# Measure of association nominal/ordinal variables

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Is there a relationship between the race of violent offenders and their victims? Data from the U.S. Department of Justice (expanded Homicide data, 2007 presented blow.

Characteristics of offenders

Characteristics of Victims White Black Other

White 2918 566 51

Black 245 2905 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 victims, 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 answer in (a) and (b) to calculate the proportional reduction in error for this table based on the independent variable. How does this statistics improve our understanding of the relationship between the two variable?

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