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School of Business, Liberty University Faizan Malik Week 6 Discussion Assignment Author Note: Faizan Malik I have no known conflict of interest to disclose. Correspondence concerning this article should be addressed to Faizan Malik: Fmalik@Liberty.edu 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. (b) Describe the results in nontechnical terms for visualization and grades. Use the group means in your description. D.8.9.6.a. Output 9.6 depicts a One-Way Analysis of Variance (ANOVA) that assessed whether there are significant differences exist between a father's education level and their corresponding scores on high school visualization tests and mathematics achievement. For Father’s education and High School Grades, (F= 4.091, df= 2 and 70, and p = 0.021), it was found that a fathers' education levels has a significant impact on high school grades and grade differences are unlikely due to chance. Similar to the previous case, the ANOVA was used to examine whether there are significant differences between the groups of father's education levels in terms of math achievement scores. The results are given as: F= 7.881, df= 2 and 70, p = 0.001, which suggests that there are substantial differences between the groups in terms of math achievement. The ANOVA results for visualization test scores show: F = 0.763, df= 2 and 70, p = 0.470, which indicates that there are no substantial differences between the groups of father's education levels and student visualization scores. D.8.9.6.b. Output 9.6 presents an analysis that looked into whether fathers' education levels have an impact on high school students' visualization test scores and math achievements. For the relationship between fathers' education and high school grades, it was discovered that the level of education fathers have significantly affects their children's high school grades, and these differences in grades aren't just random chance. Similarly, in terms of math achievement scores, the ANOVA found notable differences between education groups signifying that father's education matters for math scores as well. However, when considering visualization test scores, the ANOVA results suggest that variations in fathers' education levels don't lead to significant differences in student visualization scores. D.8.9.7 In Outputs 9.7 a and b, what pairs of means were significantly different? D.8.9.7.a. In Output 9.7, the only notable difference was overserved between individuals who had completed high school or less and those who held a bachelor's degree or a higher level of education (p=0.017).

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? D.8.9.8.a. In output 9.8, a Kruskal-Wallis test was utilized to compare average rank scores across different levels of fathers' education in relation to math achievement and competence tests. As explained by Hecke (2012), the Kruskal-Wallis test is a nonparametric statistical test used to compare the medians of three or more independent groups. It is employed when the assumptions of parametric tests like analysis of variance (ANOVA) cannot be met, such as when the data is not normally distributed or when the variances are not equal (Hecke, 2012).This analysis highlighted distinct outcomes among the three father's education groups in terms of math achievement, yielding a χ² value of 13.38 and a significant p-value of .001 within a sample of 73 participants. Subsequent Mann-Whitney tests were employed to analyze specific pairs of father's education groups, employing a corrected p-value of .017 for determining statistical significance. Fagerland and Sandvik (2009) explain that the Mann-Whitney U test, is a nonparametric statistical test used to compare two independent samples or groups to assess whether there are significant differences in the distributions of ranks between the two groups, particularly when the assumptions of parametric tests (such as a t-test) cannot be met (Fagerland & Sandvik, 2009). The study found that, students whose fathers had completed some college displayed significantly higher mean rank scores for math achievement test when compared to students with fathers holding a high school diploma or lower. This is similar to students whose fathers possessed a bachelor's degree or higher, as they exhibited higher mean rank scores for math achievement when compared to students with fathers achieving a high school diploma or less. These differences also carried medium to large effect sizes, implying practical relevance with no statistically significant divergence in math achievement between students with fathers completing some college and those with fathers achieving a bachelor's degree or higher. D.8.9.9 Compare Outputs 9.6 and 9.8 with regard to math achievement. What are the most important differences and similarities? D.8.9.9.a Output 9.6 examines variance homogeneity to determine significant differences in variances among the three groups, whereas Output 9.8 excludes this step due to the nonparametric nature of the Kruskal-Wallis test. In Output 9.6, the comparison employs a one- way ANOVA and in Output 9.8, the comparison employs the nonparametric K-W test for a comparable comparison. However, both outputs yield an identical p-value of .001, indicating notable variations in group scores. D.8.9.10 In Output 9.9: (a) Is the interaction significant? (b) Examine the profile plot of the cell means that illustrates the interaction. Describe it in words. (c) Is the main effect of academic track significant? Interpret the eta squared. (d) How about the “effect” of math grades? (e) Why did we put the word effect in quotes? (f) Under what conditions would focusing on the main effects be misleading? D.8.9.10.a. The interaction labeled "F (math gr* academic track)" did not show statistical significance in this case (F= 0.337, df= 1 and 71, p = 0.563).

D.8.9.10.b. Significant interactions are often depicted using profile plots, illustrating group means. Parallel lines on these plots suggest little interaction. The researcher proposed using two lines on the plot to represent academic tracks rather than grade levels, improving the interpretation of the significant interaction. The graph's layout could have placed either independent variable on either side for effective presentation of the interaction. D.8.9.10.c. To comprehensively assess the significant implications of math grades, one must consider both the math grades and academic majors. A comparison between students achieving high math grades and those with lower grades highlights the latter group's poorer performance in math exams (mean scores: 10.81 vs. 15.05, p= < 0.001). Additionally, a statistically significant correlation emerges between academic performance and success. It's important to note that the impact of math grades on math success seems remarkably similar for students across academic tracks, but this aspect lacks statistical significance. D.8.9.10.d. The math grades' effect size of .41, denoted by eta (not squared), points to a notable impact. The adjusted R2 (.22) is slightly less than the unadjusted R2 (.25), which gains significance as the analysis incorporated three contributing variables—math grades, academic track, and their interaction—prompting the creation of a modified R2 (.22) to effectively encompass these multifaceted factors. D.8.9.10.e. The ANOVA table, also known as the Tests of Between -Subjects Effects, is the key table and the word "effect" in the title of the table can be misleading, as the study was not a randomized experiment. As such, as explained by (Morgan et al., 2020), the researcher cannot state in the report that the differences in the dependent variable were caused by or were the effect of the independent variable (Morgan et al., 2020) D.8.9.10.f. In the presence of a significant interaction, the researcher must exercise caution while interpreting the main effects, as they might lead to potentially misleading conclusions (Morgan et al., 2020). References Fagerland, M. W., & Sandvik, L. (2009). The wilcoxon–mann–whitney test under scrutiny. Statistics in medicine , 28 (10), 1487-1497. Hecke, T. V. (2012). Power study of anova versus Kruskal-Wallis test. Journal of Statistics and Management Systems , 15 (2-3), 241-247. Morgan, G. A., Barrett, K. C., Leech, N. L., & Gloeckner, G. W. (2020). IBM SPSS for Introductory Statistics Use and Interpretation (5th ed.). New York, NY, USA

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