In murder trials7 in 20 Florida counties in two years, the death penalty was given in 19 out of 151 cases in which a white killed a white, in 0 out of 9 cases in which a white killed a black, in 11 out of 63 cases in which a black killed a white, and in 6 out of 103 cases in which a black killed a black.

(a) Construct partial tables relating D = defendant’s race and P = the death penalty verdict, controlling for V =

victim’s race. In those tables, compare the proportions of white and black defendants who received the death penalty.

(b) Construct the bivariate table, ignoring victim’s race.

Describe the association, and compare to (a).

(c) Simpson’s paradox states that the associations in partial tables can all have a different direction than the association in the bivariate table. Show that these data satisfy Simpson’s paradox, with white defendants having a lower or higher chance of the death penalty than black defendants according to whether we control victim’s race.

(d) By describing how V is associated with D (whites tending to kill whites and blacks tending to kill blacks)

and howV is associated with P (killing a white more likely to lead to the death penalty), explain why the partial association differs as it does from the bivariate association.

(e) For these variables, indicate whether each of the following diagrams seems to provide a reasonable model.

Give your reasoning.

Transcribed Image Text:

i. V P D D P ii. D VP iii. P iv. D V