4.52 Is the race of a defendant associated with the defendant’s chance of receiving the death penalty? This is a controversial issue that has been studied by many. One important data set was collected on 326 cases in which the defendant was convicted of homicide. The death penalty was given in 36 of these cases. Table 4.31 shows the defendant’s race, the victim’s race, and whether or not the death penalty was imposed.

a Construct a single 2 2 table showing penalty versus defendant’s race, across all victims.

Calculate the odds ratio and interpret it.

b Decompose the table in

(a) into two 2 2 tables of penalty versus defendant’s race, one for while victims and one for black victims.
Calculate the odds ratio for each table and interpret each one.
c Do you see any inconsistency between the results of part

(a) and the results of part (b)? Can you explain the apparent paradox?

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Classification of Defendants and Victims by Race White Defendant Black Defendant Yes No Yes No White Victim 19 Black Victim 0 132 9 11 52 6 97 Source: M. Radelet, "Racial Characteristics and Imposition of the Death Penalty, American Socialogical Review, 46, 1981, pp. 918-927.