The figure illustrates Simpson’s paradox for Example 17 on the death penalty. For each defendant’s race, the figure plots the percentage receiving the death penalty. Each percentage is labeled by a letter symbol giving the category of the victim’s race. Surrounding each observation is a circle of an area representing the number of observations on which that percentage is based. For instance, the W in the largest circle represents a percentage of 12.6 receiving the death penalty for cases with white defendants and white victims. That circle is largest because the number of cases at that combination (151) is largest. When we add results across victim’s race to get a summary result ignoring that variable, the largest circles, having the greater number of cases, have greater influence. Thus, the summary percentages for each defendant’s race, marked on the figure by an ×, fall closer to the center of the larger circles than to the center of the smaller circles.
a. Explain why a comparison of a pair of circles having the same letter in the middle indicates that the death penalty was more likely for black defendants, when we control for victim’s race.
b. Explain why a comparison of the × marks shows that overall the death penalty was more likely for white defendants than black defendants.
c. For white defendants, why is the overall percentage who got the death penalty so close to the percentage for the case with white victims?