Texas State University



Texas State UniversitySchool of Criminal JusticePh.D. Comprehensive Exam for StatisticsOctober 6, 20149:00 a.m. – 11:00 a.m.DIRECTIONS: Choose Option 1 or Option 2.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 1:Background and MotivationA perspective in criminal justice posits that criminal offending is largely situational, and that criminals do not constitute a group that is fundamentally different from a group of non-offenders. Furthermore, race and ethnicity do not have direct roles in explaining crime. Rather, areas with high levels of opportunities for crime lead to crime regardless of race. Such high-opportunity areas can lead to more serious offending via earlier ages of onset, older ages of desistance, and therefore, deeper involvement in criminal offending. Variables that typically reduce offending, such as parental supervision, may matter differently depending on opportunities for crime. 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: Parental supervision impacts an adolescent’s level of delinquency, but the effect of parental supervision on delinquency depends on area-level opportunities for crime. In other words, opportunities for crime ultimately determine the role that parental supervision plays in understanding delinquency.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 for criminal offending. The primary independent variables are: (1) a mean-centered variable measuring parental supervision; (2) a mean-centered variable measuring opportunities for crime; and (3) the product of these variables for the statistical interaction between a respondent’s parental supervision and their opportunities for crime.Hold constant the potentially confounding effects of the respondent’s: (1) verbal-related aptitude; (2) sports involvement; (3) sex; and (4) AP-test result.2.Interpret the model fit statistics for the model that you estimated.3.Based on the model that you estimated, interpret the coefficient for whether the respondent earned credit for college-level mathematics via an Advanced Placement exam.4.Based on the model you estimated, interpret (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. 5.The standard deviation of the measure for opportunities for crime is equal to 1.97. (a) What is the effect of parental supervision on criminal offending when opportunities for crime are one standard deviation below the mean level of opportunities for crime? Report the actual numerical value, and whether this effect is statistically significant at the .05 level of statistical significance.(b) What is the effect of parental supervision on criminal offending when opportunities for crime are one standard deviation above the mean level of opportunities for crime? Report the actual numerical value, and whether this effect is statistically significant at the .05 level of statistical significance.(c) Given these results and the effect of parental supervision discussed in answering question 4, explain whether and how the results support (or reject) 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 these assumptions. If evidence for problems exists, do not address problems with additional analysis.The data file contains data from 450 individual respondents. The variables relevant to the exam are named and described below.Data File Contents for ExamVariable NameVariable Descriptioncrime =A continuous measure for criminal offending. Higher values indicate more offending. Refer to units of this variable as points on the crime scale.parent=A mean-centered and continuous measure for the level of parental supervision the respondent has.crimeopp=A mean-centered and continuous measure for the respondent’s opportunities for crime.product=The product-term for the statistical interaction between parental supervision and opportunities for crime (that is, product = parent × crimeopp).verbal=A mean-centered and continuous measure for the respondent’s verbal-related skills (that is, a measure for reading comprehension and vocabulary). Higher values indicate a higher level of verbal skills. Refer to units of this variable as points on verbal-skills scale.sports=A mean-centered and continuous measure for the respondent’s level of involvement in extracurricular sports. Higher values indicate more sports involvement. Refer to units of this variable as points on the sports-involvement scale.femaleA dummy-coded variable for sex of respondent. 0 = not female1 = femaleaptest=A dummy-coded variable for whether the respondent earned college-level credit for mathematics via an Advanced Placement (AP) Exam. 0 = No1 = YesEnd of Option 1Option 2:Background and MotivationThis exam relies on the data from a sample of adolescent respondents. The theoretical motivation acknowledges that delinquent peer associations represent a major causal factor for delinquency. However, the effect of peer delinquency on personal delinquency is not some unstoppable, totally deterministic process. Through a variety of ways, (direct and indirect) parental supervision can attenuate the effect of delinquent peer associations, and can reduce delinquent peer associations in the first place (cf. Warr, 2005). The investigator tested the following hypothesis: Delinquent peer associations have a positive effect on personal delinquency, but this effect diminishes as direct parental supervision increases.The dependent variable is a continuous measure of delinquency. The primary independent variables are: (1) a mean-centered measure of the respondent’s peer delinquency; (2) a mean-centered measure of the respondent’s direct parental supervision; and (3) the product-term for the statistical interaction between peer delinquency and parental supervision.The investigator used a multivariate ordinary least squares (OLS) regression model to test the hypothesis. 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.2.Interpret (a) the y-intercept; (b) the slopes (i.e., the coefficients) for the primary independent variables; and (c) their tests of statistical significance.3.The standard deviation of the measure for parental supervision is 1.75.(a) What is the effect of peer delinquency on delinquency when parental supervision is one standard deviation above the mean level of parental supervision? Report the actual numerical value, and whether this effect is statistically significant at the .05 level of statistical significance.(b) Based on these results, and the effect of peer delinquency discussed in answering question 2, explain whether and how the results support (or reject) the motivating hypothesis.4. Explain and discuss the estimated model’s assumptions with regard to (a) collinearity; and (b) error term.5. Assume peer-reviewed articles have been published in response to the results presented. The theoretical rationale of these follow-up studies argues that parental supervision becomes more consequential at higher levels of peer delinquency. In other words, peer delinquency impacts the relationship between parental supervision and delinquency. And, the effect of parental attachment on delinquency increases as peer delinquency increases.(a) The standard deviation of the peer delinquency is 1.45. What is the effect of parental supervision on delinquency when peer delinquency is two standard deviations above the mean level of peer delinquency? Report the actual numerical value.(b) Based on these results, and the effect of parental supervision discussed in answering question 2, explain whether and how the results support (or reject) this alternative hypothesis.Table for statistics exam, option 2Ordinary least squares model explaining delinquencyN = 450VariablesCoefficientSEtPeer delinquencya*2.0070.3645.51Parental supervisiona*-1.4780.538-2.75Peer delinquencya × Parental supervisiona*-0.1920.085-2.26Agea0.9802.1450.46Family attachmenta-2.4071.846-1.30Academic aptitudea-0.5615.801-0.10Religiositya1.93111.5900.17Whiteb*-0.0680.027-2.52Constant*0.3770.1891.99Model-fit statisticsR2=0.1353 Root MSE=87.509 Fdf1=9, df2=440,=7.65, p<.05* p < .05a A continuous variable that is mean centered.b A dummy-coded variable where zero indicates absence of characteristic.End of Option 2 ................
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