Texas State University
School of Criminal Justice
Ph.D. Comprehensive Exam for Statistics
June 30, 2015
9:00 a.m. – 11:00 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 Cybele Hinson
(ch56@txstate.edu). Print out and turn in a hard copy as well with both your ID number
and name on it.
Option One:
Background and Motivation
Using individual-level data, this exam centers on the relationship between opportunities for
crime and engaging in crime. The basic premise is that an increase in opportunities for crime will
increase the frequency of engaging in criminal behavior. However, the hypothesis also asserts
that the effect of opportunities for crime on criminal behavior vary with gender.
This exam relies on the data from a sample of adolescent respondents. Estimate a multivariate
ordinary least squares regression model to test the following hypothesis:
Opportunities for crime have a positive effect on criminal offending, but this effect is smaller
among females.
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. The dependent variable is a continuous measure of
criminal offending. The primary independent variables are: (1) a continuous and meancentered measure of opportunities for crime; (2) a dummy-coded variable measuring
whether the subject is female; and (3) the mathematical product of these two variables
allowing for a statistical interaction between them.
Hold constant the potentially confounding effects of the respondent’s: (1) time spent in
community activities, which is expressed in Z scores; (2) time spent with peers, which
is expressed in Z scores; (3) a dummy-coded variable measuring whether the respondent
is a member of an academic honor society; and (4) a dummy-coded variable measuring
whether the respondent’s race is white.
2.
Interpret the model fit statistics for the model that you estimated.
Statistics Comprehensive Exam
Page 1 of 6
3.
Based on the model you estimated, interpret and discuss (a) the y-intercept; (b) the slopes
(i.e., the partial regression coefficients) for the primary independent variables; and (c)
their tests of statistical significance.
4.
Based on the model you estimated, interpret and discuss (a) the effect of time spent in
community activities on offending; and (b) its tests of statistical significance.
5.
(a) What is the effect of opportunities for crime on offending when the respondent is
male? Report the actual numerical value, and whether this effect is statistically
significant at the .05 level of statistical significance. Assume the standard error for the
effect of opportunities for crime on offending remains constant across sexes.
(b) Explain whether and how these results support the motivating hypothesis.
6.
Explain and discuss the error-term assumptions of the estimated model. Also, explain and
discuss what the residuals from the estimated model indicate with regard to outlying and
non-outlying influence. If evidence for problems exists, do not address problems with
additional analysis.
Statistics Comprehensive Exam
Page 2 of 6
The data file contains data from 300 individual respondents. The variables relevant to the exam
are named and described below.
Variable
Name
crime
crimeopp
female
Data File Contents for Exam
Variable Description
= A continuous measure for criminal offending. Higher values indicate more
offending. Refer to units of this variable as points on the criminal offending
scale.
A continuous and mean-centered measure for opportunities for crime.
Higher values indicate more criminal opportunities. Refer to units of this
variable as points on the opportunities-for-crime scale.
= A dummy-coded variable measuring whether the respondent is female.
0 = No
1 = Yes
product
The product-term for the statistical interaction between opportunite-forcrime and sex (that is, product = crimeopp × female).
comm
= A continuous and Z-scored measure of the respondent’s time spent in
community activities. Higher values indicate more time. Refer to units of
this variable as standardized units on the time-in-community-activity scale.
frndtime
= A continuous and Z-scored measure of the respondent’s time spent with
friends. Higher values indicate more time. Refer to units of this variable as
standardized units on the time-spent-with-friends scale.
honor
= A dummy-coded variable measuring whether the respondent is a member of
an academic honor society.
0 = No
1 = Yes
white
= A dummy-coded variable measuring whether the respondent’s race is white.
0 = No
1 = Yes
End of Option One
Statistics Comprehensive Exam
Page 3 of 6
Statistics Comprehensive Exam
Page 4 of 6
Option Two:
Background and Motivation
Using individual-level data, this exam centers on the relationship between opportunities for
crime and engaging in crime. The basic premise is that an increase in opportunities for crime will
increase the frequency of engaging in criminal behavior. The investigator tests the following
hypothesis:
Opportunities for crime have a positive effect on criminal offending, and this effect is
independent of sex, age, race, and time spent with family.
The investigator supplements the results by including a test of the following hypothesis:
Opportunities for crime have a positive effect on criminal offending, but this effect is smaller
among females and is independent of the effects of age, race, and time spent with family.
The investigator used a multivariate ordinary least squares (OLS) regression model to test these
two hypotheses. And, the dependent variable is a continuous measure of criminal offending. The
results of the estimation are presented in the table below.
You may use a calculator.
You will be assessed based on your responses to the following items:
1.
Interpret and discuss the model fit statistics for model 1.
2.
Based on the results for Model 1, interpret (a) the y-intercept; (b) the coefficient for
opportunities for crime; and (c) the coefficient for female.
3.
Based on the results for Model 2, interpret (a) the coefficient for opportunities for crime;
(b) the coefficient for female; (c) the coefficient for the product term (that is,
opportunities for crime × female); and these quantities’ tests of statistical significance.
4.
Based on the results, explain whether and how these results support (or reject) the
motivating hypothesis.
5.
The measure of age in years is expressed in standardized form (that is, Z scores). Based
on the results for Model 2, interpret the coefficient for age.
6.
Explain and discuss the assumptions of the estimated models. Explain and discuss the
desirable properties that such models (i.e., multivariate OLS regression models) have
when their assumptions are met.
Statistics Comprehensive Exam
Page 5 of 6
Table for statistics exam, option two
Ordinary least squares model explaining criminal offending
N = 471
Variables
Opportunities for crimea
Femaleb
Opportunities for crimea × Femaleb
Agec
Blackb
Time with familyc
Constant
Model-fit statistics
Coef.
0.56
-1.10
----0.87
0.48
-0.04
17.27
Model 1
SE
0.56
2.28
---0.60
2.99
0.39
9.46
VIF
1.17
1.03
---1.09
1.01
1.09
----
R2 = 0.0059
Root MSE = 24.32
F𝑑𝑓1=5,𝑑𝑓2=465, = 0.55, 𝑝 > .05
Coef.
-0.04
-1.99
0.82
-0.86
0.46
-0.03
17.61
Model 2
SE
1.03
2.62
1.18
0.60
3.00
0.39
9.47
VIF
3.95
1.36
4.31
1.09
1.01
1.09
----
R2 = 0.0069
Root MSE = 24.33
F𝑑𝑓1=6,𝑑𝑓2 =464, = 0.78, 𝑝 > .05
p < .05
A mean-centered continuous variable.
b A dummy-coded variable where zero indicates absence of characteristic.
c A continuous variable measured in Z scores.
*
a
End of Option Two
Statistics Comprehensive Exam
Page 6 of 6