RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

Student Name

Capella University

RSCH-FPX 7864 Quantitative Design and Analysis

Prof. Name

Date

Data Analysis Plan

Understanding the relationship between past and present performance can offer significant insights into the consistency and trajectory of student learning. While a multitude of factors contribute to a student’s success in any given course, their previous grade point average (GPA) serves as a broad indicator of their academic history and capabilities. The four variables used in this analysis (Quiz 1, GPA, Final, and Total) can be considered continuous variables.

Total-Final Correlation

Research Question: Is there a significant correlation between the total number of points earned in the class and the number of correct answers on the final exam?

Null Hypothesis: There is no significant correlation between the total number of points earned in the class and the number of correct answers on the final exam.

Alternate Hypothesis: There is a significant correlation between the total number of points earned in the class and the number of correct answers on the final exam.

GPA-Quiz1 Correlation

Research Question: Is there a significant correlation between a student’s previous grade point average (GPA) and the number of correct answers on Quiz 1?

Null Hypothesis (H₀): There is no significant correlation between a student’s previous GPA and the number of correct answers on Quiz 1.

Alternate Hypothesis (H₁): There is a significant correlation between a student’s previous GPA and the number of correct answers on Quiz 1.

Testing Assumptions

The descriptive statistics table below displays the skewness and kurtosis levels for both GPA and the final exam. While the GPA demonstrates a skewness of -0.22 and kurtosis of -0.69, the final exam has values of -0.34 and -0.28 respectively. Observing that the skewness for both metrics falls within the -1 to 1 range suggests that both distributions are fairly symmetric. Given that these values are between -0.5 and 0.5, it further reinforces that the distributions of GPA and the final exam scores are approximately symmetrical, hinting at a normal distribution in the data.

Results & Interpretation (Table 1)

	gpa	total	quiz1	final
Mean	2.862	100.086	7.467	61.838
Std. Deviation	0.713	13.427	2.481	7.635
Skewness	-0.220	-0.757	-0.851	-0.341
Kurtosis	-0.688	1.146	0.162	-0.277

Correlation Matrix (Table 2)

In the correlation matrix presented in Table 2, there is a minor positive correlation between GPA and Quiz 1, with a correlation coefficient (r) of 0.152. With 104 degrees of freedom (df = n-1), and considering a significance level of p=0.01, the observed P-value is 0.212, which is greater than 0.01. The effect size is given by 0.152², indicating that Quiz 1 accounts for 2% of the variability in GPA. These results are not statistically significant, so we cannot reject the null hypothesis.

Pearson’s Correlations

	quiz1	gpa	total	final
quiz1	—	0.152	0.121	0.499
gpa	0.152	—	0.318	0.379
total	0.121	0.318	—	0.875
final	0.499	0.379	0.875	—

p < .05, p < .01, p < .001

Conversely, the strongest correlation in the matrix is observed between the ‘final’ and ‘total’ variables. They display a notable linear correlation with r=0.875, a P-value of 0.000, and 104 degrees of freedom. The effect size here is 0.875², which is 0.765625. This implies that the ‘final’ accounts for 76% of the variation in the ‘total’. Given an alpha of 0.05, this relationship is statistically significant, leading us to reject the null hypothesis.

Additionally, the data reveals a moderate linear correlation between GPA and the Final, with r=0.379. With 104 degrees of freedom and a P-value of 0.000, the effect size is 0.379², amounting to 0.143641. This means that the Final explains 14% of the GPA’s variability. With an alpha of 0.05, the findings are significant, causing the rejection of the null hypothesis and acceptance of the alternative, which demonstrates a meaningful linear relationship exists between the GPA and Final.

Statistical Conclusions

While there’s a lack of evidence to support a significant correlation between GPA and Quiz 1 scores, the relationships between ‘final’ and ‘total’ scores, and between GPA and Final scores, are statistically significant. It is assessed that based upon the data there is insufficient evidence to claim a significant linear relationship between GPA and Quiz 1 scores.

The following conclusions can be surmised regarding this correlation:

It is relatively weak with a coefficient (r = 0.152).
Despite the presence of this slight positive correlation, the statistical significance of this relationship is not supported given the observed P-value (0.212) is larger than the chosen significance level (0.01).
The effect size indicates that only 2% of the variability in GPA can be explained by Quiz 1 scores.
There is strong evidence of a significant relationship between ‘final’ and ‘total’ scores based on this dataset.
There is a very strong linear correlation between the ‘final’ and ‘total’ scores, as indicated by the correlation coefficient (r = 0.875).
This relationship is statistically significant since the observed P-value (0.000) is less than the alpha level of 0.05.
The substantial effect size suggests that 76% of the variability in the ‘total’ can be accounted for by the ‘final’ scores.
The data supports a statistically significant linear relationship between GPA and Final scores:
There is a moderate correlation between GPA and the Final score, with a coefficient (r = 0.379).
This relationship is statistically significant as indicated by the P-value (0.000) being less than the alpha level of 0.05.
The effect size tells us that 14% of the variability in GPA can be explained by the Final scores.

Application

In veterans’ healthcare, correlation analysis offers a powerful tool for investigating the relationships between military service experiences and the emergence of specific medical conditions. By statistically examining patterns in health outcomes among veterans, researchers can determine whether certain illnesses or conditions are more prevalent in this group compared to the general population or other comparable groups.

For instance, if veterans who

were exposed to specific environments or chemicals during service consistently exhibit higher rates of a particular condition than those not exposed, a positive correlation could suggest a potential service connection. When this correlation is strong, consistent across multiple studies, and other potential causal factors are controlled for, it bolsters the argument for classifying such conditions as “presumptive” in nature.

Recognizing conditions as presumptive simplifies the process for affected veterans to access benefits and treatment, as they would no longer need to provide evidence that their condition is directly tied to their military service. Instead, the service connection would be presumed, reflecting the statistical relationship established through rigorous 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