RSCH FPX Assessment 4 ANOVA Application and Interpretation

Name

Capella University

RSCH 7864:ANOVA Application and Interpretation

Prof Name

October, 2024

Data Analysis Plan

This analysis plan for this test should involve conducting a one-way ANOVA in a statistical software called JASP, which determines whether there is any significant difference in quiz performance, about the different sections of the course, for which scores of Quiz 3 would be set out to represent students’ performance. The independent variable is categorical and has three levels corresponding to the three sections, while the dependent variable is continuous representing the scores. Research Question: Do quiz scores on Quiz 3 for students differ significantly based on the section in which they are? Null Hypothesis (H₀): There exist no significant differences in Quiz 3 scores across the various sections. Alternative Hypothesis (H₁): There exists at least one section whose mean differs from those of the other sections. This plan is justified, as we want to compare the means of some treatment groups. For such comparisons, ANOVA is appropriate and JASP happens to be such a user-friendly tool where the necessary statistical tests can be performed. Before running the ANOVA, assumptions such as homogeneity of variances will be tested using Levene’s Test in JASP to ensure the reliability of the model which would then guide further analyses, such as post-hoc tests that would identify specific group differences, should the null hypothesis be rejected.

Testing Assumptions

Assumption Check

Levene’s Test for Equality of Variances

The important assumption checked here in this one-way ANOVA assumption check is the homogeneity of variances. According to this assumption, the variation in the scores of Quiz 3 is assumed to be the same as between the sections. In this analysis, this assumption is conducted through Levene’s Test for Equality of Variances. The results can be obtained before running the ANOVA in JASP. Here is how it is conducted and an example table is present for the results of Levene’s Test:

In summary, the following table reports the results of Levene’s Test for Equality of Variances for scores on Quiz 3 by section: The F-statistic is 2.35, and the pdfs are (2, 87), representing, in turn, the number of groups and the total sample minus the number of groups.  Given the p-value of 0.102, the test did not detect a significant difference in variances between the sections. Thus, evidence is found that the assumption about the homogeneity of variances has not been violated since the variances of Quiz 3 scores in all groups are close to each other, hence it is safe to continue with standard ANOVA.

Results & Interpretation

Descriptive Statistics Table

ANOVA Table

The table of descriptive statistics provides means and standard deviations for Quiz 3 scores across the three sections. Section 2 scored the highest at 82.45, while the mean for Section 3 was the lowest at 75.15. However, such differences must be evaluated statistically to confirm whether they are significant. In the ANOVA table, it is quite evident that the F-statistic is 5.39, with a p-value of 0.007. Since the p-value is less than 0.05, we reject the null hypothesis, which indicates that quiz 3 scores are significantly different among the sections, at least one of the mean scores for the sections are significantly different from at least one other. As is evident in the results for post-hoc Tukey, the only significant difference that exists between the means is between Section 2 and Section 3, at p = 0.004; however, neither of the other comparisons, Section 1 to the other sections are significant. We conclude based on the ANOVA and post-hoc analyses that differences in scores for Quiz 3 exist by section between Section 2 and Section 3.

Statistical Conclusions

The analysis for mean score differences between the various sections carries conclusive statistical inferences based on ANOVA. On the other hand, significant differences exist in the mean scores specifically between Section 2 and Section 3. A robust F-statistic with resultant p-values derived from both ANOVA and Tukey post hoc tests supports this conclusion (Gupta & Kumar, 2024). However, although the results are statistically significant, the context wherein the said results developed has to be taken into consideration. Thus, environmental factors of a classroom, teaching methods undertaken, or variations in student populations due to sections might, therefore, lead to differences in quiz performances. Hence, although statistical evidence points towards the fact that there indeed exists a large difference, one should not negate the impact of context-based variables on the performance of students.

There are also some intrinsic limitations that one should take into account in the ANOVA test. The most important assumption is homogeneous variances. If this assumption is violated, the results could be rejected. The factor that would bias the F-test for such a condition is when the variances in the groups are significantly different. It would not then indicate the means’ differences. Further, ANOVA will just state that there is some difference without giving light on what that difference represents or why those differences exist (Blanca et al., 2023). Without more qualitative investigations or any additional quantitative analyses, such as multiple regressions or mixed-method approaches, is then necessary to understand the underlying factors that contribute to observed differences. There is therefore a great need to interpret the ANOVA results with caution and through the use of complementary analyses to appreciate the data better.

Application

The application of ANOVA in educational research, especially in evaluating students’ performance by class sections, has significant implications for educators as well as curriculum developers  (Guillén-Gámez & Mayorga-Fernández, 2020). It points to statistically significant differences between the various quiz scores for different class sections taught by respective educators, and it can mean pinpointing those teaching methods or sets of instructional strategies that produce better results for the students. Such data are important for tailoring pedagogic approaches toward enhancing learning and overall academic performance. In addition to this, it would also be possible to advise on the area of resource allocation and professional development based on whether the areas require more support or the need for training of instructors. Put differently, knowledge obtained from ANOVA could be applied in advising resource allocation and professional development programs as areas where instructors may require over/under training. In case a specific section continually underperforms below expectations, it would be easy to apply focused interventions targeting specific issues or concerns facing that set. Moreover, the outcomes may contribute to more extensive issues of equity in education so that every student can benefit from quality teaching practices responsive to individual learning needs. In general, data-driven decision-making will be facilitated by the use of ANOVA, which leads to effective learning results and student experiences.

RSCH FPX Assessment 4 Conclusion

Overall, the one-way ANOVA test on the Quiz 3 scores of different sections of students found a difference in student performance among those sections, and the differences between them especially show a distinction between Section 2 and Section 3. Indeed, such findings are further validated by descriptive statistics and post-hoc tests to identify differences between the groups (Cichoń, 2020). In conclusion, education outcomes must be statistically analyzed to provide further development for teaching practices and learning experiences. While the results will be helpful, it should be noted that the analyses assume homogeneity and are to the contextual conditions that might affect performance. The factors mentioned above allow educators to be more informed in their judgments about how to best allocate resources for instructional strategies. In effect, the present analysis draws attention to the added value statistical analysis, like ANOVA, provides in promoting evidence-based practices in an educational setting to improve continuous improvement and equitable outcomes for all learners.

RSCH FPX Assessment 4 References

Blanca, M. J., Arnau, J., García-Castro, F. J., Alarcón, R., & Bono, R. (2023). Non-normal data in repeated measures ANOVA: impact on type I error and power. Psicothema, 35(1), 21–29. https://www.psicothema.com/pi?pii=4786

Cichoń, M. (2020). Reporting statistical methods and outcomes of statistical analyses in research articles. Pharmacological Reports, 72(3), 481–485. https://link.springer.com/article/10.1007/s43440-020-00110-5

Gupta, A., & Kumar, P. (2024). Analysis of variation in foreign inflows by different categories of foreign portfolio investors. The Indian Economic Journal, 72(2), 270–286. https://journals.sagepub.com/doi/10.1177/00194662231212752

Guillén, F. D., & Mayorga, M. J. (2020). Quantitative-comparative research on digital competence in students, graduates and professors of faculty education: an analysis with ANOVA. Education and Information Technologies, 25(5), 4157–4174.https://link.springer.com/article/10.1007/s10639-020-10160-0