Selecting an appropriate statistical method is an important step in analyzing research data. Selecting the wrong statistical analysis method creates serious challenges when interpreting a study’s findings and affects the conclusions drawn from the studies (Mishra et al., 2019). In statistics, for each specific situation, there are appropriate statistical methods available for analyzing and interpreting data. Mishra et al. (2019) explain that selecting the appropriate statistical method requires knowledge concerning the assumptions and conditions of statistical methods, the nature and type of the data collected, and study objectives since appropriate statistical methods are selected based on these factors. This paper contributes to an enhanced understanding of statistical analysis methods by proposing five hypothetical research studies for five statistical analysis approaches. The statistical analysis methods include independent samples t-test, paired samples t-test, correlation, regression, and chi-square test.
Independent Samples T-Test
An important point to consider when selecting a statistical test is to assess whether the data is paired. According to Mishra et al. (2019), an independent samples t-test is used when different groups are used in a study, and each group has different subjects. For instance, comparing the means between two groups with unpaired or independent data. An independent samples t-test is used to compare two sample means from unrelated groups. Below is a hypothetical study that applies independent samples t-test.
The Hypothetical Study
A proposed hypothetical study analyses the salary differences between male and female employees within a large organization following complaints of gender pay gaps that must be addressed for fairness to prevail.
Main Variables in the Study
In the study that analyzes the salary differences between male and female employees, the independent variable is gender (male/female), and the dependent variable is employees’ salaries.
The Nature of the Data That Will Be Collected
Salary data is the first data that will be collected for the study. Salary data will be obtained for all the employees, including their gender. Data on the control variables that could influence salaries will also be collected, including job titles, years of experience, and education levels. Demographic data, including age, department, and tenure, would also be collected. Collecting employee performance data would also be important, which could help explain salary differences.
Research Question
Is there a statistically significant difference in the organization’s average salaries between female and male employees?
The Test Used
An independent samples t-test will be used. Mishra et al. (2019) say that the test is appropriate when comparing the means of two independent groups. In this case, the independent groups are male and female employees. The test will help determine whether any observed differences in average salaries are statistically significant or occur randomly based on other factors. In the t-test, the t-statistic will measure the differences between the means of the male and female groups, and the p-value will indicate whether the difference is statistically significant. A p-value of less than 0.05 would suggest a significant difference in the salaries between male and female employees.
Paired Samples T-Test
When considering whether data is paired, the independent samples t-test is not the only applicable test for unpaired data. When data is paired, such as when the same subjects are measured at different points or using different methods, a paired samples t-test is used. A paired samples t-test compares the means between two groups with paired data (Mishra et al., 2019). An example of a hypothetical research study is described below for paired samples t-test.
The Hypothetical Study
A hypothetical study that uses paired samples t-test aims to find the differences in self-esteem levels in a specific group of individuals before and after they are subjected to a self-esteem improvement program.
Main Variables in the Study
The study’s independent variable will be the intervention applied in the study. The self-esteem intervention used in the program is the independent variable since it will be manipulated or introduced to assess its impact on self-esteem levels. This means that the self-esteem levels are the dependent variable.
The Nature of the Data That Will Be Collected
Data will be collected before and after the self-esteem intervention. The data will be self-esteem ratings, which will be collected through the Rosenberg Self-Esteem Scale. The initial ratings will be used as the baseline data, and the data collected after the intervention will be compared to the initial data to determine the differences after applying the intervention.
Research Question
Do the self-esteem ratings of a group of individuals subjected to a self-esteem improvement program improve?
The Test Used
Paired samples t-test will be used for this study. According to Mishra et al. (2019), the paired samples t-test compares the mean between two groups when data is paired. Since the same subjects are measured at different time points following the application of an intervention, the data is paired, making paired samples t-test appropriate for the study.
Correlation
An intraclass correlation coefficient is calculated when both pre-post data are on a continuous scale. Correlation is a statistical measure that expresses the extent of the linear relation of two variables. Linear relation means that the variables change together at a constant rate (Mishra et al., 2019). Described below is a hypothetical study for correlation.
The Hypothetical Study
A hypothetical study for correlation examines the relationship between the number of social media users and the reported loneliness levels among young adults. This study would be useful for determining the appropriate usage of social media platforms to reduce loneliness among young adults.
Main Variables in the Study
The study would have two main variables. The independent variable would be the number of hours spent on social media daily, and the dependent variable would be the reported levels of loneliness among young adults.
The Nature of the Data That Will Be Collected
Data will be collected from young adults aged 18-25 on the self-reported number of hours they spend on social media daily. Furthermore, the three-item UCLA loneliness scale will be used to measure levels of loneliness. Liu et al. (2020) note that the loneliness scale is a self-report measure, and its three items evaluate how often an individual feels they lack companionship, how often they feel left out, and how often they feel isolated from others.
Research Question
Is there a correlation between the number of hours young adults spend on social media and their reported levels of loneliness?
The Test Used
A correlation analysis will be used for the study. For instance, Pearson’s correlation coefficient could be used to find the direction and strength of the two variables used for the study. The analysis would produce a correlation coefficient and a p-value.
Regression
Regression is a statistical analysis technique that relates a dependent variable to one or multiple independent variables. A regression model can show the association of the changes observed in the dependent variables with the changes in one or more explanatory variables (Mishra et al., 2019). A hypothetical research study for regression is discussed below.
The Hypothetical Study
A hypothetical study for regression predicts a student’s final exam scores based on their scores on previous quizzes and the number of hours they spent studying.
Main Variables in the Study
This study would have one dependent variable and multiple independent variables. The dependent variable would be the student’s score on the final exam, while the independent variables include the number of hours the student spent studying and their scores on previous quizzes.
The Nature of the Data That Will Be Collected
The data that will be collected is directly connected to the dependent and independent variables. The data will include the students’ scores in their final exams, the number of hours they spent studying, and the scores from the previous quizzes.
Research Question
To what extent do a student’s previous quiz scores and the number of hours they spend studying predict their scores on the final exam?
The Test Used
A multiple linear regression would be useful for this study. According to Mishra et al. (2019), a multiple linear regression determines the mathematical relationship between multiple independent variables and one dependent variable. A multiple linear regression would estimate the coefficients of the dependent variable to create a predictive equation for the final exam scores.
Chi-Square
A chi-square test is a nonparametric test for dichotomous or binomial data summarized as proportions or percentages (Najmi et al., 2021). Below is a hypothetical research study for the chi-square test.
The Hypothetical Study
A hypothetical study for the chi-square test compares the proportion of death and survival in non-vaccinated and vaccinated children with respiratory tract infections.
Main Variables in the Study
The main variables for the study are independent and dependent. The independent variable would be the vaccination status (whether a child is vaccinated). The dependent variable is the outcome, which is either death or survival.
The Nature of the Data That Will Be Collected
Data collection would be done from children with respiratory tract infections. The independent variable would be data concerning the children’s vaccination statuses. Depending on their caregiver’s reports, the children would be categorized as either vaccinated or not vaccinated. More required data is on the outcomes of vaccination or non-vaccination on the children. Children would get classified as either survived or deceased.
Research Question
In children with respiratory infections, does vaccination or non-vaccination cause a significant difference in the proportion of death and survival?
The Test Used
A chi-square test of independence would be conducted using the contingency table. The test will generate a chi-square test and a p-value. The chi-square statistic is useful for indicating whether there is an association between vaccination status and the outcome. A higher chi-square value indicates a stronger association, and the p-value tells the statistical significance of the association.
Conclusion
In conclusion, in statistics, there are appropriate statistical methods available for analyzing and interpreting data in specific situations. For instance, a paired samples t-test is useful when comparing the means between two groups with paired data, while an independent samples t-test is used for unpaired data. Also, correlation is a statistical measure that expresses the extent of the linear relation between two variables, regression relates a dependent variable to one or multiple independent variables, and a chi-square test is used for dichotomous or binomial data that is summarized as proportions or percentages. The examples of hypothetical research studies for the statistical analyses enhance understanding of the analysis methods. Appropriate statistical analysis techniques are useful in correctly interpreting a study’s findings and drawing conclusions.
References
Liu, T., Lu, S., Leung, D. K., Sze, L. C., Kwok, W. W., Tang, J. Y., … & Wong, G. H. (2020). Adapting the UCLA 3-item loneliness scale for community-based depressive symptoms screening interview among older Chinese: a cross-sectional study. BMJ open, 10(12), e041921.
Mishra, P., Pandey, C. M., Singh, U., Keshri, A., & Sabaretnam, M. (2019). Selection of appropriate statistical methods for data analysis. Annals of cardiac anaesthesia, 22(3), 297.
Najmi, A., Sadasivam, B., & Ray, A. (2021). How to choose and interpret a statistical test? An update for budding researchers. Journal of family medicine and primary care, 10(8), 2763.
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