RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

Student Name

Capella University

RSCH-FPX 7864 Quantitative Design and Analysis

Prof. Name

Date

Correlation Application and Interpretation

Understanding the Relationship Between Past and Present Performance

The exploration of the association between past and present performance can yield valuable insights into the consistency and trajectory of student learning. A student’s previous grade point average (GPA) serves as a broad indicator of their academic history and capabilities, contributing to their success in a given course. In this analysis, four variables (Quiz 1, GPA, Final, and Total) are treated as 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 (H₀): 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 (H₁): 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. The GPA demonstrates a skewness of -0.22 and kurtosis of -0.69, while the final exam has values of -0.34 and -0.28, respectively. Both distributions are fairly symmetric, falling within the -1 to 1 range for skewness, suggesting 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 Table 2, a minor positive correlation (r = 0.152) exists between GPA and Quiz 1. With 104 degrees of freedom (df = n-1) and a significance level of P=0.01, the observed P-value is 0.212, greater than 0.01. The effect size (r^2 = 0.023) indicates that Quiz 1 accounts for 2% of the variability in GPA, rendering the results statistically insignificant, leading to the acceptance of 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

The strongest correlation is observed between ‘final’ and ‘total’ variables (r = 0.875), with a P-value of 0.000 and 104 degrees of freedom. The effect size (r^2 = 0.765625) suggests that ‘final’ accounts for 76% of the variation in ‘total,’ leading to the rejection of the null hypothesis.

A moderate linear correlation exists between GPA and the Final (r = 0.379). With 104 degrees of freedom, a P-value of 0.000, and an effect size (r^2 = 0.143641) indicating that the Final explains 14% of the GPA’s variability, the results are statistically significant, leading to the rejection of the null hypothesis.

Statistical Conclusions:

While there is insufficient evidence to support a significant correlation between GPA and Quiz 1 scores, statistically significant relationships are found between ‘final’ and ‘total’ scores, and between GPA and Final scores.

The following conclusions can be drawn:

• The correlation between GPA and Quiz 1 scores is relatively weak (r = 0.152).
• Despite the slight positive correlation, the statistical significance is not supported (P-value = 0.212 > 0.01).
• The effect size indicates that only 2% of the variability in GPA is explained by Quiz 1 scores.

Strong evidence supports a significant relationship between ‘final’ and ‘total’ scores:

• A very strong linear correlation (r = 0.875) is observed.
• This relationship is statistically significant (P-value = 0.000 < 0.05).
• The substantial effect size suggests that 76% of the variability in ‘total’ can be accounted for by ‘final’ scores.

A statistically significant linear relationship between GPA and Final scores is also supported:

• A moderate correlation exists (r = 0.379).
• This relationship is statistically significant (P-value = 0.000 < 0.05).
• The effect size indicates that 14% of the variability in GPA can be explained by Final scores.

Application:

In veterans’ healthcare, correlation analysis serves as a powerful tool for investigating the relationships between military service experiences and the emergence of specific medical conditions. Statistical examination of health outcome patterns among veterans can identify prevalent conditions, supporting the argument for presumptive classification based on established statistical relationships.

References:

Betancourt, J. A., et al. (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

Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). SAGE.

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

Creswell, J. W. (2014). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches (4th ed.). SAGE Publications.

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

RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

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