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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.please replied the below thread;D8.9.6D8.9.6.a Describe the F, df, and p values for each dependent variable as you would in an article.To identify the differences between a father’s education and the three variables of grades in high school, visualization test, and math achievement test a one-way Analysis of Variance (ANOVA) statistic test was computed. The ANOVA test for grades in high school was calculated as F(2, 70) = 4.09, p = .021 with a statistical descriptive of HS Grad or less as (M = 5.24, SD = 1.475) some college as (M = 5.56, SD = 1.788) and BS or more as (M = 6.53, SD = 1.219). This ANOVA identifies a statistical difference between father’s education and their grades in high school.An ANOVA test for Visualization test was calculated at F(2, 70) = .763), p = .470 and descriptives calculated for HS Grad or Less at (M = 4.68, SD = 3.96), Some College as (M= 6.02, SD = 4.56), and BS or more as (M = 5.47, SD = 2.79). Based on the significance of p = .470, there is no statistical difference for father’s education and the score of the Visualization Test.For the Math Achievement Test variable, the Levene Statistic was calculated as 3.517, p = .049, which identifies that the assumptions of the One-Way ANOVA test are violated, and thus, the results of a One-Way ANOVA would not be an appropriate test statistic for identification of statistical difference.D8.9.6.b Describe the results in nontechnical terms for visualization and grades. Use the group means in your description.Problem 9.6 utilizes a One-Way ANOVA test to identify if there are statistical differences between the three ordered levels of the father’s education and the student’s visualization test score, and the student’s grades in high school. The One-way ANOVA is the appropriate statistic for this case because it is a between-subjects method with the single independent variable of the father’s education (Price et al., 2015). The group mean square for visualization was calculated at (M = 3.354) with a mean square of 11.252. The significance for the visualization score was calculated as a p = .470, which means there was no statistical difference between the father’s education and the student’s score on the visualization test.The second One-way ANOVA was calculated for the father’s education and grades in High School with the group mean of (M = 16.71) and the mean square of 279.24. Although the significance was identified a p < .001, the ANOVA test would be an inappropriate test for these variables as the Levene test identifies, based on the mean, the math achievement test is not approximately distributed, and thus, a nonparametric test should be used to calculate the statistical difference (Morgan et al., 2020).D8.9.7 In Outputs 9.7 a and b, what pairs of means were significantly different?In 9.7.a the Tukey Post Hoc test was calculated after a One-Way ANOVA for the father’s education and the student's grade in high school. As defined by Morgan et al. (2020), the Posthoc Tukey calculation is preferred when the Levene test does not show the significance for violation of equal variance. Based on the output of the Tukey analysis, the only variables that had statistical difference was the father’s education of the groups with HS grad or less and the group of students with a BS or more. The mean difference was calculated at -1.184 with a significance of p = .017.In 9.7.b a Games-Howell Posthoc test was applied to the father’s education groups against the math achievement test as the match achievement test was identified by the Levene test to have unequal variance. As suggested by Morgan et al. (2020), when the Levene test shows significance for violation of assumptions, the Games-Howell posthoc test is appropriate to identify which of the independent variable groups is responsible for significance. The outcomes of the Games-Howell test with the groups of father’s education and the math achievement score identified that the Mean Difference between HS grads or less group and Some College was -4.31 with a significance of p = .017 thus highlighting the statistical difference. The Mean Difference between HS grad or less and BS or Higher was calculated at -6.26 with a significance of p = .008, also identifying a significant difference.D8.9.8 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?When researchers wish to compare differences between groups when the independent variable is either not normally distributed or if the independent variable is ordinal, then a Kruskal–Wallis statistical test is appropriate to identify statistical differences (Scott, 2020). The significance of the Kruskal–Wallis test for father’s education groups on math achievement was significant at p = .001. The significance of the Kruskal–Wallis test on father's education on Competence score was calculated at p = .999, thus identifying that the three groups of father’s education do not have significant differences based on competence scores.Based on these findings, researchers could conclude that the level of a father's education does significantly influence the student's math achievement score but does not statistically influence the student's competence score.D8.9.9 Compare Outputs 9.6 and 9.8 with regard to math achievement. What are the most important differences and similarities?In the output of Morgan et al. (2020) Problem 9.6 and 9.8, the father’s education is compared to analyze the differences between the groups of father’s education and math achievement. In problem 9.6 the use of the One-Way ANOVA was used, and in problem 9.8 a Kruskal-Wallis test was used. The use of the One-Way ANOVA in problem 9.6 highlights using the Levene test that the variances of the groups are significant, and therefore, the One-Way ANOVA should not be used to identify differences as it violates the required assumptions. Regardless, the One-Way ANOVA was run and was calculated as F(2, 70) = 7.89, p = .001, which identifies that the father’s education groups do have a statistical impact on the results of the math achievement test.In problem 9.8 the correct statistical analysis was run using the Kruskal-Wallis test, which is a nonparametric test used when the assumption of ANOVA is violated or when the data is ordinal (Morgan et al., 2020). The Kruskal-Wallis test was calculated to 13.38 with a significance of p = .001. ANOVA is a parametric test that should only be used on normal data, while the Kruskal-Wallis test can support skewed and ordinal data (Morgan et al., 2020). Interestingly enough, both the ANOVA and Kruskal-Wallis test produced the same significance stating that the father’s education groups do have a statistical difference in relation to their influence on student's math achievement tests.D8.9.10D.8.9.10.a Is the interaction significant?No, the interaction of math grades and the academic track does not have a significant effect on math achievement. The result of the Two-Way ANOVA was calculated at F(1, 71) = .34, p = .563 would require the researcher to fail to reject the null hypothesis.D.8.9.10.b Examine the profile plot of the cell means that illustrates the interaction. Describe it in words.An output of profile plots was created to estimate the marginal means of math grades. On the Y-axis are the estimated marginal means, and on the X-axis are the math grades. Both fast track and regular track lines are drawn, with both starting on the bottom left and moving to the top right. Fast track line is higher than the normal track line and appears to have a faster growth rate than the line for the regular track.D.8.9.10.c Is the main effect of the academic track significant? Interpret the eta squared.In the ANOVA calculation, eta squared is calculated to identify the correlation ratio for a nominal independent variable and a normal dependent variable (Morgan et al., 2020). The main effect as measured by eta squared as .163 has a non-eta squared value of .403, which, based on Morgan et al. (2020), has a large effect size on the math grade variable. As ETA helps the researcher define the proportion of the variance that can be attributed to the two groups, it is clear that the academic track does have a medium to large influence on math grades. Based on the outcome of the partial eta squared value of .163, it can be said that the academic track accounts for 16.3% of the variance for match achievement.D.8.9.10.d How about the “effect” of math grades?Math grades, much like adtrac, significantly influence math achievement individually as an independent variable. The effect of the partial eta squared was calculated to be .172, meaning that about 17% of the variance in math achievement can be attributed to math grades. It is further necessary to note that the significance of p = .000 is highly significant. A non-Eta squared value of .414 would denote a medium to high effect size, much like adtrac based on Morgan et al. (2020).D.8.9.10.e Why did we put the word effect in quotes?When researchers develop studies, the use of the word “effect” in quotes denotes that the study did not utilize a randomized experiment, and thus a researcher could not determine the causation of differences in the dependent variable, which, in this case, was the match achievement test scores.D.8.9.10.f Under what conditions would focusing on the main effects be misleading?As identified by Morgan et al. (2020), the main effects of independent variables can be misleading when the results of both vary in significance levels or if they have varying levels of effects based on the ordinal category of the dependent variable (Morgan et al., 2020). As with all difference statistics, it is critical for the researcher to identify the assumptions of the statistical tools used to identify statistical differences (Terrell, 2021). The main “effects” is an aggregate of the two individual effects of the independent variables. As variables are aggregated, it can draw confusion as to which of the independent variables are the causation of the difference, and thus, the combined conditions can be misleading when reporting the main effects.ReferencesMorgan, G. A., Barrett, K. C., Leech, N. L., & Gloeckner, G. W. (2020). IBM SPSS for Introductory Statistics (6th ed.). Routledge. Price, P. C., Jhangiani, R., & Chiang, I.-C. A. (2015). Research Methods in Psychology (2nd Canadian Edition ed.). BCcampus. Scott, D. W. (2020). Statistic: A Concise Mathematical Introduction for Students and Scientists Terrell, S. R. (2021). Statistics Translated, Second Edition : A Step-By-Step Guide to Analyzing and Interpreting Data. Guilford Publications. http://ebookcentral.proquest.com/lib/liberty/detail.action?docID=6462082
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