The student must then post 1 reply to another student’s post. The reply must summarize thestudent’s findings and indicate areas of agreement, disagreement, and improvement. It must besupported 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.
D.8.9.6
(a) Output 9.6 contains three separate one-way ANOVAs that evaluated the relationship between students’ high school grades, visualization scores, math achievement scores, and their fathers’ education levels. The findings showed grades in high school differed significantly between groups F(2, 70) = 4.09, p = .021, and math achievement F(2, 70) = 7.88, p = .001. A one-way ANOVA test found no significant difference between visualization scores because the F value equaled 0.76 with p = .470.
(b) In non-technical terms, father education level determines school performance because students whose fathers obtained bachelor’s degrees performed higher in high school and math tests than students with fathers who received lower degrees. The data showed that students whose fathers completed high school earned an average high school grade of 5.34, but students whose fathers earned a bachelor’s degree scored 6.53 on average. The students who performed worst in math scored 10.09 on average, and those with the best-performing fathers achieved an average score of 16.35. The evaluation scores for visualization remained consistent across groups because their means ranged between 4.67 to 6.02, showing no substantial variation resulting from father education levels.
D.8.9.7
The Tukey HSD post hoc test in Output 9.7a showcases that grades in high school experienced a statistically significant difference between students whose fathers held degrees from high school or less and students whose fathers earned a bachelor’s degree or higher. The p-value reached .017, showing a significant mean difference of 1.184 between those groups. The analysis showed no statistical significance for the other pairwise comparisons since their p-values reached .873 and .144.
Math achievement analysis in Output 9.7b applying Games–Howell test methodology confirmed statistical significance between students with levels of education from high school graduates or less and some college and between students from these two groups and bachelor’s degree or more graduates. The calculated mean differences reached 4.31 (p = .017) for the first subgroup and 6.26 (p = .008) for the subsequent group. The “some college” group showed no statistical variation when compared to the “bachelor’s degree or more” group (p = .614), indicating their math test scores were equivalent.
Students with fathers who earned their bachelor’s degree demonstrated stronger academic achievements than those who finished their education at high school or below. They showed particular academic superiority in mathematics.
D.8.9.8
The Kruskal–Wallis nonparametric test in Output 9.8 identified any statistically important differences between the three fathers’ education groups regarding math achievement and competence measurements. The math achievement test results demonstrated a statistically significant difference between groups according to χ²(2, N = 73) = 13.38, p = .001. Math achievement levels between students varied significantly based on their fathers’ educational attainment. The mean ranking results demonstrated that students whose fathers completed high school education or less scored the lowest (28.43) while those with fathers who earned a bachelor’s degree or above achieved the highest mean ranking (48.42); between these two groups stood students whose fathers obtained some college education (43.78). Students with fathers who completed more education levels demonstrated better achievements in mathematics.
The competencies-matched group yielded an insignificant Kruskal–Wallis p-value of .999, which demonstrates that the three groups did not differ statistically for this variable. Competence ratings displayed very close alignment as high school or less education received a 36.04 mean rank, and both other groups (some college education and bachelor’s degree or higher) achieved 35.78 and 36.11 mean ranks, respectively. The study results indicate paternal education level did not affect the determined competency scores.
Kruskal–Wallis test showed that paternal education level significantly affected math achievement without impacting competence levels. The educational background significantly impacts math academic outcomes but does not affect overall competence similarly.
D.8.9.9
The statistical methodologies used in Outputs 9.6 and 9.8 to examine whether students’ math achievement scores vary by their fathers’ education levels are both different. The results of a one-way ANOVA (a parametric test that studies normally distributed data and homogeneity of variances) were presented in output 9.6. The ANOVA found that Math achievement differed significantly across the three father education groups: F(2, 70) = 7.88, p = .001. This result shows that students whose fathers have a bachelor’s degree or more scored much higher than other students in math.
On the other hand, output 9.8 employs the Kruskal–Wallis test, a nonparametric variant of ANOVA for use with conditions of normality and equal variances not applicable. Finally, this test also found a statistically significant difference in math achievement χ²(2, N = 73) = 13.38, p = .001. The same amount of significance from both tests strengthens the case that paternal education is related to differences in math achievement.
The two outputs differ mainly in the methods and assumptions used in the statistical tests. Kruskal–Wallis has better robustness when the assumptions of ANOVA are not satisfied, while ANOVA is more powerful if such assumptions are true. While the details are different, both tests reach the same conclusion: the more highly educated the father, the more a student tends to achieve in math.
D.8.9.10
(a) In Output 9.9, math grades and academic track are not statistically significant in their interaction, F(1, 71) = 0.34, p = .563, η² = .005. Then, the effect of math grades on math achievement is not very sensitive to whether the student is on a fast or regular academic track.
(b) The profile plot of the cell shows parallel lines, which suggests that parallel lines generally affect math grades and achievement for the two tracks. Even among students with mostly A–B math grades, those on the regular track did not perform better than those on the fast track.
(c) The academic track is statistically significant in its main effect, F(1, 71) = 13.87, p < .001, effect size partial eta squared of .163. This is a large effect of Cohen’s (1992) guidelines, as over 16 % of the variance in math achievement scores is explained by academic track.
(d) The main effect of math grades is also statistically significant, F(1, 71) = 14.77, p < .001, η² = .172. The higher-scoring students had mostly As and Bs compared to the lower-scoring students.
(e) Since the study was correlational, not experimental, the word effect is in quotes. Therefore, inferred causality from the observed differences is not possible.
(f) The main effects can be misleading when a significant interaction exists because the difference in the effect between the variables is masked.
