Introduction
Correlational and regression statistics are widely used in various fields of research to establish the relationships between various variables and their effects on particular areas of interest (Cramer, 2016). Correlational research design focuses on finding associations and measuring the relationship between various variables. It is often used in psychology, sociology, and various other fields where staging an experiment by isolating certain particular variables of interest is impossible. Reasons for the impossibility of the experiment could be many, such as technical impossibility, ethical considerations, or the potential to distort the relationship between factors by taking other variables out of the picture. This research design is good at studying naturally-occurring phenomena. There is one large limitation of this research design. It cannot be used to establish cause-and-effect connections, as the research does not eliminate other independent variables from the equations, which may affect the result (Cramer, 2016).
Regression analysis, on the other hand, is used to determine how an independent variable is numerically related to the dependent variable (Cramer, 2016). Its purpose is to help estimate the value of the unknown variable based on the value of a known variable. It is used to predict results, which is why it finds implementation in economics medicine, education, and predictive statistics (Cramer, 2016). While in correlation both variables are equal, and the relationship between them goes both ways, in regressions, the relationship between variable 1 towards variable 2 is different from the relationship between variable 2 towards variable 1. Understanding the implementation of these concepts is paramount to a researcher. The purpose of this paper is to evaluate two dissertation papers written between 2012 and 2017, analyze their use of both statistical methods, and determine if any factors went amiss.
Correlation Study: The Effect of Student-Teacher Rapport on High School Student Performance Rate
This study was performed by Robyn Alisha Clark of Liberty University and published in 2014 on behalf of Liberty University. The research studies the correlation between student-teacher rapport and high-school student performance rate, as well as several other co-variables that are suspected to affect the relationship between teachers and students. These co-variables are identified as the gender of the students as well as post-graduation plans that the students may have. The researcher identified the correlational method as the best way to study these relationships and provided three hypotheses to be studied in this research:
- There is a statistically significant positive relationship between student-teacher rapport and performance rate as measured by the Student-Teacher Relationship Scale and the student’s grade point average (Clark, 2014).
- There is a statically significant positive relationship between a student’s gender and student-teacher rapport level as measured by the Student-Teacher Relationship Scale (Clark, 2014).
- There is a statistically significant positive relationship between a student’s post-secondary goals/plans and student-teacher rapport level as measured by the Student-Teacher Relationship Scale (Clark, 2014).
In addition to these hypotheses, the researcher also provided a set of null hypotheses, which state that Student-Teacher rapport does not affect the student’s grade point average, is not related to the students’ gender, and has no connection to the student’s post-secondary goals and plans.
The setting for the study was a high school in the Richmond metropolitan area. To test the hypotheses, the researcher used the convenience sampling method to recruit over a hundred students to complete the survey and provide anonymous data. The respondents’ activity rate was 75 percent, which the researcher deemed acceptable. The respondents were chosen from different backgrounds, as well as with different post-graduation plans in mind to ensure sample variability. The results were analyzed using the Pearson correlation method. In the end, all three null hypotheses were not disproven (Clark, 2014).
The results of the research are surprising, considering many academic studies highlight the importance of the Student-Teacher relationship and its positive effects on student grades (Shernoff, Csikszentmihalyi, Schneider, & Shernoff, 2014). The reasons for such unusual findings could be trailed to the limitations and gaps in the research design. The study hypotheses were not tested enough due to the fact the researcher chose to limit herself to surveying the students only. This method operates on the assumption that the perceived relationship of the student towards the teacher is equivalent to the teacher’s perceptions towards the student. The second hypothesis was not tested enough due to the fact the research does not take the teacher’s gender into account. If the teachers were considered a part of the research sample, their number and variance would be considered too low for a correlation design, as the researcher mentioned that only 6 English classes were analyzed, which means that the number of teachers participating in the research was 6. Lastly, the first hypothesis did not explore the possibility of the student’s attitude towards the subject being the cause of the good or bad relationship between the teacher and the student, and not the other way around. These factors, together, contributed to questionable conclusions of the research.
A Logistic Regression Analysis of Score Sending and College Matching among High School Students
This dissertation was developed by Krystle S. Oates and submitted to the Iowa University in 2015. It examines the relationship between the scores of the high-school students and their chances of successful college matching. It is a logistic regression analysis that examines the effect of numerous variables on the result in the attempt to enable the prediction of successful college matching based on the acquired data. In addition to the main variable, which is the GPA score, the research examines the influence of numerous independent variables, such as selectivity, student background characteristics, household income, parent education, race/ethnicity, student academic characteristics, student aspirations, and preferences (Oates, 2015). The research questions for this study are as follows:
- What variables are most related to students considering a match school for their first choice institution (Oates, 2015)?
- Among students who considered a match school for their first choice institution, what variables are most related to the likelihood that these students enrolled in a match school (Oates, 2015)?
- How have student background variables related to students considering a match school for their first choice institution changed over time (Oates, 2015)?
- How have the background variables related to students considering a match school for their first choice institution changed among students who attended high schools that were serviced by state college initiative designed to advise students on applying to college (Oates, 2015)?
According to the results of the research, social, economic, and racial backgrounds have a great influence on the matching potential of the students, as underrepresented minorities and students from poor backgrounds show significantly fewer inclinations to select the matching school as the education facility of their choice (Oates, 2015). Having parents with an academic background also adds to this conclusion. Also, presenting greater aptitude towards math and physics contributes to higher percentages of the match being successful (Oates, 2015).
The selected research design for this dissertation is solid, as the purpose of the study lies in the potential of predicting the success of matching schools for high-school students. All of the presented dependent and independent variables were thoroughly researched, and the results are credible and supported by previous researches of similar nature. However, there are gaps in this research that may have the possibility of distorting the results of the logistic regression analysis. As it was shown by the number of variables introduced and analyzed by the research, numerous factors influence the end decision of the student in regards to match schools. One of the large factors is related to gender. The student’s gender is traditionally associated with preference and aptitude in certain subjects and influences potential schools of choice (Goetz, Bieg, & Ludtke, 2013). Gender is not a minor factor that could be neglected, as it could directly influence the influence of math-related activities on the choice of schools, as well as on the student’s academic characteristics and aspirations.
Conclusions
Correlational and regression research designs find wide application in scientific research. Correlational designs are used for a broader scope of research in naturally-occurring phenomena and seek to determine coefficients of correlation between two dependent factors. Regressional research, on the other hand, is often used for establishing numerical codependence and enabling the researchers to predict the unknown variables based on the known ones. As it is possible to see in the examples presented in this paper, the ability to identify these variables is paramount to both the correlational and regression designs, and a failure to include them in the research could potentially lead the research astray, as it is possible to see in the first example.
References
Clark, R. A. (2014). Correlation study: The effect of student-teacher rapport on high school student performance rate. Web.
Cramer, H. (2016). Mathematical methods of statistics. New Jersey, NJ: Princeton University Press.
Goetz, T., Bieg, M., & Ludtke, O. (2013). Do girls really experience more anxiety in mathematics? Psychological Science, 24(10), 2079-2087.
Oates, K. S. (2015). A logistic regression analysis of score sending and college matching among high school students. Web.
Shernoff, D. J., Csikszentmihalyi, M., Schneider, B., & Shernoff, E. S. (2014). Student engagement in high school classrooms from the perspective of flow theory. Applications of Flow in Human Development and Education, 18(2), 475-494.