RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation RSCH-FPX 7864 Quantitative Design and Analysis 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):
|
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 (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.
|
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 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