PSYC FPX 4700 Assessment 5 Research Report

Name

Capella University

PSYC FPX 4700 Statistics for the Behavioral Sciences

Prof. Name

Date

PSYC FPX 4700 Assessment 5 Research Report

Data analysis is essential for identifying patterns, relationships, and trends within research data. In this PSYC FPX 4700 Assessment 5 research report, data from 105 students were examined using descriptive statistics and Pearson correlation analysis. The results showed several significant positive relationships among Quiz 1 scores, GPA, total course scores, and final exam scores. The strongest relationship was between total score and final exam score (r = .875, p < .001), while the relationship between Quiz 1 and GPA was weak and not statistically significant (r = .152, p = .121). Although these findings demonstrate meaningful associations among academic variables, they do not establish cause-and-effect relationships. Importantly, because the research question concerns differences in Quiz 1 means across three course sections, a one-way ANOVA—not Pearson correlation—is the appropriate test for that question.

Purpose of the Research and Data Analysis

Data analysis involves organizing, examining, transforming, and interpreting collected information to produce meaningful findings that can support research conclusions and decision-making (Kelley, 2020). Before statistical procedures are conducted, researchers should prepare and evaluate the dataset to reduce errors and improve the quality of the analysis (Côté, 2021).

The purpose of this PSYC FPX 4700 Assessment 5 analysis is to examine academic performance data collected from three sections of a course. Four variables were analyzed: Quiz 1 score, GPA, total course score, and final exam score. The analysis considers both the distribution of these variables and the relationships among them.

Variables and Scales of Measurement

The dataset contains four quantitative variables: Quiz 1, GPA, Total Score, and Final Exam Score.

Quiz 1 represents the number of points earned by each student on the first quiz. Because students can receive different numerical scores across a defined range, Quiz 1 is treated as a continuous quantitative variable in this analysis.

GPA represents each student’s grade point average. The values range from 0.00 to 4.00. Although GPA can sometimes be converted into categories, the numerical values in this dataset are treated as a continuous variable for the purposes of the statistical analysis.

Total Score represents students’ overall numerical performance in the course. It is a quantitative continuous variable because the scores can vary across a numerical range.

Final Exam Score represents the numerical score earned on the final examination. Like the other academic performance measures, it is treated as a continuous quantitative variable.

Research Question and Hypotheses

The research question focuses on whether students in the three course sections achieved different average Quiz 1 scores.

Research question: Is there a statistically significant difference in mean Quiz 1 scores across the three course sections?

The hypotheses are:

• Null hypothesis (H₀): There is no statistically significant difference in mean Quiz 1 scores across the three course sections.

• Alternative hypothesis (H₁): There is a statistically significant difference in mean Quiz 1 scores across the three course sections.

A one-way analysis of variance (ANOVA) is generally appropriate for this research question because it compares the mean of a continuous outcome variable across three independent groups.

The Pearson correlation analysis included in the dataset answers a different question. Pearson correlation evaluates whether two quantitative variables have a linear relationship. Therefore, the correlation results cannot determine whether the mean Quiz 1 scores are significantly different among the three course sections.

Testing Statistical Assumptions

Descriptive statistics were used to examine the distributions of the four variables. There were 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 values provide an initial indication of the shape of the distributions. Quiz 1 showed the greatest negative skewness at -0.851, while the other variables showed smaller departures from symmetry. Overall, the values do not suggest an extreme departure from normality based on commonly used practical guidelines.

However, skewness and kurtosis should not be the only methods used to evaluate normality. Researchers should also consider visual methods such as histograms and Q-Q plots. When conducting a one-way ANOVA, independence of observations and homogeneity of variance should also be evaluated.

Descriptive Statistics and Academic Performance

The mean Quiz 1 score was 7.47, with scores ranging from 0 to 10. The standard deviation of 2.481 indicates that students’ Quiz 1 performance varied to a meaningful degree.

The mean GPA was 2.8622, with values ranging from 1.08 to 4.00. The relatively small negative skewness indicates that the distribution was reasonably balanced, although scores were somewhat concentrated toward the higher end.

Students had an average total course score of 100.09, with scores ranging from 54 to 123. The standard deviation of 13.427 demonstrates variation in overall course performance.

The mean final exam score was 61.84, with scores ranging from 40 to 75. The standard deviation of 7.635 indicates noticeable differences in final examination performance among students.

Taken together, these descriptive statistics show that the 105 students varied in their academic performance. This variation provides a useful basis for examining relationships among Quiz 1, GPA, total course performance, and final exam scores.

Pearson Correlation Results

Pearson correlation was used to examine the direction and strength of linear relationships among the four quantitative variables.

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 Correlation Findings

The relationship between Quiz 1 and GPA was weak and positive (r = .152, p = .121). Because the p-value is greater than .05, the relationship is not statistically significant. Therefore, the data do not provide sufficient evidence to conclude that Quiz 1 performance and GPA have a statistically significant linear relationship in this sample.

A strong positive relationship was found between Quiz 1 and Total Score (r = .797, p < .001). Students who earned higher Quiz 1 scores generally tended to have higher overall course scores. The relationship was statistically significant and substantially stronger than the relationship between Quiz 1 and GPA.

The correlation between Quiz 1 and Final Exam Score was moderate and positive (r = .499, p < .001). This finding suggests that students who performed better on Quiz 1 also tended to perform better on the final examination.

The relationship between GPA and Total Score was also statistically significant (r = .318, p < .001). Although the correlation was positive, its magnitude was moderate. This means that students with higher GPAs tended to have higher overall course scores, but GPA did not account for all of the variation in total scores.

Similarly, GPA and Final Exam Score demonstrated a moderate positive relationship (r = .379, p < .001). Students with higher GPAs generally tended to achieve higher final exam scores.

The strongest relationship in the dataset was between Total Score and Final Exam Score (r = .875, p < .001). This very strong positive correlation indicates that students with higher total course scores generally also had higher final examination scores.

Statistical Conclusion

The Pearson correlation analysis identified several statistically significant positive relationships among the academic variables. The strongest association was between total course score and final exam score, followed by the relationship between Quiz 1 and total score.

The analysis also showed that Quiz 1 and GPA were not significantly correlated. The correlation of r = .152 with p = .121 does not provide sufficient evidence of a statistically significant linear relationship between these two variables.

However, these correlation findings cannot answer the original research question about whether mean Quiz 1 scores differ across the three course sections. Because the research question involves comparing the means of three independent groups, a one-way ANOVA should be conducted. Without the ANOVA results, it would not be appropriate to conclude that the three sections have significantly different Quiz 1 means.

Limitations of the Analysis

Several limitations should be considered when interpreting the findings.

First, the sample includes only 105 students from the course being studied. The results may therefore not generalize to students enrolled in other courses, institutions, or populations.

Second, the analysis focuses on only four academic variables. Other factors could influence student performance, including attendance, study time, previous academic achievement, instructional strategies, motivation, socioeconomic circumstances, and learning environment.

Third, correlation does not establish causation. Even when a correlation is statistically significant, the results cannot demonstrate that one variable directly causes changes in another. For example, the strong relationship between total score and final exam score does not mean that a higher total score causes a higher final exam score.

Finally, statistical assumptions should be assessed before drawing conclusions from inferential tests. For ANOVA, researchers should pay particular attention to independence of observations, approximate normality, and homogeneity of variances.

Alternative Explanations for the Findings

Several factors may explain the relationships observed in this dataset. Students who perform well academically may have stronger study habits, greater motivation, higher levels of engagement, better preparation, or greater familiarity with the course material. These characteristics could affect multiple measures of academic performance at the same time.

The very strong relationship between total score and final exam score also deserves careful consideration. If the final examination contributes substantially to the calculation of the overall course score, a strong correlation between the two variables would be expected. Therefore, the correlation should be interpreted in the context of how the total score was calculated.

Recommendations for Future Research

Future research could expand the analysis by including variables such as attendance, study habits, student engagement, instructional strategies, demographic characteristics, and previous academic performance. A larger and more diverse sample could also improve the generalizability of the findings.

Most importantly, future analysis should directly address the original research question by conducting a one-way ANOVA comparing Quiz 1 scores across the three course sections. If the ANOVA produces a statistically significant result, post hoc tests could be used to determine which specific course sections differ from one another.

Researchers could also consider longitudinal or experimental designs when the goal is to investigate potential causal relationships rather than simply identify associations.

Application to Psychology and Healthcare Research

Statistical techniques such as correlation and analysis of variance are widely used in psychology, nursing, healthcare, and behavioral research. These methods allow researchers to identify relationships among variables and compare outcomes across different groups.

For example, researchers may examine whether physical activity is associated with emotional intelligence among college students. Sanchez et al. (2019) demonstrated how correlational methods can be used to investigate relationships between behavioral and psychological variables.

In psychology and healthcare research, similar statistical approaches can be applied to variables such as treatment participation, symptom severity, emotional well-being, academic functioning, quality of life, and health behaviors. Identifying statistically meaningful relationships can help researchers develop questions for future studies.

Nevertheless, researchers must distinguish between association and causation. Correlational findings can identify patterns that deserve further investigation, but experimental or appropriate longitudinal designs are generally better suited for evaluating causal effects.

Key Takeaways

The analysis of 105 students identified several important relationships among academic performance measures. Quiz 1 and GPA were not significantly correlated, while Quiz 1 was strongly associated with total course score and moderately associated with final exam performance. GPA was also significantly associated with total and final scores.

The strongest relationship was between total score and final exam score (r = .875, p < .001). This represents a very strong positive association.

The findings should be interpreted as evidence of statistical relationships rather than causal effects. Furthermore, Pearson correlation does not answer the original question of whether Quiz 1 means differ across three course sections. A one-way ANOVA is the appropriate statistical procedure for directly testing that question.

Frequently Asked Questions

What is the purpose of data analysis in research?

Data analysis helps researchers organize, evaluate, and interpret collected information. It allows researchers to identify patterns, relationships, differences, and trends that can contribute to evidence-based conclusions.

What statistical test should be used to compare Quiz 1 scores across three course sections?

A one-way ANOVA is generally appropriate for comparing the mean Quiz 1 score across three independent course sections. It determines whether there is evidence that at least one group mean differs from the others.

What does 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. Positive values indicate that higher values of one variable tend to occur with higher values of the other.

What does an r value of .875 mean?

An r value of .875 indicates a very strong positive linear relationship. In this dataset, it describes the relationship between total course score and final exam score. Students with higher total scores generally tended to have higher final exam scores.

Is the relationship between Quiz 1 and GPA statistically significant?

No. The correlation between Quiz 1 and GPA was r = .152, p = .121. Because the p-value exceeds the conventional .05 significance level, the relationship is not statistically significant.

What is the strongest correlation in the dataset?

The strongest correlation is between Total Score and Final Exam Score, with r = .875 and p < .001. This indicates a very strong, statistically significant positive relationship.

Does a statistically significant correlation prove causation?

No. A statistically significant correlation indicates that two variables are associated, but it does not demonstrate that one variable causes the other. Other variables may explain or contribute to the observed relationship.

Why might total score and final exam score have such a strong correlation?

One possible explanation is that both measures reflect overall academic performance. In addition, if the final examination contributes substantially to the total course score, the two measures would naturally be expected to have a strong relationship.

Why are statistical assumptions important?

Statistical assumptions help determine whether a particular statistical procedure is appropriate for a dataset. Evaluating assumptions such as normality, independence, and homogeneity of variance helps researchers produce more reliable and defensible findings.

What should be done if the ANOVA is statistically significant?

If a one-way ANOVA shows a statistically significant difference among the three course-section means, post hoc comparisons can be conducted to identify which specific sections differ from each other.

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