Texas State University
School of Criminal Justice
Ph.D. Comprehensive Exam for Statistics
October 13, 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 definitions favorable
toward delinquency, the strength with which they are held, and engaging in delinquency. The
basic premise is when definitions favorable to delinquency increase, delinquency also increases.
However, definitions are usually “so weakly held” that they alone have little impact on behavior
(Akers, 1999, p. 66). The hypothesis therefore also acknowledges that definitions favorable to
delinquency matter more when these definitions are strongly held.
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:
The effect of definitions favorable to delinquency on delinquency increases as the strength with
which these definitions are held increases.
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
delinquency. The primary independent variables are: (1) a continuous measure of
definitions favorable to delinquency that is expressed in Z scores; (2) a continuous
measure of the strength with which the individuals holds these definitions that is also
expressed in Z scores; and (3) the mathematical product of these two Z-scored variables
allowing for a statistical interaction between them.
Hold constant the potentially confounding effects of the respondent’s: (1) attachment to
family, which is expressed in Z scores; (2) religiosity, which is expressed in Z scores; (3)
a dummy-coded variable measuring whether the respondent is male; and (4) a dummycoded variable measuring whether the respondent’s race is black.
2.
Interpret the model fit statistics for the model that you estimated.
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3.
Based on the model you estimated, and while being mindful of the ways in which
variable values are expressed, 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.
(a) What is the effect of delinquent definitions on delinquency when the strength with
which these definitions are held is one standard deviation above the mean strength?
Report the actual numerical value.
(b) Explain whether and how these results support the motivating hypothesis.
5.
Diagnose the estimated model with regard to problematic levels of outlying and nonoutlying influence. Discuss the evidence that is relevant to this diagnosis. If evidence for
problems exists, do not address problems with additional analysis.
6.
(a) Explain and discuss collinearity and multicollinearity in the context of linear
regression.
(b) Based on the estimated model, examine collinearity and multcollinearity. Discuss
whether levels of collinearity are problematic. If problematic levels exist, do not attempt
to address problems with additional analysis.
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The data file contains data from 900 individual respondents. The variables relevant to the exam
are named and described below.
Variable
Name
delin
deldef
Data File Contents for Exam
Variable Description
= A continuous measure for the respondent’s amount of delinquency. Higher
values indicate more delinquency. Refer to units of this variable as points on
the delinquency scale.
A continuous and Z-scored measure of the respondent’s definitions that are
favorable to delinquency. Higher values indicate more delinquent
definitions. Refer to units of this variable as standardized units on the
definitions favorable to delinquency scale.
strength
= A continuous and Z-scored measure of the strength with which the
respondent holds their definitions. Higher values indicate definitions are
more strongly held. Refer to units of this variable as standardized units on
the strength of holding definitions scale.
product
The product-term for the statistical interaction between definitions that are
favorable to delinquency and the strength with which definitions are held
(that is, product = deldef × strength).
familyz
= A continuous and Z-scored measure of the respondent’s attachment to their
family. Higher values indicate more attachment to family. Refer to units of
this variable as standardized units on the attachment to family scale.
religz
= A continuous and Z-scored measure of the respondent’s level of religiosity.
Higher values indicate more religiosity. Refer to units of this variable as
standardized units on the religiosity scale.
male
= A dummy-coded variable measuring whether the respondent is male.
0 = No
1 = Yes
black
= A dummy-coded variable measuring whether the respondent’s race is black.
0 = No
1 = Yes
End of Option One
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Option Two:
Background and Motivation
Using individual-level data from a sample of adolescent respondents, this exam centers on the
relationship between definitions favorable toward delinquency, the strength with which they are
held, and engaging in delinquency. The basic premise is when definitions favorable to
delinquency increase, delinquency also increases. However, definitions are usually “so weakly
held” that they alone have little impact on behavior (Akers, 1999, p. 66). The hypothesis
therefore also acknowledges that definitions favorable to delinquency matter more when these
definitions are strongly held.
The investigator tests the following hypothesis:
The effect of definitions favorable to delinquency on delinquency increases as the strength with
which these definitions are held increases.
The investigator used a multivariate ordinary least squares (OLS) regression model to test this
hypothesis. The dependent variable is a continuous measure of self-reported delinquency. 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.
Based on the results, explain and discuss the F test and the model fit statistics.
2.
While being mindful of the ways in which the variable values are expressed, interpret (a)
the coefficient for definitions favorable to delinquency; (b) the coefficient for the strength
with which the definitions are held by the respondent; (c) the coefficient for the product
term (that is, delinquent definitions × strength of definitions); and (d) these quantities’
tests of statistical significance.
3.
(a) Based on the results, what is the effect of delinquent definitions on delinquency when
the strength with which these definitions are held is one standard deviation above the
mean strength? Report the actual numerical value.
(b) Based on the numerical value reported above, what is the t value for this effect?
Assume the standard error for the effect of delinquent definitions on delinquency is
constant across levels of strength of definitions. Report the actual numerical value. Is this
effect statistically significant at the .05 level of statistical significance?
(C) Explain whether and how these results support the motivating hypothesis.
4.
Based on the results, interpret (a) the coefficient for male; and (b) the y-intercept value.
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5.
Explain and discuss the model’s assumptions regarding collinearity and whether levels
are problematic in the presented results.
6.
Explain and discuss other assumptions of the OLS model. Also, explain and discuss
the desirable properties that OLS estimates have when their assumptions are met.
Table for statistics exam, option 2
Ordinary least squares model explaining delinquency
N = 1,624
Variables
Delinquent definitionsa
Strength of definitionsa
Delinquent definitionsa × Strength of definitionsa
Maleb
Whiteb
Family attachmenta
Member of academic honor societyb
Constant
Coefficient
*1.350
0.393
*0.929
SE
0.508
0.515
0.442
VIF
1.29
1.32
1.13
*1.853
-0.412
*-0.974
0.309
1.380
0.908
1.275
0.472
1.950
1.998
1.03
1.02
1.10
1.23
--
R2 = 0.0169
Model-fit statistics
Root MSE = 18.047
F𝑑𝑓1=7,𝑑𝑓2=1616, = 3.96, 𝑝 < .05
p < .05
A continuous variable expressed in Z scores.
b A dummy-coded variable where zero indicates absence of characteristic.
*
a
End of Option Two
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