Data Analysis Plan Understanding the Relationship Between Past and Present Performance RSCH-FPX 7864 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?

RSCH-FPX 7864 Quantitative Design and Analysis

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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 (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 Conc

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