RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

Name

Capella University

RSCH-FPX 7864 Quantitative Design and Analysis

Prof. Name

Date

Data Analysis Plan

Understanding the interplay between historical and contemporary performance can yield valuable insights into the stability and development of student learning. Numerous elements contribute to a student’s achievement in any specific course; however, a student’s prior grade point average (GPA) serves as a broad reflection of their academic background and abilities. In this analysis, four continuous variables are examined: Quiz 1, GPA, Final Exam, and Total points.

Total-Final Correlation

• Research Question: Is there a meaningful correlation between the total points accumulated in the course and the number of correct responses on the final examination?
• Null Hypothesis (H₀): No significant correlation exists between the total points earned in the course and the number of correct answers on the final exam.
• Alternate Hypothesis (H₁): A significant correlation exists between the total points earned in the course and the number of correct answers on the final exam.

GPA-Quiz 1 Correlation

• Research Question: Is there a significant correlation between a student’s prior GPA and their performance on Quiz 1?
• Null Hypothesis (H₀): There is no significant correlation between a student’s prior GPA and the correct answers on Quiz 1.
• Alternate Hypothesis (H₁): A significant correlation exists between a student’s prior GPA and the correct answers on Quiz 1.

Testing Assumptions

The descriptive statistics presented in the table below illustrate the skewness and kurtosis values for both GPA and the final exam scores. The GPA shows a skewness of -0.22 and a kurtosis of -0.69, while the final exam reveals skewness of -0.34 and kurtosis of -0.28. Since the skewness for both measures remains within the -1 to 1 range, it indicates that the distributions are largely symmetrical. Additionally, the values falling between -0.5 and 0.5 further support the notion that the distributions of GPA and final exam scores approximate a normal distribution.

Results & Interpretation

Table 2 shows a weak positive correlation between GPA and Quiz 1, represented by a correlation coefficient (r) of 0.152. With 104 degrees of freedom (df = n-1) and a significance threshold of P=0.01, the calculated P-value is 0.212, which exceeds 0.01. The effect size is 0.152², equal to 0.023104, indicating that Quiz 1 explains only 2% of the variability in GPA. These results lack statistical significance, meaning the null hypothesis cannot be rejected.

RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

Conversely, the strongest correlation in the matrix is identified between the final and total variables, which demonstrate a significant linear relationship with r=0.875, a P-value of 0.000, and 104 degrees of freedom. The effect size of 0.875², amounting to 0.765625, indicates that the final exam accounts for 76% of the variation in the total score. This relationship is statistically significant with an alpha of 0.05, prompting rejection of the null hypothesis. Furthermore, a moderate linear correlation between GPA and the final score is also apparent, with r=0.379. The associated P-value of 0.000, alongside 104 degrees of freedom, indicates that the effect size of 0.379² equals 0.143641, suggesting that the final exam explains 14% of the variability in GPA. Given the significance of the findings, the null hypothesis is rejected, affirming that a substantial linear relationship exists between GPA and the final score.

Statistical Conclusions

While there is insufficient evidence to substantiate a significant correlation between GPA and Quiz 1 scores, significant relationships have been identified between final and total scores, as well as between GPA and final scores. The following conclusions can be drawn regarding these correlations:

• The correlation between GPA and Quiz 1 is relatively weak, with a coefficient of r = 0.152.
• Although a slight positive correlation exists, the statistical significance is not upheld since the observed P-value (0.212) exceeds the selected significance level (0.01).
• The effect size indicates that only 2% of GPA variability can be attributed to Quiz 1 scores.

Conversely, there is strong evidence for a significant relationship between final and total scores based on this dataset:

• A robust linear correlation is present between final and total scores, indicated by a correlation coefficient of r = 0.875.
• This relationship is statistically significant, as the observed P-value (0.000) is below the alpha level of 0.05.
• The substantial effect size implies that 76% of the variability in the total score is explained by the final exam results.

Furthermore, data supports a statistically significant linear relationship between GPA and final scores:

• A moderate correlation exists between GPA and final score, with a coefficient of r = 0.379.
• This relationship is statistically significant, with the P-value (0.000) being lower than the alpha level of 0.05.
• The effect size reveals that 14% of the variability in GPA is explained by final exam scores.

Application

In the realm of veterans’ healthcare, correlation analysis serves as a powerful method for exploring the relationships between experiences during military service and the development of specific medical conditions. By rigorously examining health outcome patterns among veterans, researchers can ascertain whether certain illnesses or conditions are more prevalent within this population compared to the general public or other comparable groups. For instance, if veterans exposed to particular environments or chemicals during their service display higher incidence rates of a specific condition than those who were not exposed, a positive correlation could imply a potential service-related connection. When such correlations are robust, consistent across various studies, and control for other potential causal factors, it strengthens the argument for designating these conditions as “presumptive.” Recognizing conditions as presumptive streamlines the process for affected veterans to secure benefits and treatment, as they are no longer required to provide proof that their condition is directly linked to their military service. Instead, the service connection is presumed based on the statistical relationships established through comprehensive research.

References

Betancourt, J. A., Granados, P. S., Pacheco, G. J., Reagan, J., Shanmugam, R., Topinka, J. B., Beauvais, B. M., Ramamonjiarivelo, Z. H., & Fulton, L. V. (2021). Exploring health outcomes for U.S. veterans compared to non-veterans from 2003 to 2019. Healthcare (Basel, Switzerland), 9(5), 604. https://doi.org/10.3390/healthcare9050604

Creswell, J. W. (2014). Research design: Qualitative, quantitative, and mixed methods approaches (4th ed.). SAGE Publications.

Field, A. (2018). Discovering statistics using IBM SPSS statistics (5th ed.). SAGE.

RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

Gravetter, F. J., & Wallnau, L. B. (2016). Statistics for the behavioral sciences (10th ed.). Cengage Learning.

McHugh, M. L. (2013). The Chi-square test of independence. Biochemia Medica, 23(2), 143-149.