STAT 310 Homework #7 Two-Way ANOVA

STAT 310 – Homework #11 ~ Analysis of Categorical Data (28 points)

1 – Gender and Violent Victimization In a study of violent victimization of women and men Porcerelli et al., in their paper “Violent Victimization of Women and Men: Physical and Psychiatric Symptoms” in the Journal of the American Board of Family Practice (2003), collected information from 679 women and 345 men ages 18 to 64 years at several family practice centers in the metropolitan Detroit area. Patients filled out a health history questionnaire that included a question about victimization. The following table shows the sample subjects cross- classified by gender and type of violent victimization reported. The victimization categories are defined as no victimization, partner victimization (and not by others), victimization by a person other than a partner (fried, family member, or stranger), and those who reported multiple victimization.

Type of Violent Victimization Gender No Victimization Partner Nonpartner Multiple Row Total Women 611 34 16 18 679 Men 308 10 17 10 345 Column Total 919 44 33 28 1024

Can we conclude on the basis of these data that victimization status and gender are not independent? If there is evidence of a relation discuss the nature of that relationship. (4 pts.)

2 – Race and Violent Victimization Amongst Women In the same study above the race of the respondent was also recorded. For the 644 African-American and Caucasian women we have the following results.

Type of Violent Victimization Gender No Victimization Partner Nonpartner Multiple Row Total Caucasian 356 20 3 9 388 African-American 226 11 10 9 256 Column Total 582 31 13 18 644

Can we conclude on the basis of these data that victimization status and race are not independent for women? If there is evidence of a relationship discuss the nature of that relationship. (4 pts.)

3 - Election Poll Five candidates have just entered the race for mayor of a large city. To determine whether any of the candidates has an early lead in popularity, a poll is conducted. Some 2,000 voters are asked to indicate the candidate they prefer. A summary of their responses is shown in the table below.

CANDIDATE I II III IV V Frequency 385 493 628 235 259

a) Do the data provide sufficient evidence to indicate a preference for at least one of the five candidates? State your final conclusion in words. (4 pts.)

b) Candidate III, who clearly has the early advantage based on our sample, would like a range of values that is very likely to reflect the actual proportion of voters who prefer her. Construct and interpret such an interval. (4 pts.)

4 – Childhood Sexual Abuse and Gender The purpose of a study conducted by Lipschitz et al. presented in their paper “Prevalence and Characteristics of Physical and Sexual Abuse among Psychiatric Outpatients” published in Psychiatric Services (1996) was to examine, using a questionnaire, the rates and characteristics of childhood abuse and adult assaults in a large general outpatient population. Subjects consisted of 120 psychiatric outpatients (86 females, 34 males) in treatment at a large hospital-based clinic in an inner-city area. Forty-seven females and six males reported incidents of childhood sexual abuse.

a) Set up a 2 X 2 table displaying the results of this portion of their survey. (2 pts.)

b) Is there evidence to suggest a difference in the sexual child abuse rates between men and women? Use an appropriate test and state your conclusion. (3 pts.)

c) Construct a 95% CI for the difference in the percentage of men and women who were sexually abused as children. Interpret this interval in practical terms. (3 pts.)

d) What is the relative risk of sexual child abuse associated with being a woman in this population? Interpret this quantity. (2 pts.)

e) What is the odds ratio for sexual child abuse associated with being a woman in this population? Interpret this quantity. (2 pts.)