This is an example (Alan Agresti, Categorical Data Analysis. Second Edition, 2002, pg 48-50) illustrating the effects of racial characteristics on wether persons convicted of homicide received the death penalty. The 674 subjects analyzed (see t_2_6.csv) were the defendants in indictments involving murder cases in Florida between 1976 and 1987. The variables are “Death_penalty” verdict (yes, no), “Defendant_race” (black, white), “Victim_race” (black, white).
make "df (csv.read "t_2_6.csv [char char char])
df.struct :df
dataframe: 674 observations, 3 variables
Victim_race (char): "white" "white" "white" "white" "white" "white" "white" "white" "white" "white" ...
Defendant_race (char): "white" "white" "white" "white" "white" "white" "white" "white" "white" "white" ...
Death_penalty (char): "no" "no" "no" "no" "no" "no" "no" "no" "no" "no" ...
df.print st.freq :df [Death_penalty Defendant_race Victim_race ]
Death_penalty Defendant_race Victim_race N
<char> <char> <char> <num>
yes black black 4.00
no black black 139.00
no white black 16.00
yes black white 11.00
no black white 37.00
yes white white 53.00
no white white 414.00
Ignoring victims’ race, the death penalty was imposed less often on black defendants (7,85%) than on white defendants (10,97%).
df.print st.proportions :df [Death_penalty Defendant_race]
Death_penalty Defendant_race N N1 %
<char> <char> <num> <num> <num>
yes black 15.00 191.00 7.85
no black 176.00 191.00 92.15
yes white 53.00 483.00 10.97
no white 430.00 483.00 89.03
Controlling for victims’ race by keeping it fixed, the death penalty was imposed more often on black defendants than on white defendants.
df.print st.proportions :df [Death_penalty Defendant_race Victim_race ]
Death_penalty Defendant_race Victim_race N N1 %
<char> <char> <char> <num> <num> <num>
yes black black 4.00 143.00 2.80
no black black 139.00 143.00 97.20
no white black 16.00 16.00 100.00
yes black white 11.00 48.00 22.92
no black white 37.00 48.00 77.08
yes white white 53.00 467.00 11.35
no white white 414.00 467.00 88.65
The explanation of this apparent paradox is straightforward:
- blacks killed preferably blacks (143 blacks vs 48 whites), the opposite whites (467 whites vs 16 blacks)
- regardless of defendant’s race the death penalty was at that time much more likely when the victims where white than when the victims where black.