Saint Josephs University Statistics Worksheet

I’m working on a criminal justice writing question and need a sample draft to help me learn.

Question 1:

• Write a results paragraph describing ONLY correlations that are statistically significant at p < 0.05 level. When interpreting statistically significant correlations you should focus on strength of association and directionality of the association (i.e. positive or negative)

The written descriptions should include significance (0.05 or less), directionality, and magnitude of the correlation. You should only describe correlations that are statistically significant (ie, when the p-value for a correlation is below the significance criterion of 0.05). I have provided an example write up from another project (NOT YOUR PROJECT)

Jacob Cohen’s rule of thumb for magnitude (or strength of relationship) that we are using in this class (absolute values):

Example paragraph:

(The example paragraph below is from another project that does not contain all the same variables as your project. Therefore, you should not use this specific paragraph, but this does give you some guidance as to what we expect. The most important thing to remember is that you should only interpret correlations that are statistically significant by describing the magnitude and direction of the statistically significant correlations)

Table 2 shows Pearson product moment correlations among dependent, independent, and statistical control variables for the full analysis sample. The fear of crime scale has positive and statistically significant correlations with victimization (r = ##; p < .## ) and neighborhood disorder (r = ##, p < ##). The fear of crime scale has a negative and statistically significant correlation with gender (r = ##; p < ##). The magnitude of these relationships is range from small to moderate. University Area residents who report being victims of crime in the past six months are significantly more fearful of crime in their neighborhood at night compared to those who do not report being victims of crime. On average, females report feeling more fearful (or less safe) in the University area at night compared to males. Residents who perceive neighborhood disorder to be more of a problem also report higher scores on the fear of crime scale, indicating they are more fearful at night in their neighborhood compared to those who perceive neighborhood disorder to be less of a problem. Fear of crime has a negative and statistically significant correlation with age (r = ##; p < ##), indicating that younger residents are more fearful of crime in their neighborhood. Gender has negative and statistically significant correlations with victimization (r = ##; p < ##) and neighborhood disorder (r = ##; p < ##). Females, on average, are more likely to report being victims of violent crime and perceive more neighborhood disorder compared to their male counterparts.

Generic examples for the written part (with hypothetical values and variables):

• A positive, statistically significant, and strong relationship
  • Example: There is a positive and statistically significant relationship between X and Y (r =. 75; p < 0.05). Specifically, individuals who have higher scores on variable X will tend to have higher scores on Y as well. Furthermore, the relationship between X and Y is strong, suggesting that the relationship is quite consistent.
• A negative, statistically significant, and moderate relationship
  • Example: There is a moderate negative and statistically significant relationship between X and Y (r = -.30; p < 0.05). Individuals who have higher scores on variable X will tend to have lower scores on Y.
• A binary variable and a continuous variable
  • Explanation: With a binary variable (e.g., victimization) and a continuous variable (e.g., fear of crime), the correlation is a special type of the Pearson Product Moment Correlation called a point-biserial correlation. The example below is hypothetical – you do not have a life satisfaction variable in your data!
  • Example: The relationship between victimization and fear of crime is statistically significant and positive; however, the magnitude of the relationship is small (r = -0.05; p < 0.05). This suggests that, on average, those who have experienced victimization in the past six months tend to also report more fear of crime
  • Table 2. Bivariate correlations between Independent, Dependent, and Statistical Control Variables (n = 500)

  • 	X1	X2	X3	X4	X5	X6
    X1: Fear of Crime	1.00	-0.3738*	-0.1066*	-0.1900*	0.2778*	0.1827*
    X2: Collective Efficacy	-0.3738*	1.00	0.1330*	0.0199	-0.3237*	-0.1515*
    X3: Age	-0.1066*	0.1330*	1.00	-0.0247	-0.1265*	0.0003
    X4: Sex (1 = Male)	-0.1900*	0.0199	-0.0247	1.00	0.1163*	0.1919*
    X5: Disorder	0.2778*	-0.3237*	-0.1265*	0.1163*	1.00	0.2193*
    X6: Victim (1=Yes)	0.1827*	-0.1515*	0.0003	0.1919*	0.2193*	1.00

    Note: * = p < 0.05

  Question 2: I have used the 5 easy steps for multivariate linear regression to write a paragraph of results specific to your linear regression results. However, I have left several “blanks” in this paragraph that you must complete by using the correct word(s) to describe the linear regression results. Write a discussion section that is 2 double spaced pages in length (12 font). This section should accomplish the following:

• • Summarize your findings as they relate to your null and research hypotheses – what was anticipated or predicted about the association between perceptions of collective efficacy and fear of crime and what did you discover?
  • Discuss your findings as they relate to published research on collective efficacy, as well as studies on collective efficacy and fear of crime. (for example, are your findings consistent with past research or not; if your findings are different from past studies why do you think this is so?).
  • Discuss at least two limitations of your study. This could be sample limitations, how the outcome was operationalized and measured, the exclusion of potentially important predictors; generalizability; measurement concerns regarding primary variables or statistical control variables etc.).
  • Finally, identify two important directions for future research on collective efficacy and fear of crime that can build on research you have conducted in this course on collective efficacy and fear of crime. (this is where you can be creative in defining a modest research agenda that builds on your research examining perceptions of collective efficacy and fear of crime)

Table 2. Multivariate Linear Regression Results Predicting Fear of Crime at Night Among Adult Residents of the University Area (n = 500)

Independent Variables	b	SE	Beta
Perceptions of Collective Efficacy	-0.3062281	0.0459909	-0.2785088
Victimization (victim=1)	0.2345025	0.058232	0.1658101
Neighborhood Disorder	0.1567292	0.039603	0.1678922
Gender (male = 1)	-0.2613904	0.0437398	-0.2392226
Black	-0.1163207	0.0509832	-0.108349
Hispanic	0.0956982	0.0642722	0.0697364
Other	-0.0686426	0.1004201	-0.0289358
Age	-0.0022789	0.001775	-0.0527902
Constant =	3.276717	0.1478916	–
F- statistic =	20.93	20.93	20.93
Adjusted R2 =	0.2421	0.2421	0.2421

Note: * = p <0.05