15.46 The prisoner’s dilemma, cross-cultural research, and hypothesis testing: In a classic prisoner’s dilemma game with money for prizes, players who cooperate with each other both earn good prizes. If, however, your opposing player cooperates but you do not (the term used is defect), you receive an even bigger payout and your opponent receives nothing. If you cooperate but your opposing player defects, he or she receives that bigger payout and you receive nothing. If you both defect, you each get a small prize. Because of this, most players of such games choose to defect, knowing that if they cooperate but their partners don’t, they won’t win anything. The strategies of U.S. and Chinese students were compared. The researchers hypothesized that those from the market economy (United States) would cooperate less (i.e., would defect more often) than would those from the nonmarket economy (China). Here are the observed values. Defect Cooperate China 31 36 United States 41 14

a. How many variables are there in this study? What are the levels of any variables you identified?

b. Which hypothesis test would be used to analyze these data? Justify your answer.

c. Conduct the six steps of hypothesis testing for this example, using the above data.

d. Calculate the appropriate measure of effect size. According to Cohen’s conventions, what size effect is this?

e. Report the statistics as you would in a journal article.

f. Draw a table that includes the conditional proportions for participants from China and from the United States. g. Create a graph with bars showing the proportions for all four conditions. h. Create a graph with two bars showing just the proportions for the defections for each country. i. Calculate the relative risk (or relative likelihood) of defecting, given that one is from China versus the United States. Show your calculations. j. Explain what we learn from this relative risk. k. Now calculate the relative risk of defecting, given that one is from the United States versus China. Show your calculations. l. Explain what we learn from this relative risk. m. Explain how the calculations in parts (i) and (k) provide us with the same information in two different ways.