Comparing Groups 2: ANOVA Chris Busi 820 July 1, 2024 ✓ Solved

Comparing Groups 2: ANOVA Chris BUSI 820 July 1, 2024

In Output 9.6: (a) Describe the F, df, and p values for each dependent variable as you would in an article. Grades in h.s: F (2,70) = 4.091, p = .021 Visualization test: F (2,70) = .763, p = .470 Math achievement: F (2.70) = 7.881, p = .001 The way these are reported is correct based on Morgan et al. (2020); in addition, the authors describe the df numbers as representing effect and error, while the F helps understand variation and the p identifies if that value is significant. The p values for the first and third variable are

(b) Describe the results in nontechnical terms for visualization and grades. Use the group means in your description. The visualization test results, F (2,70) = .763, p = .470, highlight that there is not a difference between the three groups as the p > .05. For grades in h.s., F (2,70) = 4.091, p = .021, the results demonstrate that there is a difference between the groups, and by reviewing the means table it is evident that student grades are higher when their father has more education.

D.8.9.7 In Outputs 9.7 a and b, what pairs of means were significantly different? In 9.7a, the Tukey HSD test verified a significant difference in the high school or less and bachelor’s degree or more levels of father’s education on grades in hs because these levels are not presented in the homogeneous table. In 9.7b, the means were different between the hs graduate or less and some college means, as well as hs graduate or less and bachelor’s degree. The p values were p =.017 and p = .008, respectively, both less than .05.

D.8.9.8 In Output 9.8, interpret the meaning of the sig. values for math achievement and competence. What would you conclude, based on this information, about differences between groups on each of these variables? The p = .001 for math is significant and concludes that math grades are different between the different levels of education, while the p = .999 for competence is not significant so no conclusions are drawn regarding differences.

D.8.9.9 Compare Outputs 9.6 and 9.8 with regard to math achievement. What are the most important differences and similarities? The primary differences are in that Output 9.8 the means are based on ranks. In addition 9.6 provides the Levene statistics to identify variance equality, while 9.8 is only ran when one already knows the variances are unequal or other problems exist for normality. The most interesting thing to note is the p value is identical ( p = .001), so both tests identify the significance the same.

D.8.9.10 In Output 9.9: (a) Is the interaction significant? The interaction is not considered significant because the p value is .563. Using ANOVA’s in real practice, Senguttuvel et al. (2021) used this method to study the interactions between environment and types of rice in how they grow. This study provides a good example of how ANOVA is useful in practice.

(b) Examine the profile plot of the cell means that illustrates the interaction. Describe it in words. The plots display positive correlations in increased grades with math achievement for both tracks, however the authors point out not to discuss plots in this problem because the interaction was not significant.

(c) Is the main effect of academic track significant? Interpret the eta squared. Yes, because its p

(d) How about the “effect” of math grades? The p

(e) Why did we put the word effect in quotes? The authors do this because cause and effect of the variables is not what is meant by the table in identifying significance in the differences.

(f) Under what conditions would focusing on the main effects be misleading? The authors discuss how this occurs when there are significant interactions, which require a review of the simple effects as well.

Paper For Above Instructions

The Analysis of Variance (ANOVA) is a statistical method used to compare means among multiple groups to understand if at least one group is significantly different from the others. The current study employs ANOVA to analyze the impact of the father's educational level on students' performance across multiple dependent variables, including high school grades, visualization test scores, and math achievement. This paper will summarize and interpret the relevant outputs from ANOVA conducted on the specified data sets and discuss the implications of the findings in both academic and practical contexts.

In Output 9.6, the results indicate significant differences in high school grades associated with the father's education level. Specifically, the F-value for high school grades is F(2,70) = 4.091, with a p-value of 0.021, indicating a statistically significant result (p 0.05). Such discrepancies emphasize how academic achievement can vary based on familial educational backgrounds, particularly in high school grades. Lastly, for math achievement, we observe a significant F-value of F(2,70) = 7.881 with a p-value of 0.001, implying that differences in education level are likewise influential on math performance among students.

The interpretation of the results reveals a nuanced view of the interplay between education and student performance. The visualization results articulated a lack of significant differences among groups, meaning regardless of paternal education status, visualization scores remain relatively consistent. This indicates that factors outside of familial educational background may play a more substantial role in the performance of students in visualization assessments. However, with regard to high school grades and math achievement, the findings underscore an overarching trend where increased educational investment by parents correlates positively with their children's academic success.

According to Output 9.7, the post-hoc Tukey HSD test presents critical insights into which specific educational levels show significant differences in grades. The analysis highlights that significant differences exist between the 'high school or less' category compared to 'bachelor’s degree or more' and also between 'high school graduate or less' and 'some college.' The p-values for these differences were p = 0.017 and p = 0.008, respectively, both indicating statistically significant differences.

Furthermore, Output 9.8 addresses math achievement and the significance values associated with both math grades and competence levels. The notable p-value of 0.001 for math grades indicates a strong statistical correlation between education levels and math achievement, while the p-value for competence (0.999) implies no significant differences exist amongst groups concerning competence scores.

In making a comparison between Outputs 9.6 and 9.8, we realize that while both outputs indicate significant findings regarding math grades with identical p-values (p = 0.001), they differ in the types of statistical information presented. Output 9.6 includes the Levene’s test for equality of variances, which is essential for establishing the appropriateness of ANOVA assumptions, while Output 9.8's focus on ranks signals an analysis that assumes previous knowledge of potential variances and distribution issues.

Output 9.9 begins by evaluating the significance of the interaction between academic track and grades. The interaction's p-value of 0.563 indicates it is not significant. Interestingly, while the study of Senguttuvel et al. (2021) utilized ANOVA to explore interactions in environmental factors influencing rice cultivation, the same ANOVA methodology in this context provides insights into the academic field regarding how parental education shapes student performance.

Profile plots visualize mean cell scores; however, in this case, no discussion of plots is warranted due to the non-significance of interactions. The main effect of academic track is significant with p

The significance of math grades further emphasizes that achieving higher scores correlates with higher academic achievement, marked by an eta value of 0.41, indicating a large effect. The phrase "effect" highlights a cautious interpretation of causality; while statistical significance is established, deriving direct causal relationships from the data requires further inquiries.

In conclusion, while significant interactions may warrant a deeper dive into main effects, this paper illustrates that the educational background of parents noticeably influences student performance in various dependent variables, emphasizing the ongoing needs for educational policies that target family engagement and academic support.

References

• Morgan, G.A., Leech, N., Gloeckner, G., & Barrett, K.C. (2020). IBM SPSS for introductory statistics: Use and interpretation (6th ed.). Routledge.
• Senguttuvel, P., Sravanraju, N., Jaldhani, V., Divya, B., Beulah, P., Nagaraju, P., Manasa, Y., Prasad, A. S. H., Brajendra, P., Gireesh, C., Anantha, M. S., Suneetha, K., Sundaram, R. M., Madhav, M. S., Tuti, M. D., Subbarao, L. V., Neeraja, C. N., Bhadana, V. P., Rao, P. R., ... Subrahmanyam, D. (2021). Evaluation of genotype by environment interaction and adaptability in lowland irrigated rice hybrids for grain yield under high temperature. Scientific Reports, 11(1).