Question 11 0.5 pts Is there a relationship between the race of violent offender

Question

Question 11 0.5 pts Is there a relationship between the race of violent offenders and their victims? Data from the U.S. Department of Justice (2003) are presented in Table 12.6 Table 12.6 Data for the Race of Violent Offenders and the Race of Victims Characteristics of Victim Victim White Black Other Characteristics of Offender Other 58 White Black 3,000 227 51 483 2,852 28 109 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? (Hint: E1- errors of prediction made when the independent variable is ignored)

Explanation / Answer

Solution:

Following is the completed table:

6819

(a) If we ignore the independent variable, then mode of the dependent variable, race of victims, (highest row total) is 3541. And N is 6819 so errors will we make is

E1 = 6819 - 3541 = 3278

(b) Now take into account the independent variable, the number of errors of prediction will we make for those offenders who are white will be

White offenders = 3278 - 3000 = 278

who are black will be

balck offenders = 3363 - 2852 = 511

who are others will be

other offenders = 178 - 109 = 69

So total numbers of errors will be

E2 = 278 + 511+ 69 = 858

(c) So the proportional reduction in error for this table based on the independent variable will be

= E1- E2/E1 = 3278 - 858/ 3278 = 0.74

If we rely on the offenders race to predict the victim race, we will reduce the erro of prediction by 74%.

Characteristics of Victim Characteristics of Offenders Total White Black Other White 3000 483 58 3541 Black 227 2852 11 3090 Other 51 28 109 188 Total 3278 3363 178

6819

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