Texas State University
School of Criminal Justice
Ph.D. Comprehensive Exam for Statistics
October 23, 2012
8:00 a.m. – 10:00 a.m.
DIRECTIONS: Choose Option One or Option Two. Save two electronic copies of your answer
(one with just your ID number assigned to you, the other with your ID number and name).
Email both copies to dv14@txstate.edu; print out a hard copy as well with both your id
number and name written on it.
Option 1:
Background and Motivation
This exam focuses on an individual’s fear of criminal victimization. The central question
concerns whether the number of safeguards (e.g., home security system, extra locks, extra
lighting) reduces fear of victimization. It is possible, however, that the effect of safeguards on
fear of criminal victimization depends on the extent to which neighbors in the area are
involved in crime prevention efforts.
Estimate an ordinary least squares multiple regression model to test the following hypothesis:
Home safeguards have a negative effect on an individual’s fear of being a victim of a crime,
but this effect changes with levels of crime prevention efforts by the individual’s neighbors.
Hold constant the potentially confounding effects of (1) area crime rate; (2) sex of respondent;
(3) whether the respondent owns a gun; and (4) whether the respondent’s race is white.
You may use a calculator.
You will be assessed based on your responses to the following items:
1.
Using the data file described below, use SPSS to estimate a multivariate ordinary least
squares regression equation with fear of victimization as the dependent variable. The
primary independent variables are home safeguards, intensity of neighborhood crime
prevention efforts, and the statistical interaction of neighborhood crime prevention efforts
and number of home safeguards. The secondary variables (that is, the control variables)
are: number of crimes in the area last year, sex, gun ownership, and race.
2.
Interpret the model-fit statistics associated with the model you estimated.
3.
Based on the model you estimated, interpret (a) the y-intercept; (b) the slopes (i.e., the
coefficients) of the primary independent variables; (c) the slope of the respondent race
variable; and (d) their tests of statistical significance.
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4.
Examine measures of collinearity and determine whether levels of multicollinearity seem
problematic for the model you estimated. If problems exist, however, do not attempt to
address problems with additional analysis.
5.
Examine measures of outlying and non-outlying influence, and discuss whether levels of
influence seem problematic for the model you estimated. If problems exist, do not
attempt to address problems with additional analysis.
6.
Assume the standard deviation of area crime prevention efforts is 0.621.
A. What is the effect of home safeguards on fear of victimization when neighborhood
crime prevention efforts are 1 standard deviation below the mean effort?
A. -0.443
B. 0.026
C. 0.146
D. 0.162
E. 0.178
B. What is the effect of home safeguards on fear of victimization when neighborhood
crime prevention efforts are at the mean effort?
A. -0.443
B. 0.026
C. 0.146
D. 0.162
E. 0.178
C. What is the effect of home safeguards on fear of victimization when neighborhood
crime prevention efforts are 1 standard deviation above the mean effort?
A. -0.443
B. 0.026
C. 0.146
D. 0.162
E. 0.178
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The data file contains data from 500 respondents. The variables relevant to the exam are named
and described below.
Variable
Name
fear
Data File Contents for Exam
Variable Description
= A continuous measure for fear of criminal victimization. Higher values
indicate the respondent is more fearful of victimization. Refer to units of this
variable as points on the fear of victimization scale.
guards
= A mean-centered and continuous measure of safeguards in a respondent’s
home. Refer to units on this scale as number of home safeguards.
crprev
= A mean-centered and continuous measure of crime prevention efforts in a
respondent’s neighborhood. Higher values indicate higher intensities of
neighborhood crime prevention efforts. Refer to units on this scale as points
on the crime prevention effort scale.
product
= The product-term for the statistical interaction between neighborhood crime
and age (that is, product = guards × crprev).
ncrime
= A continuous measure for the neighborhood crime rate. Higher values
indicate more criminal activity in the respondent’s neighborhood. Refer to
units of this variable as neighborhood crimes per year.
male
= A dummy-coded variable for respondent sex where 1 = Male and 0 = Not
Male.
owngun
= A dummy-coded variable for whether respondent owns a gun.
0 = respondent does not own a gun
1 = respondent does own one or more guns
white
= A dummy-coded variable for respondent race where 1 = White and 0 = Not
White.
End of Option 1
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Option 2:
Background and Motivation
This exam focuses fear of criminal victimization. The hypothesis here is that victimization in
the past increases fear of victimization, but this effect depends on (that is, interacts with) the
number of home safeguards (e.g., home security system, extra locks, extra lighting).
The table below presents results from multivariate regression using data from 2,021
respondents.
Fear of victimization is a continuous variable where higher values indicate higher amounts of
fear.
The number of safeguards is mean centered and prior victimization is a dummy-coded
variable where a value of 1 indicates that the respondent has been a victim of crime in the last
year. The product-term statistical interaction is based on these two measures.
You may use a calculator.
You will be assessed based on your responses to the following items:
1.
Interpret the estimates and tests of statistical significance for the effects of (a)
victimization; (b) safeguards; and (c) the product of these variables. Do the results in the
table support the hypothesis?
2.
The standard deviation of the age is 1.7. Allow its mean to equal the average number of
safeguards, and let one standard deviation above and below the mean represent high and
low safeguard levels, respectively. Based on the results, what is the effect of criminal
victimization on fear of victimization at the lower level? Report the actual numerical
value of this partial regression coefficient.
3.
Interpret the coefficient for education in years.
4.
Report the standard error (that is, the actual numeric value) for the education coefficient.
5.
Based on the results and while being mindful of the table’s footnotes regarding variable
coding, interpret the constant (that is, the y-intercept).
6.
The authors reported a variance inflation factor (VIF) for each variable. Discuss (a)
collinearity; (b) regression assumptions concerning collinearity; (c) strengths and
weaknesses of using the VIF as a measure of collinearity; and (d) whether collinearity
levels are problematically high.
7.
The model sum of squares, which is sometimes called the sum of squared explained
̂ i -Y
̅ )2, is 1,094.65. The mean squared explained variation
variation and notated as ∑(Y
is 5.34. What is the total sum of squares? The total sum of squared deviations is notated
̅̅̅)2. Report the actual numerical value.
as ∑(𝑌𝑌 − 𝑌
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Table for statistics exam, option 2
Ordinary least squares model explaining fear of criminal victimization
N = 2,021
Variables
Coefficient
t-statistic
VIF
Victim of crime last yeara
Number of residential safeguardsb
Victim of crime last yeara × Number of safeguardsb
0.210
0.209
-0.002
6.660
6.020
-0.100
1.14
1.32
1.30
Ageb
Male a
Married a
Education in years b
Whitea
Years lived at current residence b
Constant
-0.025
-0.547
-0.400
-0.449
-0.216
-0.003
3.863
-6.160
-5.280
-3.660
-3.890
-1.430
-0.510
23.370
1.65
1.01
1.12
1.08
1.04
1.73
--
R2 = 0.0925
Model Statistics
Root MSE = 2.3115
F𝑌𝑌1 =9,𝑌𝑌2 =2011, = 22.76, 𝑌 < .05
*
p < .05
A dummy-coded variable where zero indicates absence of characteristic.
b
A continuous variable that is mean centered.
a
End of Option 2
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