RSCH FPX 7864 Assessment 4 Data Analysis and Application Template

Student performance variables undergo correlation analysis as part of this research assessment to identify potential associations between data points. The research investigates the relationship between prior academic achievements and preliminary evaluation results and their influence on final education results. Knowledge about these associations helps educators gain significant insights regarding student success and guides their educational approach. The document presents a detailed plan for data analysis with assumption testing results alongside interpretations, statistical findings, and practical usages of correlation in education.

Data Analysis Plan

The variables for assessment need to be either categorical or continuous. The category variable consists of values that show distinct groups or categories but lack numerical significance between these elements (except for ordinal categories). Examples include gender (male, female) and treatment type (drug A, drug B, placebo). Continuous Variables represent measurable variables that span an entire scale because they exist with any possible number value between defined intervals (Andrade, 2021). For example, age (e.g., 25.4 years) and blood pressure (e.g., 120.5 mmHg). This analysis involves four key variables:

• Final Grade (continuous)
• Grade Point Average (GPA) (continuous)
• Quiz 1 Score (continuous)
• Total Cumulative Grade (continuous)

The measurement type uses a continuous scale, thus enabling a wide spectrum of numerical data values independent of fixed categories. Although researchers collected demographic data and assessment practices during the investigation, this study excludes them from specific analyses. This research includes 105 student participants, and the statistical significance cutoff point is 0.05.

Total Grade–Final Grade Correlation

• Research Question: Does a student’s academic record show a meaningful positive connection to their score from the current class?
• Null Hypothesis (H₀): The analysis shows that total cumulative grade does not influence final grade outcomes.
• Alternative Hypothesis (Hₐ): The total cumulative grade statistically correlates with final grade performance.

GPA–Quiz 1 Score Correlation

• Research Question: Student academic performance on their first quiz shows a connection to previous GPA.
• Null Hypothesis (H₀): The statistical analysis shows a non-existent relationship between students’ academic average (GPA) and their performance on Quiz 1.
• Alternative Hypothesis (Hₐ): The research results show a statistically meaningful linear relationship between academic grades and Quiz 1 scores.

Testing Assumptions

The table above includes all four variables and information on skewness and kurtosis. The measurement of data distribution symmetry appears as skewness and a zero value implies perfect symmetry. A normal distribution is indicated by skewness values falling between -1 and +1; however, values exceeding ±2 demonstrate a clear deviation from normality. Kurtosis evaluates how a distribution extends beyond its mean position by assessing its peak shape. A kurtosis reading of 0 usually indicates a normal distribution and acceptable statistics fall from -1 to +1. Values beyond ±2 should be examined as they may suggest that the normality assumption is no longer valid. The following table is the easy layout of the interpretation (Hatem et al., 2022). 

RSCH FPX 7864 Assessment 4 Data Analysis and Application Template

The standard errors for skewness measurement (0.236) and kurtosis measurement (0.467) provide a basis for measuring their values’ significance. The skewness and kurtosis measurements exist within a ±2 standard error range from zero, which verifies that normality deviations are insignificant. The required normality condition for correlation analysis remains valid for this test. All skewness and kurtosis values for quiz 1, GPA, total, and final exist between -2 and +2, which meets the acceptable criteria and demonstrates no severe deviations. Minor deviations in quiz one, total scores, and total score kurtosis do not compromise the normality requirement for correlation analysis due to Pearson’s correlation strength in large sample sizes (n=105). We can initiate the correlation analysis due to passing the normality assumption evaluation.

Results & Interpretation

The matrix below displays Pearson’s correlation coefficients among the four variables: quiz1, GPA, total, and final. The term is a statistical measure that quantifies the strength and direction of the linear relationship between two variables and is denoted by “r” (Vaughn, 2023). Three factors will be analyzed for correlation analysis. Firstly, degrees of freedom (df) in correlation analysis evaluate test reliability by indicating the number of values that can vary through the formula n – 2.

Secondly, the correlation coefficient (r) measures the direction and intensity of the relationship between variables while taking values from -1 to 1. Positive r indicates direct relation, negative r shows inverse relation, and close to zero r suggests no linear relation exists. Lastly, the outcome of p < 0.05 establishes statistical significance that leads to rejecting the null hypothesis, which confirms that the relationship between variables occurs beyond random chance (Bonell, 2023).

Total-Final Correlation 

• Degrees of Freedom (df): 103 
• Pearson’s r: 0.875 
• p-value: < .001

Students who achieve higher total scores receive higher final grades in their classes, and an extremely strong statistically significant relationship is found. We reject the null hypothesis because the p-value is lower than 0.001, which proves the positive association between the total score and the final grade.

GPA–Quiz1 Correlation

• Degrees of Freedom (df): 103
• Pearson’s r: 0.152
• p-value: 0.121

The GPA and Quiz 1 scores exhibit a weak positive relation, which becomes insignificant when statistically tested. The results indicate that we should keep the null hypothesis because the obtained p-value exceeds 0.05. The available data does not prove that GPA and Quiz 1 scores have a meaningful relationship.

Statistical Conclusions

The results from correlation analysis showed that total scores strongly predicted final grades (r = 0.875) at a very significant level (p < .001) since students with wholesome academic records generally achieved better exam results. The connection between GPA scores and Quiz 1 results (r = 0.152, p = 0.121) proved weak and non-statistically important, showing that GPA data did not effectively forecast individual exam outcomes.

The analysis contains certain fundamental restrictions. It avoids the possibility of causation according to the correlation between variables because its results fail to acknowledge external factors similar to test anxiety and motivation or course difficulty. The research results may not apply to a broader population because the sample was sufficient but not large enough. Unaccounted variables, nonlinear relationships, and confounding variables could impact the observed results. Future studies should study these elements or implement regression analysis to regulate other variables (Cox, 2020).

Application

Academic research and education find correlations useful for understanding the connections between factors affecting student success and institutional performance. Study habits and academic achievement are suitable candidates for correlation analysis because they measure the number of weekly study hours and GPA or exam scores. Knowledge about positive variable relationships supports educators in creating research-backed approaches to enhance learning results. The study by Hammond et al. (2023) emphasizes that when educators receive evidence-based information about cognitive development, social learning, and emotional growth, they become better capable of providing optimal learning spaces for their students.

Examining class attendance levels and final examination scores would make an effective pair of variables. Finding a significant positive correlation would validate the significance of classroom engagement, thus supporting attendance requirements and policy-based attendance promotion. A study by Brew et al. (2021) states that academic success heavily depends on four elements: socioeconomic status, family involvement, education standards, student drive, and school facility support.

According to the authors, these factors create intricate relationships that determine students’ performance. Relationship analysis can help create educational curriculum plans, student support operations, and early intervention procedures to improve academic achievement. Using correlations in this way allows me to make data-informed decisions in both academic advising and curriculum development. It helps me better understand the factors influencing success and tailor interventions accordingly.

References

Andrade, C. (2021). A student’s guide to the classification and operationalization of variables in the conceptualization and design of a clinical study: Part 2. Indian Journal of Psychological Medicine, 43(3), 265–268. https://doi.org/10.1177/0253717621996151 

Bonell, J. K. H. (2023). Interpreting P values in 2023. Journal of Patient-Centered Research and Reviews, 10(3), 102–103. https://doi.org/10.17294/2330-0698.2064 

Brew, E. A., Nketiah, B., & Koranteng, R. (2021). A literature review of academic performance, an insight into factors and their influences on academic outcomes of students at senior high schools. Open Access Library Journal, 8(6), 1–14. https://doi.org/10.4236/oalib.1107423 

Cox, L. A. (2020). Implications of nonlinearity, confounding, and interactions for estimating exposure concentration-response functions in quantitative risk analysis. Environmental Research, 187, 109638. https://doi.org/10.1016/j.envres.2020.109638 

Hammond, L. D., Schachner, A. C. W., Wojcikiewicz, S. K., & Flook, L. (2023). Educating teachers to enact the science of learning and development. Applied Developmental Science, 28(1), 1–21. https://doi.org/10.1080/10888691.2022.2130506 

RSCH FPX 7864 Assessment 4 Data Analysis and Application Template

Hatem, G., Zeidan, J., Goossens, M., & Moreira, C. (2022). Normality testing methods and the importance of skewness and kurtosis in statistical analysis. BAU Journal – Science and Technology, 3(2). https://doi.org/10.54729/KTPE9512 

Vaughn, D. L. H. (2023). Pearson Correlation Coefficient – An overview. Www.sciencedirect.com. https://www.sciencedirect.com/topics/social-sciences/pearson-correlation-coefficient