PSYC FPX 4700 Assessment 5 Research Report
Student Name
Capella University
PSYC FPX 4700 Statistics for the Behavioral Sciences
Prof. Name
Date
PSYC FPX 4700 Assessment 5 Research Report
Data analysis helps researchers organize, evaluate, and interpret information to identify meaningful patterns and relationships. In this research report, the analysis examines quiz scores, GPA, total scores, and final exam scores for 105 students. The Pearson correlation results show that Quiz 1 has a weak and statistically nonsignificant relationship with GPA, while Quiz 1, GPA, total scores, and final exam scores show several statistically significant positive relationships. Most notably, total scores are strongly associated with final exam scores (r = .875, p < .001), while GPA has a moderate positive relationship with final exam scores (r = .379, p < .001). These findings describe associations among the variables but do not establish cause-and-effect relationships.
Research Purpose and Data Analysis
Data analysis involves examining, organizing, transforming, and interpreting data to generate useful information for decision-making (Kelley, 2020). Before statistical tests are performed, researchers typically clean and prepare the data to improve the accuracy and reliability of the findings (Côté, 2021).
The purpose of this analysis is to examine student academic data collected across three sections of a course. The variables include Quiz 1 scores, GPA, total scores, and final exam scores. The analysis focuses on the distribution of the variables and the relationships among them.
Variables and Scales of Measurement
Four variables were included in the analysis: Quiz 1, GPA, Total Score, and Final Exam Score.
Quiz 1 is a quantitative variable representing the number of points students received on the first quiz. Because the score can vary numerically within a defined range, it can be treated as a continuous variable for the purposes of this analysis.
GPA represents students’ grade point averages. GPA is recorded numerically on a scale such as 0.00 to 4.00. Although GPA may sometimes be grouped into categories for reporting purposes, the numerical GPA values used in this analysis are treated as a continuous variable.
Total Score represents students’ overall numerical score in the course. It is a continuous quantitative variable because students can receive different numerical scores across a range.
Final Exam Score represents the numerical score earned on the final examination and is also treated as a continuous variable.
Research Question and Hypotheses
The original research question asks whether there is a significant difference in mean Quiz 1 scores across the three sections of the course.
Research question: Is there a statistically significant difference in mean Quiz 1 scores across the three course sections?
Null hypothesis (H₀): There is no statistically significant difference in mean Quiz 1 scores across the three sections of the course.
Alternative hypothesis (H₁): There is a statistically significant difference in mean Quiz 1 scores across the three sections of the course.
A one-way analysis of variance (ANOVA) would normally be used to answer this research question because it compares the mean of a continuous outcome across three independent groups. The Pearson correlation output provided in this report addresses a different question: whether pairs of continuous variables are linearly related. Therefore, the correlation table alone cannot be used to determine whether Quiz 1 means differ among the three course sections.
Testing Statistical Assumptions
The descriptive statistics provide information about the distribution of the four variables. The dataset contains 105 valid observations for each variable.
| Variable | N | Minimum | Maximum | Mean | SD | Skewness | Kurtosis |
|---|---|---|---|---|---|---|---|
| Quiz 1 | 105 | 0 | 10 | 7.47 | 2.481 | -0.851 | 0.162 |
| GPA | 105 | 1.08 | 4.00 | 2.8622 | 0.71266 | -0.220 | -0.688 |
| Total | 105 | 54 | 123 | 100.09 | 13.427 | -0.757 | 1.146 |
| Final | 105 | 40 | 75 | 61.84 | 7.635 | -0.341 | -0.277 |
The skewness and kurtosis statistics provide an initial indication of whether the distributions substantially depart from normality. The variables show some degree of skewness, particularly Quiz 1, which has a skewness of -0.851. However, the values do not indicate an extreme departure from normality based on common practical guidelines.
It is important to note that normality should not be evaluated using skewness and kurtosis alone. Visual methods such as histograms and Q-Q plots, as well as the assumptions of the specific statistical test being used, should also be considered. For a one-way ANOVA, researchers should additionally examine independence of observations and homogeneity of variances.
Descriptive Interpretation of the Data
The average Quiz 1 score was 7.47, with scores ranging from 0 to 10. The standard deviation of 2.481 indicates noticeable variation in students’ quiz performance.
The mean GPA was 2.8622, with values ranging from 1.08 to 4.00. The relatively small negative skewness suggests that GPA scores were reasonably balanced, although more students may have been concentrated toward the higher end of the scale.
The mean total score was 100.09, with scores ranging from 54 to 123. The final exam had a mean score of 61.84 and a standard deviation of 7.635, with scores ranging from 40 to 75.
Overall, the descriptive statistics indicate meaningful variation among students in academic performance, providing an appropriate basis for examining relationships between the variables.
Pearson Correlation Results
The Pearson correlation analysis examined the linear relationships among Quiz 1, GPA, Total Score, and Final Exam Score.
| Variables | Pearson r | p-value | Interpretation |
|---|---|---|---|
| Quiz 1 and GPA | .152 | .121 | Weak, not statistically significant |
| Quiz 1 and Total | .797 | < .001 | Strong, statistically significant |
| Quiz 1 and Final | .499 | < .001 | Moderate, statistically significant |
| GPA and Total | .318 | < .001 | Moderate, statistically significant |
| GPA and Final | .379 | < .001 | Moderate, statistically significant |
| Total and Final | .875 | < .001 | Very strong, statistically significant |
Interpretation of the Statistical Findings
The correlation between Quiz 1 and GPA was r = .152, p = .121. Because the p-value is greater than the conventional significance level of .05, this relationship is not statistically significant. The result indicates only a weak positive association between Quiz 1 performance and GPA in this sample. Therefore, there is insufficient statistical evidence to conclude that Quiz 1 scores and GPA are linearly related.
A strong positive relationship was found between Quiz 1 and Total Score (r = .797, p < .001). This indicates that students with higher Quiz 1 scores tended to have higher total course scores. The relationship is statistically significant and relatively strong.
Quiz 1 was also positively associated with Final Exam Score (r = .499, p < .001). This represents a moderate positive relationship, suggesting that students who performed better on Quiz 1 tended to earn higher final exam scores.
The relationship between GPA and Total Score was statistically significant (r = .318, p < .001). Although the correlation is positive, its magnitude is moderate, indicating that students with higher GPAs tended to have higher total course scores.
A moderate positive correlation was also observed between GPA and Final Exam Score (r = .379, p < .001). This statistically significant relationship suggests that higher GPA was associated with higher final examination performance in this sample of 105 students.
The strongest relationship in the correlation matrix was between Total Score and Final Exam Score (r = .875, p < .001). This very strong positive correlation indicates that students with higher total scores generally also had higher final exam scores.
Statistical Conclusion
The Pearson correlation analysis demonstrates several statistically significant positive relationships among the academic variables. The strongest association occurred between total scores and final exam scores, followed by the relationship between Quiz 1 and total scores.
However, the correlation analysis does not provide evidence regarding whether the average Quiz 1 scores differ across the three course sections. That research question requires a comparison of group means, such as a one-way ANOVA. Therefore, the statement that there was a statistically significant difference in mean Quiz 1 scores across the three sections cannot be supported by the Pearson correlation output provided here.
The analysis does support the conclusion that several academic performance variables are significantly related. In contrast, the relationship between Quiz 1 and GPA was not statistically significant.
Limitations of the Statistical Analysis
Several limitations should be considered when interpreting these findings.
First, the sample consists of 105 students from the course being examined. Because the sample may not represent students from other courses, institutions, or populations, the findings may have limited generalizability.
Second, the analysis includes only a small number of academic variables. Factors such as attendance, study time, previous academic performance, instructional methods, socioeconomic characteristics, and student motivation may also influence academic outcomes.
Third, correlation analysis measures association rather than causation. A statistically significant correlation does not demonstrate that one variable causes another. For example, the strong relationship between total and final scores does not establish that a higher total score causes higher final exam performance.
Finally, assumptions associated with statistical procedures should be carefully evaluated. Normality, independence, and homogeneity of variance are particularly important when conducting inferential tests such as ANOVA.
Alternative Explanations and Future Research
Several factors could explain the observed relationships. Students who perform well academically may have stronger study habits, greater engagement, better preparation, or previous knowledge of the course material. These factors could influence multiple academic outcomes simultaneously.
The strong relationship between total and final scores may also partly reflect how the total score is constructed. If the final examination contributes substantially to the total course score, a strong correlation between these variables would be expected.
Future studies could examine whether student demographics, instructional strategies, attendance, study behaviors, or learning environments influence academic performance. Researchers could also use larger and more diverse samples to improve the precision and generalizability of the findings.
A future analysis should specifically compare Quiz 1 scores among the three course sections using a one-way ANOVA. If the ANOVA is statistically significant, post hoc comparisons could then be conducted to determine which sections differ from one another.
Application to Psychology and Healthcare Research
Data analysis techniques such as correlation and group-comparison tests are widely applicable in psychology, healthcare, and nursing research. Researchers can use these methods to investigate relationships between interventions, behaviors, academic performance, and health outcomes.
For example, correlational research can be used to examine relationships between physical activity and emotional intelligence among college students. Sanchez et al. (2019) investigated this type of relationship and demonstrated how correlational methods can be used to explore associations between behavioral and psychological variables.
In psychological research, similar methods can be used to examine relationships among treatment participation, symptom severity, academic functioning, emotional well-being, and quality-of-life measures. These analyses can help researchers identify patterns that warrant additional investigation.
However, researchers should distinguish between identifying an association and demonstrating an intervention effect. Experimental or longitudinal research designs are generally better suited to evaluating causal relationships.
Key Takeaways
The analysis of 105 students produced several important findings. Quiz 1 and GPA were not significantly correlated, whereas Quiz 1 was strongly associated with total scores and moderately associated with final exam scores. GPA was also significantly associated with total and final scores. The strongest relationship occurred between total and final scores.
The findings should be interpreted as evidence of statistical associations rather than causal relationships. In addition, the Pearson correlation analysis cannot determine whether mean Quiz 1 scores differ across three course sections. A one-way ANOVA would be the appropriate statistical procedure for directly testing that research question.
Frequently Asked Questions
What is the main purpose of data analysis in research?
The main purpose of data analysis is to organize, examine, and interpret collected information so researchers can identify patterns, relationships, and meaningful findings. Statistical analysis can also help researchers make evidence-based conclusions.
What statistical test should be used to compare quiz scores across three course sections?
A one-way ANOVA is generally appropriate when comparing the mean of a continuous variable, such as Quiz 1 score, across three independent groups. The analysis requires assumptions such as independent observations and appropriate variance and distributional conditions.
What does a Pearson correlation measure?
Pearson correlation measures the strength and direction of a linear relationship between two quantitative variables. The correlation coefficient ranges from -1 to +1.
What does a correlation of r = .875 mean?
An r value of .875 indicates a very strong positive linear relationship between two variables. In this analysis, total score and final exam score had this relationship. It means higher values of one variable tend to occur with higher values of the other.
Is the relationship between Quiz 1 and GPA statistically significant?
No. The correlation between Quiz 1 and GPA was r = .152 with p = .121. Because the p-value is greater than .05, the relationship is not statistically significant at the conventional significance level.
Does correlation prove causation?
No. Correlation demonstrates an association between variables but does not establish that one variable causes another. Establishing causation generally requires an appropriate experimental or longitudinal research design and careful control of potential confounding factors.
Why is the correlation between total score and final score so strong?
The strong correlation may occur because both measures represent academic performance and the final examination may contribute to the overall course total. The exact explanation depends on how the total score was calculated.
What is the strongest correlation in this dataset?
The strongest correlation is between Total Score and Final Exam Score, with r = .875 and p < .001. This represents a very strong, statistically significant positive relationship.
Why are statistical assumptions important?
Statistical assumptions help researchers determine whether a statistical test is appropriate for the data. Violations of important assumptions can affect the validity and interpretation of statistical results.
References
Côté, C. (2021). 4 types of data analytics to improve decision-making. Harvard Business School Online. https://online.hbs.edu/blog/post/types-of-data-analysis
Kelley, K. (2020, May 27). What is data analysis? Process, methods, and types explained. Simplilearn. https://www.simplilearn.com/data-analysis-methods-process-types-article
Sanchez, J. A., Diez-Vega, I., Esteban-Gonzalo, S., & Rodriguez-Romo, G. (2019). Physical activity and emotional intelligence among undergraduate students: A correlational study. BMC Public Health, 19, 1–10. https://doi.org/10.1186/s12889-019-7576-5
PSYC FPX 4700 Assessment 5 Research Report
Vasileiou, K., Barnett, J., Thorpe, S., & Young, T. (2018). Characterising and justifying sample size sufficiency in interview-based studies: Systematic analysis of qualitative health research over a 15-year period. BMC Medical Research Methodology, 18, Article 148. https://doi.org/10.1186/s12874-018-0594-7