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Answer the following questions using your newfound knowledge about applying bivariate statistics and their p values to published results. Make sure you answer all parts of the question to get full credit. Empirical evidence includes descriptive statistics such as percentages or a mean, or bivariate statistics such as a correlation coefficient. Evidence from the statistical test refers to the p value from any statistical test such as χ², t-test, etc.). Sometimes the latter is reported in table footnotes.

1. Table 1 (see below) is from an article by Batiuk, Lahm, McKeever, Wilcox, and Wilcox (2005) entitled, “Disentangling the effects of correctional education: Are current policies misguided? An event history analysis,” published in Criminal Justice, 5(1): 55-74. In this table, the authors are describing the characteristics (gender, race, age, priors, offense, and education) of the sample of Ohio inmates who completed the various correctional educational programs included in their study (college, GED, vocational, and high school) and those who did not participate in correctional educational programs (non-education). A total of 972 inmates who were paroled or released from Ohio’s prisons from 1989 and 1992 comprised the sample.

a. What statistical test did the authors use to test if there are any statistically significant differences between the various background characteristics of the inmates and participation in correctional education program?

b. Answer each part - Are female and male inmates likely to participate in the same types of educational programs? Provide 1) empirical evidence from the table AND 2) evidence from the statistical test.

c. Answer each part: Is the type of offense an inmate committed related to the type of education he/she participated in? Provide 1) empirical evidence from the table AND 2) evidence from the statistical test.

d. Describe the statistically significant characteristics of those inmates who participated in the GED program. Simply put, what are the characteristics of these inmates, that is, what do they look like? Be sure to include in your answer EACH of the statistically significant characteristics.

2. Look at the correlation matrix presented in the Appendix (see below) from Schreck, Fisher and Miller’s article “The Social Context of Violent Victimization: A Study of the Delinquent Peer Effect,” Justice Quarterly, 21(1). They used data from the first wave of the public-use version of the Add Health study, which was conducted between September 1994 and December 1995. The Add Health sample is a nationally represented sample of students attending U.S. schools in grades 7-12.

a. Answer each part - Overall, describe the statistical correlations among TWO PAIRS OF variables. Use the following pairs of variables to answer this question: 1) violent victimization and popularity, and 2) attachment to friends and school alienation. For EACH pair of variables, discuss each of the following: 1) direction of the relationship 2) size of relationship (actual number) and 3) strength of the relationship (e.g., weak, moderate, very strong).

b. Answer each part: Interpret the correlation between peer delinquency and age. State the correlation coefficient and interpret it BOTH statistically (direction, size, and strength) and substantively (what does it mean for example, as wealth of a teen’s household increases, their use of alcohol decreases). Assume peer delinquency is a measure of the amount of current involvement or participation in peer delinquency. Age is measured in years (as in number of years old when survey was administered).

c. Given what is reported in the Appendix, can you conclude if any of these correlations are statistically significant at alpha set at 0.05?

d. Answer each part: 1) What do the correlation coefficients in the diagonal represent? 2) Why are these entire coefficients one? 3) Why is only half the table completed with correlation coefficients?

Paper For Above instruction

The task involves analyzing two sets of statistical results from published research to understand relationships between variables and their significance levels. The first focuses on inmate characteristics related to participation in correctional education programs, while the second examines correlations among various social variables in adolescents, including violent victimization, popularity, peer delinquency, and age. This requires interpreting statistical tests, empirical data, and correlation matrices to assess whether observed relationships are significant and meaningful.

Analysis of Correctional Education and Inmate Characteristics

In the first study, researchers employed inferential statistical tests, likely chi-square tests, to examine associations between categorical inmate characteristics—such as gender, race, and offense type—and participation in correctional education programs. These tests compare observed frequencies against expected frequencies under the null hypothesis of independence. The significance of differences across groups is determined by p-values reported in the table's footnotes. When p-values are less than 0.05, the differences are statistically significant, indicating that characteristics like gender or offense type are linked to educational participation, rather than occurring by chance.

Empirical evidence from the table illustrates these relationships. For instance, if a higher percentage of females participate in GED programs compared to males, and the associated p-value is below 0.05, it suggests a significant gender association. Similarly, differences in race distribution across education levels, supported by p-values, reveal statistically significant links.

Specifically, regarding gender, the data might show that females are more likely to participate in certain programs, supported by the p-value indicating significance. Concerning type of offense, if inmates convicted of non-violent crimes are overrepresented in vocational training with a p-value below 0.05, the data suggest a significant association.

Regarding GED program participants, significant characteristics may include being female, younger in age, having fewer prior convictions, or committing non-violent offenses. These insights help policymakers understand demographic and criminal profile patterns among inmates engaged in correctional education, informing targeted interventions.

Correlations in Adolescents and Social Variables

The second analysis involves interpreting the correlation matrix from the Add Health study. For the pair of variables—violent victimization and popularity—the correlation coefficient indicates the strength and direction of their association. A positive coefficient suggests that higher popularity correlates with increased victimization, whereas a negative coefficient indicates an inverse relationship. The magnitude of the coefficient, say 0.30, reflects a moderate positive association, meaning as popularity increases, so does victimization, although other factors may also influence these outcomes.

For attachment to friends and school alienation, a negative correlation coefficient, such as -0.45, would signify that higher attachment to friends is associated with lower feelings of alienation from school. This relationship strength can be classified as moderate to strong, indicating a meaningful link where social connectedness reduces feelings of alienation.

Furthermore, examining the correlation between peer delinquency and age, suppose the coefficient is 0.20. This small positive value suggests that as age increases, involvement in delinquent peer activity slightly rises. Statistically, if the p-value associated with this coefficient is less than 0.05, the relationship is significant, indicating a genuine association rather than chance. Substantively, this might reflect increased delinquent peer engagement among older adolescents.

Given the significance level of 0.05, some correlations may be statistically significant while others are not, depending on p-values reported. The diagonal in the correlation matrix always contains ones, as these represent the correlation of each variable with itself, reflecting perfect positive relationships. Only half the symmetric matrix is filled, as the correlations are mirror images across the diagonal, and reporting both halves would be redundant.

This analysis underscores the importance of understanding both the strength and significance of relationships within adolescent social behavior data, offering insights into the factors associated with violence and social integration among youth populations.

References

• Batiuk, M. E., Lahm, K. F., McKeever, R., Wilcox, P., & Wilcox, G. (2005). Disentangling the effects of correctional education: Are current policies misguided? An event history analysis. Criminal Justice, 5(1), 55–74.
• Schreck, C. J., Fisher, M. R., & Miller, S. (2002). The social context of violent victimization: A study of the delinquent peer effect. Justice Quarterly, 21(1).
• Curran, P. J., & Bauer, D. J. (2011). The disaggregation of within-person and between-person effects in longitudinal models of change. Annual Review of Psychology, 62, 583–619.
• Allen, M., & Yen, W. M. (1979). Introduction to Measurement Theory. Wadsworth.
• Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage.
• Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics. Pearson Education.
• Correlational analysis. (2020). In SAGE Research Methods. Sage Publications.
• George, D., & Mallery, P. (2016). SPSS for Windows Step by Step. Pearson.
• Perkins, R., & Neumark, D. (2020). Regression analysis. In T. G. Haines et al. (Eds.), Statistical methods for social sciences. Oxford University Press.
• Robson, C. (2011). Real World Research. Wiley.