment described in Exercise 8.8 without first carrying out
any power calculations. He tried to run 20 subjects in each group, but he accidentally tipped
over a rack of cages and had to void 5 subjects in the experimental group. What is the power
of this experiment?
8.10 We have just conducted a study comparing cognitive development of low- and normal-
birthweight babies who have reached 1 year of age. Using a scale we devised, we found that
the sample means of the two groups were 25 and 30, respectively, with a pooled standard de-
viation of 8. Assume that we wish to replicate this experiment with 20 subjects in each group.
If we assume that the true means and standard deviations have been estimated exactly, what
is the a priori probability that we will find a significant difference in our replication?
8.11 Run the t test on the original data in Exercise 8.10. What, if anything, does your answer to
this question indicate about your answer to Exercise 8.10?
8.12 Two graduate students recently completed their dissertations. Each used a t test for two inde-
pendent groups. One found a significant t using 10 subjects per group. The other found a signif-
icant t of the same magnitude using 45 subjects per group. Which result impresses you more?
8.13 Draw a diagram (analogous to Figure 8.1) to defend your answer to Exercise 8.12.
8.14 Make up a simple two-group example to demonstrate that for a total of 30 subjects, power
increases as the sample sizes become more nearly equal.
8.15 A beleaguered Ph.D. candidate has the impression that he must find significant results if he
wants to defend his dissertation successfully. He wants to show a difference in social aware-
ness, as measured by his own scale, between a normal group and a group of ex-delinquents.
He has a problem, however. He has data to suggest that the normal group has a true mean of
38, and he has 50 of those subjects. He has access to 100 high-school graduates who havem 0 =5.8m 0 =5.8