Law
The descriptive research design is a method that seeks to accurately and systematically describe a phenomenon, population, or situation. It can answer the when, how, what, where questions, and not the why questions. As such, this design could help the police where these crimes are occurring, when they are occurring, how they are occurring, and what is causing them.
The historical research design is a type of research method that studies the meaning of events that occurred in the past so as to deduce the facts and explain the cause of events, and their impact in the present events. The design is used to preserve and interpret facts, and to provide an understanding of the effect of the past occurrences on the current and future events.
Cross-sectional and longitudinal studies are similar in that they are both observational. These types of study are also different. The main dissimilarity is that whereas cross-sectional studies interrogate a new sample of individuals every time they are conducted, longitudinal studies observe a similar group of individuals for some time.
Cross-sectional designs may either be descriptive or analytical. A descriptive cross-sectional study seeks to measure and assess a condition and possible related aspects at a certain point in time for a certain population (Dantzker & Hunter, 2011). Analytical cross-sectional studies seek to investigate associations between factors. Longitudinal designs may either be cohort or panel studies. Panel studies observe a similar group or sample for some time, whereas cohort studies follow cohorts as they change over time. These designs could contribute to the study by helping to identify the crime patterns and hence help in establishing what causes them and their effects
Correlational and causal-comparative research has several purposes. For instance, correlational research purposes to ascertain how related 2 or more variables are (Dantzker & Hunter, 2011). Causal-comparative research seeks to establish a cause-effect relationship between 2 or more groups.
A community safety program is recommended where police and the public work together to address the crimes. The public plays a more active role in identifying criminals and reporting them; the police conduct more patrols. Evaluative research will clarify outcomes of the program and hence establish if it was a success.

Reference
Dantzker, M., & Hunter, R. (2011). Research methods for criminology and criminal justice. Jones & Bartlett Publishers.

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