Evaluating Sampling Method and Sample Size of a Population

Evaluating Sampling Method and Sample Size of a Population

Sample Selection

A stratified sample of 75 doctors, 75 lawyers and 75 engineers who belong to a professional organization that you belong to

The initial phase involves classifying the population into distinct categories, namely doctors, lawyers, and engineers, forming the basis for strata definition. Subsequently, a simple random sample will be drawn at each stage, with a designated sample size of n=75. Stratified sampling offers two paramount advantages in this context. Firstly, it ensures the representation of specific subgroups within the ultimate sample, a crucial consideration if certain groups are smaller in size. Secondly, it enhances precision in estimation. Stratified sampling allows for a more accurate approximation by not overlooking between-strata variability. By employing this method, there is a potential to reduce the required sample size while maintaining a specified level of accuracy, thereby optimizing the efficiency of the sampling process.

A simple random sample of 150 subscribers to your local newspaper

The initial step in this research procedure involves the identification and compilation of potential participant sources into a unified dataset. In situations involving a sizable population, the creation of an extensive database becomes necessary to accommodate a potentially large sample size. Subsequently, employing database sorting functions, 150 individuals are randomly selected for inclusion in the local newspaper sample. The utilization of simple random sampling is pivotal in ensuring the practicality, implementation, and mitigation of researcher bias. Simple random sampling, as a probability sampling method, guarantees that all subjects within the target population have equal and unbiased opportunities for selection in the sample, thereby enhancing the overall fairness and representativeness of the sampling process.

 A systematic sample of 250 subscribers from a subscriber list of a trade publication.

In this procedural approach to systematic sampling from a subscriber list population, each component is systematically assigned a unique number within the sequence of 1 to 250. The first step involves numbering each subscriber in sequence from 1 to 250. Following this, the determination of the sample size is crucial. For instance, if the desired sample size is 100, the starting point would be 1000. To achieve the required 100 samples, a division of 1000 by 10 is executed, resulting in the necessary 100 samples. In this specific case, with n=250, the initial selection would be 2500, and by dividing it by 10, the required 250 samples are obtained. The systematic sampling technique is characterized as a presumptive method where components are selected from a target population, with the initial component chosen randomly. Subsequently, the remaining components of the sample are systematically selected at fixed intervals, as outlined by Chandler et al. (2019). This method is particularly effective in averting statistical bias, ensuring a methodical and unbiased representation of the population in the sample selection process.

A Priori Power Analysis

The data, when computed, resulted in a bell-shaped normal distribution graph, as depicted in Figure 1 below. The additional results are presented in Figure 2.

Figure 1

Results from G*Power

Figure 2

Additional Results

For this examination, the researcher assumes that the results stem from a sample size larger than what they can obtain. Employing the compromise function t-test to compute alpha and beta for an experiment half the size yielded the following outcomes: α=0.08 and β=0.03461, resulting in a new power of 0.6538271, equivalent to 65%, as illustrated in Figure 2. The findings suggest that the researcher should avoid utilizing a smaller sample size due to the increased likelihood of errors (Kang, 2021). The only potential trade-off to this probability would involve securing a larger sample size from the chosen population. If this becomes a consideration, substantial time may be required to recruit additional participants or expand the study’s population (Etikan & Babatope, 2019).

ANOVA

ANOVA resembles conducting a t-test. While a t-test compares the means of two groups, an ANOVA compares the means of three groups to establish a statistically significant difference. Proper use of ANOVA reduces the likelihood of type I errors (Weiers, 2011). Researchers typically view ANOVA as fixed effects, omnibus, and one-way. The sample size employed indicates a small effect size involving three groups, with α= 0.05 and β= 0.2. G-Power data reveals a critical F-value of 3.0479, a total population (N) of 177, and an actual power of 0.2008373, equivalent to 20%, as depicted in Figure 3. In simpler terms, there is an 80% likelihood of achieving significance (Lakens & Caldwell, 2021). Given the considerable sample size, a researcher should acknowledge that collecting and analyzing data from such a sample is beyond the practical means allotted.

Figure 3

ANOVA Results

Intended Research Sampling Method

To initiate the proposed research sampling method, the researcher should commence by defining the study’s objectives. The research aims to scrutinize gaps in current studies, focusing on the analysis of existing research to identify and address deficiencies. The overarching goal is to enhance the effectiveness of current studies in addressing the complexities associated with violent crime.

Statement of Problem

Urban areas are grappling with a significant but inadequately addressed issue—the persistent cycle of violence that results in the loss of lives, shattered families, and the devastation of communities. The existing studies fall short of adequately addressing the multifaceted aspects of this problem, including the culture of crime, control mechanisms to deter criminal activities, and the insufficient availability of mental health resources to address the psychological impact on victims or witnesses of violent crimes.

Understanding the foundation of violent crime requires an exploration of the theoretical framework explaining its existence. Galtung’s (1990) culture of crime theory provides a comprehensive three-dimensional framework: direct, structural, and cultural (Paulson & Tikly, 2023). Despite being introduced over two decades ago, recent substantial research indicating any significant alterations to Galtung’s theory is noticeably absent. A key challenge in addressing violence lies in the absence of universally accepted norms regarding acceptable and unacceptable behavior, particularly concerning what could be deemed “harmful” beyond culture-specific social norms. While comprehensive studies on violent crime often focus on domestic violence and violence against women and children, minimal attention has been directed towards understanding urban violence at a community level and its underlying reasons. This research aims to bridge this gap and contribute to a more holistic understanding of urban violence and its cultural dynamics, providing valuable insights for effective interventions.

The landscape of addressing violent crimes in America has seen little robust intervention since the enactment of the Violent Crime Control and Law Enforcement Act of 1994 by former U.S. President William Clinton. Despite an overall decline in violent crime since the late 1990s and an increase in law enforcement officers, a concerning upward trend was observed from 2019 to 2022 (Statista, 2022). The rise in violent crime is attributed, in part, to a growing distrust between the community and law enforcement. Despite an outdated crime control act and an influx of police officers patrolling urban communities, there is limited evidence demonstrating that alternative solutions have been effectively implemented to reduce violent crime.

To comprehend the persistence of a cycle of violence, a crucial yet unchallenged factor is the impact of mental health. While it is theorized that structure plays a pivotal role in violent crime, the nature and extent of this structure and whether it can be altered have undergone minimal analysis and research. Structural violence is deeply ingrained in the social structure, comprising systems governed by laws and organizations. Alarming disparities persist, as studies reveal that minorities lack equal access to or receive the same quality of mental health services compared to whites (Cook et al., 2019). Further research suggests that minority groups are less likely to access mental health counseling (Rodgers et al., 2021). The absence of mental health involvement in a culture entrenched in violence could perpetuate the cycle, causing lasting psychological damage to those who have experienced violence (Peltonen et al., 2020). Addressing these issues is critical for breaking the cycle of violence in urban communities.

Statement of Purpose

The central aim of this quantitative research is to delve into the correlation between instances of violence in neighborhoods and the subsequent recurrence of violence within the same community. Additionally, the study endeavors to scrutinize the efficacy of introducing a control mechanism as a means to curtail violent crime in the sampled community. Lastly, it seeks to probe into the potential impact of cultivating a culture of mental health counseling within minority communities. Through a rigorous quantitative analysis, this research aspires to enrich the understanding of the intricate dynamics surrounding violence, evaluate the effectiveness of preventive measures, and elucidate the role of mental health support in fostering overall community well-being, with a specific focus on minority populations.

By employing quantitative methodologies, this study intends to contribute nuanced insights into the multifaceted nature of violence, moving beyond mere occurrences to understand the underlying patterns and potential preventive measures. The investigation into the implementation of a control mechanism aims to explore innovative ways to reduce the prevalence of violent crime, thereby enhancing community safety. Moreover, delving into the establishment of a culture of mental health counseling within minority communities is poised to shed light on the transformative potential of psychological support, not only in addressing the aftermath of violence but also in preventing its recurrence.

The research is in line with the broader societal objectives of fostering safer, healthier, and more resilient communities. Through a systematic exploration of these interconnected facets, this study aspires to inform evidence-based policies as well as the interventions that can help contribute to the well-being and security of urban communities, particularly those that have a high representation of minority populations. In essence, this quantitative research endeavors to provide actionable insights that could be key in guiding the development of targeted strategies for violence prevention and community enhancement.

Research Questions

Research Question 1:

Does the occurrence of violent crimes in urban communities contribute to an environment conducive to further violent criminal activities?

Research Question 2:

Would the implementation of a control measure in a selected urban community result in a reduction in violent crime?

Research Question 3:

Can the introduction of a standardized mental health resource in urban communities lead to a decrease in the incidence of violent crimes?

In this research, the study population comprises 150 participants, and the investigation will span a duration of three years. Data collection will involve accessing statistics from reliable sources, including the Bureau of Justice Statistics (BJS), Federal Bureau of Investigation Uniform Crime Reporting Data (FBIUCR), Sample Surveys, and Local Court cases. To ensure a comprehensive understanding, surveys will be administered to individuals within and outside the criminal justice system, covering those who have experienced environmental violence and those who have not. This will include individuals with criminal justice involvement who have received mental health services and those who have not, examining their potential for recidivism. A stratified testing method will be employed to systematically gather this diverse data, providing a nuanced analysis of the multifaceted factors influencing the cycle of violence and mental health implications within the selected population.

Conclusion

The primary aim of this project was to evaluate sampling methods and determine an appropriate sample size for the development of a quantitative research design plan. The researcher outlined recommended steps for sample selection and emphasized the critical evaluation of the sampling plan. Utilizing the G-Power software, data were processed to calculate the sample size for two specific vignettes. The assignment culminated in the identification of a suitable sampling method for the researcher’s proposed quantitative descriptive research application, incorporating a detailed description of the target population. This process provided a comprehensive understanding of the steps involved in preparing and implementing a robust sampling strategy, contributing to the foundation of a well-structured quantitative research design plan.

References

Chandler, J., Rosenzweig, C., Moss, A. J., Robinson, J., & Litman, L. (2019). Online panels in social science research: Expanding sampling methods beyond mechanical Turk. Behavior Research Methods, 51. https://doi.org/10.3758/s13428-019-01273-7

Cook, B. L., Hou, S. S.-Y., Lee-Tauler, S. Y., Progovac, A. M., Samson, F., & Sanchez, M. J. (2019). A review of mental health and mental health care disparities research: 2011-2014. Medical Care Research and Review, 76(6), 683–710. https://doi.org/10.1177/1077558718780592

Etikan, I., & Babatope, O. (2019). A basic approach in sampling methodology and sample size calculation review article. MedLife Clinics, 1, 1006. https://www.medtextpublications.com/open-access/a-basic-approach-in-sampling-methodology-and-sample-size-calculation-249.pdf

Kang, H. (2021). Sample size determination and power analysis using the G*Power software. Journal of Educational Evaluation for Health Professions, 18(17), 17. https://doi.org/10.3352/jeehp.2021.18.17

Lakens, D., & Caldwell, A. R. (2021). Simulation-based power analysis for factorial analysis of variance designs. Advances in Methods and Practices in Psychological Science, 4(1), 251524592095150. https://doi.org/10.1177/2515245920951503

Paulson, J., & Tikly, L. (2023). Reconceptualizing violence in international and comparative education: Revisiting Galtung’s framework. Comparative Education Review. https://doi.org/10.1086/726372

Peltonen, K., Ellonen, N., Pitkänen, J., Aaltonen, M., & Martikainen, P. (2020). Trauma and violent offending among adolescents: a birth cohort study. J Epidemiol Community Health, 74(10), 845–850. https://doi.org/10.1136/jech-2020-214188

Rodgers, C. R. R., Flores, M. W., Bassey, O., Augenblick, J. M., & Cook, B. L. (2021). Racial/Ethnic disparity trends in children’s mental health care access and expenditures from 2010 to 2017: Disparities remain despite sweeping policy reform. Journal of the American Academy of Child & Adolescent Psychiatry. https://doi.org/10.1016/j.jaac.2021.09.420

Statista. (2022). U.S.: violent crime rate graph 1990-2022 | Statista. Statista; Statista. https://www.statista.com/statistics/191219/reported-violent-crime-rate-in-the-usa-since-1990/

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This assignment consists of three parts:

(1) Sample Selection

Recommend the steps that should be taken to draw the particular sample described below. Format your response as a procedure.

A stratified sample of 75 doctors, 75 lawyers, and 75 engineers who belong to a professional organization that you belong to.
A simple random sample of 150 subscribers to your local newspaper.
A systematic sample of 250 subscribers from a subscriber list of a trade publication.
(2) A Priori Power Analysis

Download the G*Power software provided, and then use the software to submit the following:
a. Calculate the estimated sample size needed when given these factors:

one-tailed t-test with two independent groups of equal size
small effect size (see Piasta, S.B., & Justice, L.M., 2010)
alpha =.05
beta = .2 (Reminder: Power = 1 – beta)
Assume that the result is a sample size beyond what you can obtain. Use the compromise function to compute alpha and beta for a sample half the size.
Indicate the resulting alpha and beta.
Analyze the result and decide if the study should be conducted with a smaller sample size. Explain your rationale.
In the context of Type I and Type II error.
Include a visual of the G* Power output matrix.
b. Calculate the estimated sample size needed to perform an ANOVA (fixed effects, omnibus, one-way) when given these factors:

ANOVA (fixed effects, omnibus, one-way)
small effect size
alpha =.05
beta = .2
3 groups
Include a visual of the G* Power output matrix.
(3) Intended Research Sampling Method

Describe the sampling method that would be appropriate for your intended research.

Outline the problem statement, purpose statement, and research questions.
Describe the population of interest (also referred to as the theoretical population).
Identify the sampling frame to be used to recruit participants.
List criteria to be met for an interested person to participate in the research study.
Compute an estimated sample size.
Describe the recruitment procedure that might be used to draw the actual sample.
Length: Your paper should be between 5 – 10 pages, not including the title and reference page. Results of the G* power analysis that will add length to the paper.

References: Include a minimum of five (5) scholarly sources.