Student name

RSCH-FPX 7864 Quantitative Design and Analysis

Capella University

Professor Name

Submission Date

Data Analysis Plan

An efficient data analysis methodology also involves the application of systematic data collection and data analysis methodologies that help the researcher to achieve their goals in research. The established framework enables researchers to perform the data analysis in a systematic way, resulting in credible findings with substantive explanations (Ncube & Ngulube, 2024). The research tries to analyze the possible correlations among the main student academic performance variables, i.e., first-quiz-test results and last-exam-test grades, cumulative point gains, and past grade point average (GPA). The results of the research will identify such meaningful trends in student achievement that can influence future education policies.

The study examines four core variables:

1. Quiz 1 Score: The number of correct answers given on the first test. The scoring is zero to the highest amount of score that can be attained. The score of Quiz 1 is a continuous variable.
2. Final Exam Score: A numerical measure that will show the number of correct answers provided during the final assessment session. The score range starts at the zero point and is expanded to the highest possible limit. Final examination score is a continuous variable.
3. Total Points Earned: Aggregate numeric measure that involves all academic assessment scores that were Figure 1. Total academic evaluation scores amassed during the semester. This range is between zero baselines and the maximum feasible aggregate total. The amount of points accumulated is a continuous variable.
4. GPA: Scholastic performance metric calculated on a numerical framework from 0.00 (minimum) to 4.00 maximum, representing the average of all completed course grades. GPA constitutes a continuous variable.

Total-Final Correlation

• Research Question

Is there an association between students’ cumulative points across the semester and the final examination achievement?

• Hypotheses

Null Hypothesis (H0): Cumulative points over the semester of students and final examination achievement do not correlate. H0: ρ = 0.

Alternative Hypothesis (Ha): There is an association between students’ cumulative points across the semester and the final examination achievement. Ha: ρ ≠ 0

Quiz 1 and GPA Correlation

• Research Question

Is there a relationship between students’ cumulative academic performance metric and the outcomes on the first quiz?

• Hypotheses

Null Hypothesis (H0): Students have no association between the cumulative performance metric in academic performance and the results in the first quiz. H0: ρ = 0.

Alternative Hypothesis (Ha): There is a relationship between students’ cumulative academic performance metric and the outcomes on the first quiz. Ha: ρ ≠ 0.

Testing Assumptions

Table 1: Descriptive Statistics

The information should be checked in the course of statistical analysis since it is imperative to ensure that all the conditions are satisfied to apply the test, as the checks will assist in giving the validity of the findings and selecting an appropriate statistical procedure (Ramachandran, 2025). The high range percentage of students concerning cumulative examination summation and end-term evaluation percentage was approximately 73.82%. The negative value of skewness, Quiz1, is the lowest of all the variables, which is -0.826. According to the analysis, the GPA exhibits some negative skewness of =0.096. Both variables have skewness and standard deviation values that indicate compliance with the acceptable statistical range. The tail thickness of the distribution can be measured through Kurtosis, i.e., larger values, which indicate an extended tail and outlier data. 

The Kurtosis values are moderate for all the variables, with the grade point average of .832 to 0.657 in the cumulative scores. The standard deviations of the variables do not indicate the irregularity of the Kurtosis. As per the analysis, the variables are satisfactorily normal since TOTAL (-0.758), GPA (-0.096), Final (-0.606), and Quiz1 (-0.826) contain negative skewness values, which are within an acceptable range (within 2.0). The kurtosis (-0.832) to (0.657) (GPA) to Total is of low value of non-normal distribution that falls below the limit of 3.0. The results indicate that the variables follow a normal distribution and meet the normality requirement. Based on the findings, it is determined that the null hypothesis could not be accepted in Total-Final correlation (r=0.659, p=0.001), which proved the existence of significant correlation. Still, it could not be accepted in Quiz1-GPA (r=0.142, p=0.149), which failed to provide sufficient evidence to reject the null hypothesis.

Results and Interpretation

Table 2: Pearson’s Correlations Between Academic Performance Variables

The Pearson correlation coefficient is used to measure the strength and direction of the linear relationship between continuous variables, with values of +1 to -1, with higher values depicting stronger relationships. The correlation analysis indicates that there are some strong and moderate correlations: The performance on Quiz 1 is significantly correlated with Total points (r=0.601, p<0.001) and moderately correlated with Final exam performance (r=0.422, p<0.001). The GPA has a weak relationship with Quiz 1 (r=0.142, p=0.149), but it has a weak, significant relationship with Total points (r=0.137, p=0.164) and Final exam performance (r=0.233, p=0.017), respectively. According to the analysis, the highest relationship is found between Total points and Final exam performance (r=0.659, p<0.001). Judging by the results, the null hypothesis of Total-Final correlation is rejected because the p-value is very significant (p<0.001).

In contrast, the null hypothesis of Quiz1-GPA correlation is accepted since it is not statistically significant with the p=0.149 p-value. The results show that performance during semesters (Total points) demonstrates the ability to predict performance in final examinations, but the previous academic history (GPA) features little predictability in pre-assessment tasks. The notably strong correlations among GPA and subsequent performance indicators indicate that academic history progressively gains importance as the coursework advances, which makes it possible to intervene in the case of struggling students with the help of a thoroughly developed achievement assessment and not an individual assessment examination.

Statistical Conclusions

Correlation analysis between the predictor variables was used to prove the hypotheses of the relationship existing between the performance at various stages of assessment. The statistical findings revealed that various academic indicators are highly correlated with one another. Quiz 1 performance had significant relationships with Total points (r=0.601, p=0.001) as well as a moderate relationship with final exam outcomes (r=0.233, p=0.017). Where GPA showed a weak correlation with Quiz 1 (r=0.142, p=0.149) but a moderately significant correlation with total points (r=0.137, p=0.164) and final exam results. The highest correlation was determined as between total points and final exam results (r=0.659, p<0.001, p<0.05), which is a clear rejection of the null hypothesis.

The tendencies in the statistics prove the fact that the current semester scores are more credible in forecasting the final assessment scores than the previous academic performance. The weak but non-significant correlation of the results of Quiz 1 and GPA (p=0.149) indicates that past performance does not provide a strong predictive power to determine the first course. The findings suggest that the teacher will have to design the intervention plans based on the current trends in coursework rather than on the historical academic achievements of the students, and the staff will have to pay attention to the particular skills acquisition instead of addressing the previous gaps in the education process (Wheeler and Bach, 2020).

Limitations

There were several major weaknesses in the correlation analysis. Although strong relationships were detected, causation could not take place since there exists a two-way relationship between correlations. Potential impacts of confounding factors that might have affected the relationships were not discussed. The analysis was concerned with the direct relationships only, and more sophisticated patterns were not observed, which could otherwise have been identified through multiple regression analysis. The sample size is a limitation that minimized the statistical power, especially when the researcher tested the GPA-Quiz 1 associations. The quantitative research lacked qualitative data, which supported the study in terms of learning styles and teaching methods among students, which would have helped in the better understanding. A multiple regression analysis would have given more details regarding the concomitant impact of a set of variables on the difference between the scores (Zhou et al., 2024). Additional investigations with more methodologies and data collections would be useful in the understanding of the processes that might be working behind the academic affiliations reported in the current exploratory research.

Application

The correlation research that could be conducted in the nursing school sphere might be the investigation of the correlations between the number of clinical simulation hours and the pass rate through the National Council Licensure Examination of Registered Nurses (NCLEX-RN), and the impact of the length of the practical training on the professional licensure success. The effects of the level of staffing on the patient safety outcomes in nursing practice may be demonstrated by the relationships between the nurse-to-patient ratio and the incidence of medication errors in the nursing practice, as the academic performance did in Quiz 1 in terms of success in the future. The post-discharge follow-ups may be linked to the hospital readmission rates, which suggests that nursing leadership may be effective in terms of care coordination. The examples have mentioned that correlation analysis could be utilized in making valuable inferences in the nursing environments since the statistics could be used to determine significant relationships between variables. Correlation-based evidence-based practices have also shown a positive impact on patient results and efficiency in healthcare companies (Connor, 2023).

The null hypothesis of statistically significant correlations is rejected, confirming the existence of statistically substantial meaningful associations that can be used in evidence-based decision-making. The awareness of the relationships enables nursing professionals to develop certain interventions that could be used to address some problematic areas and develop statistically validated models of clinical quality improvements (Flaubert et al., 2021). The concept of healthy methodologies that is anchored on the application of statistical correlation evidence, coupled with the application of compassionate clinical judgment, has the potential to aid in the development of effective interventions.