Question
A researcher intends to determine which variables are more likely to predict public assaults against the police in Kentucky. The variable represents the 2012-2016 average
A researcher intends to determine which variables are more likely to predict public assaults against the police in Kentucky. The variable represents the 2012-2016 average assault rates per 100,000 people. The following correlation matrix shows the relationship between assaults against the police in the state and the 2006-2010 average homicide rates per 100,000, and other socio-demographic variables at the county level in KY, based on 2010 US Census data. Relationships among the independent variables are included as well. Table 1 includes the Pearson correlation coefficients corresponding to bivariate relationships among five variables. The unit of analysis is the county (N = 120). Note: The analysis is based on real data. [15 points]
Table 1. Assaults against the police in Kentucky (N = 120): Intercorrelation matrix
Measures | Police Assault | Poverty | Homicide Rate | AA% | FHH% |
Assault against POLICE rate | 1 |
|
|
|
|
Poverty level | -.297 | 1 |
|
|
|
Homicide rate | -.176 | .452 | 1 |
|
|
% African Americans (AA%) | .316 | -.292 | .040 | 1 |
|
% Female Head of Households (FHH) | .325 | .291 | .199 | .408 | 1 |
- Identify the dependent (DV) and the independent (IV) variables
- Formulate the null and alternative hypotheses [Note: a null hypothesis should be formulated for each relationship the DV has with the selected IVs]. You should have 4 null hypotheses [see column 1 of the correlation matrix].
- Knowing that N = 120 (the number of counties in KY), test the null hypotheses youve formulated [see the critical values of Pearsons r, at the corresponding df and p< .05, 2-tail test]. You should list the value of the critical Pearsons r.
- Reach a statistical conclusion for each test [it should be 4 tests] that examines the bivariate relationship between the dependent variable and the selected independent variables and interpret your findings. What characteristics appear to have those counties that registered a higher incidence of public assaults against the police in KY? What variables are significantly related to assault against the police and what is the direction of the relationship?
- What percentage of the variation in assaults against the police is explained by the percentage of female-headed households at the county level? [Hint: calculate the coefficient of determination to answer the question].
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