RSCH FPX 7864 Assessment 2 Correlation Application and Interpretation

RSCH FPX7 864 Assessment 2

Correlation Application and Interpretation

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Student name

RSCH-FPX7864

Capella University

Professor Name

Submission Date

Data Analysis Plan

A detailed data analysis methodology involves methods and processes of information collection and analysis that will help the researcher to achieve the research objectives. The developed research framework allows scientists to perform data analysis systematically, which allows them to achieve reliable findings with meaningful conclusions (Sarker, 2021). The study aims at examining any possible correlations between the important student academic achievement variables of quiz 1 scores and final examination scores, cumulative points obtained and past grade point average (GPA). The research study results will provide important patterns of student performance that can be used to influence future teaching strategies.

The study examines four key variables:

1. Quiz 1 score: The number of correctly chosen answers during quiz 1. The point range extends from zero to the highest possible score, representing a continuous variable.

1. Final Exam Score: A cumulative numeric measure that is the number of correct responses delivered during the last assessment period. The possible range of scores begins at zero and continues as far as possible, which is a continuous variable.
2. Total Points Earned: Accumulative numerical evaluation of a combination of cumulative scholastic performance measures gathered throughout the academic term. Scores go up to the maximum cumulative possible maximum and down to the lowest possible baseline of zero. This is a continuous variable.

4. GPA: Scholastic achievement measure computed using a numeric range spanning 0.00 (lowest possible) through 4.00 maximum, indicating mean performance across all completed coursework. This represents a continuous variable.

Total-Final Correlation

Research Question

Is there a connection between students’ overall credit earnings throughout the semester and final examination performance?

Hypotheses

Null Hypothesis (H0): There is no correlation between students’ total accumulated course points and scores on the final exam. H0: ρ = 0

Alternative Hypothesis (Ha): A correlation is present between the total points students earn during the course and the final examination. Ha: ρ ≠ 0

Quiz 1 and GPA Correlation

Research Question

Is there a relationship between students’ academic performance scores and results on the initial assessment?

Hypotheses

Null Hypothesis (H0): Initial assessment outcomes show no apparent correlation with students’ subsequent academic achievement indicators. H0: ρ = 0

Alternative Hypothesis (Ha): Academic performance indicators demonstrate a strong relationship between learners’ cumulative grade point averages and initial assessment results. Ha: ρ ≠ 0

Testing Assumptions

Table 1: Descriptive Statistics

Descriptive Statistics
Quiz1		GPA		Total		Final
Skewness	-0.851	-0.220	-0.757	-0.341
Std. Error of Skewness	0.236	0.236	0.236	0.236
Kurtosis	0.162	-0.688	1.146	-0.277
Std. Error of Kurtosis	0.467	0.467	0.467	0.467

Data verification is statistically tested to ensure the conditions are satisfied to apply a suitable test to justify the reliability of the results and the reasonableness of the selection of an analytical technique (Dul et al., 2020). The descriptive statistics analysis obtained the values of skew and kurtosis, which were used to determine the skewness directionality in the data. Descriptive testing of Quiz 1 showed skewness of -0.851 and kurtosis of 0.162. As far as the GPA variable is concerned, the calculated skewness was -0.220, and kurtosis was -0.688 after analysis. The third variable had -0.341 skewness with -0.277 kurtosis on completion of descriptive testing. With regard to the total variable, the skewness and kurtosis values were found to be -0.757 and 1.146, respectively. The negative values of skew proved the left-shifted tendencies of data distribution in the histogram display. On the other hand, the positive values of kurtosis after analysis indicated that Quiz 1 scores and total points had high peak characteristics. In addition, descriptive analysis showed that the skewness and kurtosis values of all variables fell within the boundaries of -2 to +2 of normality. The descriptive statistics demonstrate that the assumption of normality is used, as the results obtained meet the reasonable normality parameters. Also, the data about the variables shows that they follow a normal distribution, which justifies continuing with correlation analysis to identify the level of association.

Results & Interpretation

Table 2: Pearson’s Correlations Between Academic Performance Variables

Pearson’s Correlations
Variable				Quiz1		GPA		Total		Final
1. quiz1	Pearson’s r	—
p-value	—
2. gpa	Pearson’s r	0.152	—
p-value	0.121	—
3. total	Pearson’s r	0.797	***	0.318	***	—
p-value	< .001	< .001	—
4. final	Pearson’s r	0.499	***	0.379	***	0.875	***	—
p-value	< .001	< .001	< .001	—
* p < .05, ** p < .01, *** p < .001

The Pearson correlation analysis was performed to test the association of the two variables. In the correlation, the degree of association was reflected in the correlation coefficient r. The p-value is another element that is important in interpreting the results. The p-value determines whether the data inference is in favor of the null or the alternative hypothesis. The results of correlation analysis between the total points and the final examination score of the learners are presented below: r(103) = 0.875, p <.001. The r was 0.875, meaning that there was a positive relationship between total points and the final score of the learner. Also, the null hypothesis was rejected because the calculated value of p is lower than the level of significance of 0.05 and strongly indicates that there is a correlation between the total score and the final score.

The results of the correlation analysis between the learner’s GPA and the score on quiz 1 produced the following results: r(103) = 0.152, p < 1.21. The r was 0.152, a weak relationship between the variables. Based on the circumstances of the outcome, the p-value of the results is greater than 0.05, and the null hypothesis is, therefore, not rejected; that is, there is no significant relationship between variables. The insignificance of the relationship between the variables meant that Quiz 1 did not predict the GPA of the learner at the end of the entire course. The results of the data analysis reported that the variables of the total point and final examination scores showed a higher level of association than the variables of GPA-Quiz 1.

Statistical Conclusions

The descriptive analysis assists the researcher in evaluating the normality of the data by looking at both the negative and positive values of skewness and kurtosis. The results of the descriptive analysis revealed that student GPA and final exam scores are negative, which supports the fact that the data follows a normal distribution. The correlation test is used to find relationships between the GPA-quiz 1 variables and the overall final scores achieved by learners.

The p-value and the r-analysis can assist in interpreting the outcome and recognising the relationships. These results were obtained through correlation analysis between total points and final exam performance in students: (103) = 0.875, p <.001. The r value of 0.875 indicates that the variables are strongly correlated; the p value of less than 0.001 indicates that the relationships between the variables are statistically significant. Findings indicated that good classroom students generally have high final exam results. Moreover, the correlation analysis between student GPA and quiz 1 showed the following results (103) = 0.152, p < 1.21. The r value of 0.152 shows weak correlation between the variables, whereas p is less than 1.21, which shows that there is no significant correlation between Quiz 1 and student GPA scores. Hence, self-assessment instruments such as quiz 1 results are not able to forecast student GPA because other contextual variables can influence learner performance.

Limitations

There were several significant limitations to the correlation analysis. Although there were strong associations identified, causality could not be determined because the correlations were bidirectional. Potential external variables that might have influenced the associations were not investigated. The analysis focused only on direct correlations without looking at more complex relationships that could have been revealed by multiple regression. The sample size was small, and this minimized the statistical power, especially when testing the GPA-Quiz 1 correlations. The quantitative approach failed to capture additional qualitative data on the learning methods and instructional strategies that students use, which could have been useful. Multiple regression would have given a clue on how different factors work together to influence the variation of the scores (Maulud & Abdulazeez, 2020). More research, with broader methodologies and different data sources, may assist in uncovering the mechanisms behind the academic relationships revealed in the initial research.

Application

In physical therapy, correlation analysis may be used to explore the relationship between exercise frequency and mobility improvement to show the effect of treatment intensity on patient improvement. In the pharmacy practice, relationships between the rate of medication compliance and clinical outcomes may describe the impact of compliance on the effectiveness of the therapy, similar to how baseline measurements reflect the future success of treatment. The efficiency of operating room scheduling might be related to the rates of surgical complications, and hospital leadership would be informed about workflow optimization approaches. The applications demonstrate how correlation analysis provides significant insights in all medical settings since it identifies significant relationships between variables. Evidence-based practices based on correlation results have shown not only clinical improvements but also administrative ones in clinics that have adopted them (Hashish & Alsayed, 2020). This correlation will help the association of medical practitioners to develop a few plans from the explicit areas of the issues and present scientifically calculated models of the development of the provision of healthcare (O’Malley et al. 2024). The combination of quantitative correlation results with empathetic analytical assessment allows scaling of effective strategies by using proper methodologies.