Is there a relationship between the race of violent offenders and their victims? Data from the U.S. Department of Justice (Expanded Homicide Data Table 5, 2007) are presented below:
|
Characteristics of Offender |
| Charcteristics of Victim |
White |
Black |
Other |
| White |
2,918 |
566 |
51 |
| Black |
245 |
2,905 |
11 |
| Other |
50 |
25 |
95 |
a) Let's treat race of offenders as the independent variable and race of victims as the dependent variable. If we first ignore the independent variable and try to predict race of victim, how many errors will we make?
b) If we now take into account the independent variable, how many errors of prediction will we make for those offenders who are white? Black offenders? Other offenders?
c) Combine the answers in (a) and (b) to calculate the proportional reduction in error for this table based on the independent variable. How does this statistic improve our understanding of the relationship between the two variables?