RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

Name

Capella university

RSCH-FPX 7864 Quantitative Design and Analysis

Prof. Name

Date

Correlation Application and Interpretation

This study examines four dependent variables: students’ final grade, cumulative grade point average (GPA), first quiz score, and overall course grade. It incorporates demographic data, standardized test outcomes, and instructors’ formative evaluation practices across three instructional units. The primary objective is to evaluate how closely students’ final grades correspond to their GPAs. Both the cumulative grade and the final exam score are continuous variables, permitting any value within their ranges (Sayyed et al., 2023). Although the first quiz score is discrete, demographic attributes such as gender were hypothetically considered. A total of 105 participants were analyzed using a significance threshold of $\alpha = 0.05$.

Correlation Analysis

Analysis Area	Research Question	Null Hypothesis (H₀)	Alternative Hypothesis (Hₐ)
Total–Final Correlation	Does a student’s final exam score reflect their cumulative GPA?	There is no linear relationship between final exam scores and cumulative GPA.	Final exam scores are positively correlated with cumulative GPA.
GPA–Quiz 1 Correlation	Is there a significant relationship between GPA and Quiz 1 performance?	There is no linear relationship between GPA and Quiz 1 scores.	GPA and Quiz 1 scores are positively correlated.

Testing Assumptions

Descriptive statistics (skewness and kurtosis) were computed for final exam scores and GPA to assess normality. Values within acceptable limits indicated that both distributions followed a normal pattern (Verostek et al., 2021). The GPA distribution exhibited skewness = -0.220 and kurtosis = -0.688. Final exam scores showed skewness = -0.341 and kurtosis = -0.277, suggesting slight negative skew but overall normality. Quiz 1 scores and total grades revealed minor departures from normality: Quiz 1 skewness = -0.5, kurtosis = -1.2; total grades skewness = 0.8, kurtosis = 2.1.

Variable	Skewness	Kurtosis	Normality Status
GPA	-0.220	-0.688	Normal
Final Exam	-0.341	-0.277	Normal
Quiz 1	-0.500	-1.200	Acceptable Deviation
Total Grade	0.800	2.100	Minor Positive Skew

Analysis of Decision-Making Process

Continuous variables in this study include final grades, cumulative GPAs, and total course grades, all measured on interval scales. The first quiz score is discrete, counting correct responses. Formulating hypotheses for correlational research requires specifying linear associations (Thompson, 2021). For example, the null hypothesis for total and final grades states: “There is no linear correlation between total and final grades,” whereas the alternative posits: “A linear correlation exists between total and final grades.” Similar formulations apply to GPA versus Quiz 1 analysis.

Results and Interpretation

Correlation coefficients were calculated at $\alpha = 0.05$. A Pearson’s r of 0.88 (p = 0.001) between cumulative GPA and final exam scores indicates a very strong positive relationship, leading to rejection of the null hypothesis (Wu et al., 2021). In contrast, the correlation between GPA and Quiz 1 was r = 0.152 (df = 103, p = 0.112), a weak, non-significant association, so the null hypothesis is retained (Westrick et al., 2020).

Variables	Pearson’s r	Degrees of Freedom	p-Value	Interpretation
GPA & Final Exam	0.880	103	0.001	Strong, significant positive correlation
GPA & Quiz 1	0.152	103	0.112	Weak, non-significant correlation

Statistical Conclusions

Statistical analysis confirms a significant positive correlation between cumulative GPA and final exam scores, whereas the link between GPA and Quiz 1 did not reach significance at the 0.05 level. These conclusions consider sample size, potential biases, measurement precision, and confounding variables (Rand et al., 2020; Wiernik & Dahlke, 2020). Future research should employ larger, randomized samples and control confounders to reinforce these findings.

Application

Correlation methods are vital for uncovering relationships in biostatistics and beyond (Moriarity & Alloy, 2021). In neurology, correlational studies between age and cognitive decline elucidate mechanisms underlying Alzheimer’s disease, informing early interventions (Azam et al., 2021). Likewise, correlations between neural structures and motor skills guide diagnostics and therapies for movement disorders (Newell, 2020).

References

Azam, S., Haque, Md. E., Balakrishnan, R., Kim, I.-S., & Choi, D.-K. (2021). The ageing brain: Molecular and cellular basis of neurodegeneration. Frontiers in Cell and Developmental Biology, 9. https://doi.org/10.3389/fcell.2021.683459

Moriarity, D. P., & Alloy, L. B. (2021). Back to basics: The importance of measurement properties in biological psychiatry. Neuroscience & Biobehavioral Reviews, 123, 72–82. https://doi.org/10.1016/j.neubiorev.2021.01.008

RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

Rand, K. L., Shanahan, M. L., Fischer, I. C., & Fortney, S. K. (2020). Hope and optimism as predictors of academic performance and subjective well-being in college students. Learning and Individual Differences, 81, 101906. https://doi.org/10.1016/j.lindif.2020.101906

Sayyed, R. A., Awwad, F. A., Itriq, M., Suleiman, D., Saqqa, S. A., & AlSayyed, A. (2023). The pass/fail grading system at Jordanian universities for online learning courses from students’ perspectives. Frontiers in Education, 8. https://doi.org/10.3389/feduc.2023.1186535

Thompson, M. E. (2021). Grade expectations: The role of first-year grades in predicting the pursuit of STEM majors for first- and continuing-generation students. The Journal of Higher Education. https://doi.org/10.1080/00221546.2021.1907169

Verostek, M., Miller, C. W., & Zwickl, B. (2021). Analyzing admissions metrics as predictors of graduate GPA and whether graduate GPA mediates Ph.D. completion. Physical Review Physics Education Research, 17(2). https://doi.org/10.1103/physrevphyseducres.17.020115

Westrick, P. A., Schmidt, F. L., Le, H., Robbins, S. B., & Radunzel, J. M. R. (2020). The road to retention passes through first year academic performance: A meta-analytic path analysis of academic performance and persistence. Educational Assessment, 26(1), 35–51. https://doi.org/10.1080/10627197.2020.1848423

Wiernik, B. M., & Dahlke, J. A. (2020). Obtaining unbiased results in meta-analysis: The importance of correcting for statistical artifacts. Advances in Methods and Practices in Psychological Science, 3(1), 94–123. https://doi.org/10.1177/2515245919885611

RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

Wu, H., Guo, Y., Yang, Y., Zhao, L., & Guo, C. (2021). A meta-analysis of the longitudinal relationship between academic self-concept and academic achievement. Educational Psychology Review. https://doi.org/10.1007/s10648-021-09600-1