13.58 Death penalty and race The three-dimensional contingency table shown is from a study of the effects of racial characteristics on whether individuals convicted of homicide receive the death penalty. The subjects classified were defendants in indictments involving cases with multiple murders in Florida between 1976 and 1987.

a. Based on the percentages shown, controlling for victims’
race, for which defendant’s race was the death penalty more likely?

b. Let y = death penalty verdict (1 = yes, 0 = no), let d be an indicator variable for defendant’s race 11 = white, 0 = black), and let v be an indicator variable for victims’
race 11 = white, 0 = black). The logistic regression prediction equation is

According to this equation, for which of the four groups is the death penalty most likely? Explain your answer.
13.59 Death penalty probabilities Refer to the previous exercise.

a. Based on the prediction equation, when the defendant is black and the victims were white, show that the estimated death penalty probability is 0.233.

b. The model-estimated probabilities are 0.011 when the defendant is white and victims were black, 0.113 when the defendant and the victims were white, and 0.027 when the defendant and the victims were black.
Construct a table cross-classifying defendant’s race by victims’ race and show the estimated probability of the death penalty for each cell. Use this to interpret the effect of defendant’s race.

c. Collapse the contingency table over victims’ race, and show that (ignoring victims’ race) white defendants were more likely than black defendants to get the death penalty. Comparing this with what happens when you control for victims’ race, explain how Simpson’s paradox occurs.

Transcribed Image Text:

Death penalty verdict by defendant's race and victims' race Defendant's Victims' Death Penalty Percent Race Race Yes No Yes White White 53 414 11.3 Black 0 16 0.0 Black White 11 37 22.9 Black 4 139 2.8