**Discussion Assignment Instructions**

The student must then post 1 reply to another student’s post. The reply must summarize the student’s findings and indicate areas of agreement, disagreement, and improvement. It must be supported with scholarly citations in the latest APA format and corresponding list of references. The minimum word count for Integrating Faith and Learning discussion reply is 250 words.

**Comparing Groups 2: ANOVA**

Chris

BUSI 820

July 1, 2024

Discussion Week 8

**D.8.9.6 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 < .05, so the differences in groups is determined to be significant.

*Unless noted, the Morgan et al. (2020) textbook is the source for all answers in this thread.

**(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* < .001. The eta squared of .163 helps provide variation statistics for the different tracks, so in this problem it shows 16.3% is the amount of variance in tracks.

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

The *p* < .001, *eta* = .41 show a statistical difference that higher grades correlate with higher achievement with a large effect.

**(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.

**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), 15825-15825. __https://doi.org/10.1038/s41598-021-95264-4__Links to an external site.