RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation Data Analysis Plan: Understanding the Relationship Between Past and Present Performance

The exploration of the association between past and present performance can provide 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):

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 (r² = 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.

The strongest correlation is observed between the ‘final’ and ‘total’ variables (r = 0.875), with a P-value of 0.000 and 104 degrees of freedom. The effect size (r² = 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 (r² = 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 Conclu