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# Cross tabulation and error

Is there a relationship between the race of violent offenders and their victims? Date from the US Department of Justice are presented below:

Characteristics of Offenders
Traits 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 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 variable?

Question #2:
Do women and men have different opinions about affirmative action? Based on a subsample of the 2008 GSS, the output shows respondents sex (SEX) and attitudes toward affirmative action (DISCAFF: are whites hurt by affirmative action?)

Whites hurt by affirmative action
Very likely: (male=66), (female=93), (total=159)
Somewhat likely: (male=193), (female=260), (total=453)
Not very likely: (male=172), (female=179), (total=351)
TOTAL: (male=431), (female=532), (total=963)

a) Which is the independent variable?
b) What are the differences in attitudes between men and women?
c) What might be some other reasons that influence attitudes toward welfare spending? Suggest at least two reasons,

#### Solution Summary

The solution does cross tabulation to determine how many errors will be made in the data and to make predictions for the data.

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