6. Lets continue our analysis of offenders and victims of violent crime. In the

Question

6. Lets continue our analysis of offenders and victims of violent crime. In the following table,US Department of Justice 2011 data for the sex of offenders and the sex of victims are reported. Sex of Offender Sex of Victim Male Female Male 3,760 1,590 Female 450 140 Source: U.S. Department of Justice, Expanded Homicide Data, Table 6, 2011. a. Treating sex of offender as the independent variable, how many errors of prediction will be made if the independent variable is ignored? How many fewer errors will be made if the independent variable is taken into account? Combine your answers in (a) and (b) to calculate lambda. Discuss the relationship between b. c. these two variables. d. Which lambda is stronger, the one for sex of offenders/victims or race of offenders/victims (Exercise 5)?

Explanation / Answer

a)

Treating sex of offender as independent variable, the modal frequency of the victim variable (dependent variable) will be

5350 vs 590 (comparing column totals - the one that is bigger becomes the modal frequency)

e1 = number of errors in prediction when the independent variable is ignored.

n = total frequency = 5350+590 = 5940

e1 = n - modal frequency = 5940-5350 = 590

b)

Number of errors in prediction when the independent variable is taken into account

e2 = e21 +e22

e21 = total row1 - modal frequency of row1 = 4210-3760 = 450

e22 = total row2 - modal frequency of row2 = 1730-1590 = 140

e2 = 450+140 =590

c)

lambda = (e1 - e2)/e1 = (590-590)/590 = 0

lambda ranges from 0 to 1.

If it is close to 0 then the relationship is weak, and close to 1 indicates the relationship is strong.

There is no relationship between the variables sex of offender and sex of victim.

d)

lambda if we calculate keeping sex of offender as the independent variable will also be 0.

Hence both in their individual choices as independent variable don't result in any reduction of errors.

offender m f victim m 3760 450 4210 f 1590 140 1730 5350 590 5940

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