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Jan 9, 2024

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Data Analysis and Application Template Marissa Gbenga Capella University Data Analysis Plan ● Quiz 1: Continuous ● GPA: Continuous ● Total: Continuous ● Final: Continuous Research Question: Is there a relationship between students' performance on Quiz 1 (X) and their performance on the Final Exam (Y)? Null Hypothesis (H0): There is no significant correlation between students' performance on Quiz 1 and their performance on the Final Exam. In other words, the correlation coefficient (ρ) between Quiz 1 scores and Final Exam scores is equal to 0. Alternative Hypothesis (H1): There is a significant correlation between students' performance on Quiz 1 and their performance on the Final Exam. The correlation coefficient (ρ) between Quiz 1 scores and Final Exam scores is not equal to 0.

Testing Assumptions 1. The normality assumption for the variables quiz1, gpa, total, and final was rigorously tested using the Shapiro-Wilk test, skewness, kurtosis, and visual inspection. The Shapiro-Wilk results, with p-values all below 0.05, indicate a significant departure from normality for each variable. Additionally, skewness and kurtosis values suggest deviations from a perfectly normal distribution, especially in quiz1 and gpa. These findings are consistent across statistical measures, raising concerns about the normality assumption. As a result, caution should be exercised when interpreting results from analyses that assume normality, and alternative methods or robust statistical approaches may be considered to account for the non-normal distribution of the data.

Results and Interpretation The correlation between Quiz 1 and GPA is small and statistically nonsignificant (p > 0.05). Therefore, we fail to reject the null hypothesis, suggesting no significant correlation between Quiz 1 and GPA.The correlation between Total and Final is large and statistically significant (p < 0.001). Therefore, we reject the null hypothesis, indicating a significant positive correlation between the total points and final exam scores.The correlation between GPA and Final is moderate and statistically significant (p < 0.001). We reject the null hypothesis, suggesting a meaningful positive correlation between GPA and Final exam scores. Statistical Conclusions In this analysis, I explored the relationships between students' performance on Quiz 1, their GPAs, the total points earned in the class, and their performance on the Final Exam. The Pearson's correlation coefficients revealed interesting patterns. The correlation between

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Quiz 1 and GPA was small and nonsignificant, indicating that students' initial quiz performance did not significantly correlate with their overall academic achievement. However, a strong and significant positive correlation emerged between total points earned in the class and performance on the Final Exam, suggesting that students who performed well throughout the course tended to excel in the final assessment. Additionally, a moderate and significant positive correlation was found between GPA and Final Exam scores, reinforcing the idea that students with higher GPAs generally performed better in the final examination. Despite these insights, it's crucial to acknowledge the limitations of this statistical test. Correlation does not imply causation, and the observed associations do not establish a directional relationship between variables. Furthermore, the dataset, while informative, is limited to a specific context, and the results may not be generalizable to other academic settings. To enhance the robustness of future investigations, researchers might explore additional factors such as study habits, attendance, or socio-economic background, which could contribute to a more comprehensive understanding of academic performance. In terms of alternate explanations, it's possible that unmeasured variables, such as individual study habits or external stressors, could influence the observed correlations. Future research could delve deeper into these potential factors and employ experimental designs or longitudinal studies to uncover causal relationships. Additionally, examining the impact of teaching methods or class engagement on student outcomes could offer valuable insights for educators aiming to enhance academic performance. These avenues for future exploration underscore the dynamic nature of student success and invite continuous inquiry into the multifaceted factors influencing academic achievement. Application

. In the field of psychology, particularly in clinical psychology, this type of analysis could be applied to understand the correlation between various therapeutic interventions and improvements in patients' mental health. For instance, one might explore the relationship between the frequency of therapy sessions (X) and the reduction in symptoms (Y) for individuals with specific mental health disorders. This analysis could provide insights into the effectiveness of different therapeutic approaches and guide clinicians in tailoring treatments based on individual needs. The value of such an analysis lies in its potential to enhance evidence-based practices in psychology. By identifying patterns and relationships between variables, clinicians can make more informed decisions about treatment plans. For example, if the analysis reveals a significant correlation between the use of cognitive-behavioral therapy techniques and symptom reduction in a certain population, it could suggest the efficacy of these techniques for that particular group. This not only contributes to the refinement of therapeutic practices but also promotes more personalized and effective mental health interventions.

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