RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation Data Analysis Plan For effective data analysis, there should be a systematic process for the collection of data and an analytical method for the analysis of the data. The approach will allow for a comprehensive review of the gathered data, which will help in creating valid research results (Tumiran, 2024). This research will try to investigate the possible relationship among the important factors affecting the students’ academic performances, which are the first quiz, final exams, cumulative points of the students in the course, and the previous GPA. The variables of the research are: In Test 1, A continuous variable that represents the number of correct responses obtained in the first test, with a scale of 0 up to the maximum possible score. Final Exam Score: the number of items correct on the final examination, on a scale of zero to the maximum possible, is a continuous variable. Total Points Earned: A continuous variable that is used to represent the total of all possible points that have been accumulated in an academic year. A continuous variable that represents a student’s past academic performance in a quantitative manner, ranging from 0.00 to 4.00 points. (Grade Point Average) Total-Final Correlation Research Question Is there a statistically significant relationship present between the total number of points a student earns during a semester and performance in the final examination? Hypotheses Null Hypothesis (H0) There is no statistically significant relationship present between the total points a student earns during a semester and performance in the final examination. H₀: ρ = 0. Alternative Hypothesis (Ha) There is a statistically significant relationship present between the total points a student earns during a semester and performance on the final examination. Hₐ: ρ ≠ 0. Quiz 1 and GPA Correlation Research Question Is students’ prior academic achievement, as measured by GPA, statistically related to performance in the first quiz? Hypotheses Null Hypothesis (H0): Students’ prior academic achievement, as measured by GPA, is not statistically related to performance in the first quiz. H₀: ρ = 0. Alternative Hypothesis (Ha): Students’ prior academic achievement, as measured by GPA, is statistically related to performance in the first quiz. Hₐ: ρ ≠ 0. Testing Assumptions Table 1: Descriptive Statistics Making the assumption test in statistical analysis is one of the important steps to ensure that the results of the research are valid and reliable. Descriptive statistics show that approximately 73.82% of the students did better in the cumulative semester points and final exam results. Among the variables included, Quiz 1 had the most negative skewness (-0.826) while the GPA had very low negative skewness (-0.096), which is near symmetry. The skewness and standard deviation of all the variables considered were within acceptable levels. The values for the variables ranged from −0.832 for GPA to 0.657 for total points earned, which were close to a normal distribution. There was no alarming trend in the measures of variability, and overall,l the data met the assumptions of being approximately normally distributed. In particular, the values of Skewness were less than the high limit of ±2.0 value as follows: total points earned: −0.758; GPA: −0.096; final exam performance: −0.606; Quiz 1 performance: −0.826. The skewness and Kurtosis values of the data between -2.0 and +2.0 are considered as approximately normal, which allows performing parametric statistical tests (Demir, 2022). Likewise, the values of kurtosis did not exceed ±3.0, further confirming the normal assumptions. The results of the correlation analysis showed that there was a strong and statistically significant positive association between total semester points and the performance of the students in the final examination, with r = 0.659 and p < 0.001, thus the null hypothesis was rejected. Conversely, Quiz 1 performance and GPA had a weak correlation that was not statistically significant (r = 0.142, p = 0.149), and the null hypothesis was maintained. Results & Interpretation Table 2: Pearson’s Correlations between Academic Performance Variables Pearson’s correlation coefficient (r) was used to measure the correlation between two continuous variables, where r is between −1 and +1, and the closer r is to +1 or −1 the stronger the correlation. Some interesting findings came from the correlation test. Cumulative semester points were significantly correlated with performance on Quiz 1 (r = 0.601, p < 0.001). Furthermore, Quiz 1 was moderately and significantly correlated with the final exam, with r = 0.422, p < 0.001. In contrast, grade point average (GPA) was also weakly correlated with performance on Quiz 1 (r = 0.142, p = 0.149), indicating that performance was not related to academic achievement on the initial assessments of the course. Based on the classic definition of correlation coefficients, 0.10, 0.30, and 0.50 are small, medium, and large effect sizes, respectively (Zieliński, 2025). Also, the correlation between the GPA and the cumulative points won during the semester was weak (r = 0.137, p = 0.164), but it was not significant. Nevertheless, a weak but significant correlation (r = 0.233, p = 0.017) was found between GPA and performance on the final examination. The highest correlation that was observed in the analysis was the total points earned in the semester and performance in the final examination (r = 0.659, p < 0.001). The above p-value is very small, meaning that the null hypothesis stating that there is no correlation between the performance in the semester and the result of the final exam can be rejected. Conversely, the null hypothesis with respect to the Quiz 1 score and the GPA was not rejected as it is not statistically significant. As a general rule, the findings of this study indicate that performance during the semester is a good guide to success at semester examinations, whereas that of previous semesters has little influence on the initial returns and appears to be of secondary importance towards the end of the course. Statistical Conclusions Some of the hypotheses were supported by the correlation analysis, which showed that a number of the academic performance measures collected at various assessment