Exercises 243been classed as delinquent in the past. Or, he has access to 25 high-school dropouts who have
a history of delinquency. He suspects that the high-school graduates come from a population
with a mean of approximately 35, whereas the dropout group comes from a population with
a mean of approximately 30. He can use only one of these groups. Which should he use?
8.16 Use G*Power or similar software to reproduce the results found in Section 8.5.
8.17 Let’s extend Aronson’s study (discussed in Section 8.5) to include women (who, unfortu-
nately, often don’t have as strong an investment in their skills in mathematics). For women we
expect means of 8.5 and 8.0 for the Control and Threatened condition. Further assume that the
estimated standard deviation of 3.10 remains reasonable and that their sample size will be 25.
Calculate the power of this experiment to show an effect of stereotyped threat in women.
8.18 Assume that we want to test a null hypothesis about a single mean at a5.05, one-tailed.
Further assume that all necessary assumptions are met. Could there be a case in which we
would be more likely to reject a true than to reject a false one? (In other words, can
power ever be less than a?)
8.19 If s515, 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?)Discussion Questions
8.20 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 fa-
vor members of their own group, it has been shown that even if you create groups on the ba-
sis 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?
8.21 In the hypothetical study based on Aronson’s work on stereotype threat with two independ-
ent groups, I could have all male students in a given lab section take the test under the same
condition. Then male students in another lab could take the test under the other condition.
a. What is wrong with this approach?
b. What alternatives could you suggest?
c. There are many women in those labs, whom I have ignored. What do you think might
happen if I used them as well?
8.22 In the modification of Aronson’s study to use a matched-sample ttest, I always gave the
Control condition first, followed by the Threat condition in the next week.
a. Why would this be a better approach than randomizing the order of conditions?
b. If I give exactly the same test each week, there should be some memory carrying over
from the first presentation. How might I get around this problem?
8.23 Why do you suppose that Exercises 8.21 and 8.22 belong in a statistics text?
8.24 Create an example in which a difference is just barely statistically significant at a5.05.
(Hint: Find the critical value for t, invent values for a 1 and a 2 and n 1 and n 2 , and then solve
for the required value of s.) Now calculate the retrospective power of this experiment.H 1H 0 :m 0 = 100 H 1 :m 0. 100H 0