RSCH-FPX7864_RousselDawn_4-1

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ANOVA Application and Interpretation Dawn Roussel Capella University RSCH-FPX7864 Quantitative Design and Analysis Dr. Brock Boudreau 10/24/2023 1

Data Analysis Plan An ANOVA was performed on a single factor, is based on grades. Section, the class section, and Quiz 3, the number of correct answers on Quiz 3, are the variables to be investigated in this analysis. Section is categorical and is the independent variable. Quiz 3 is continuous and is the dependent variable. Research Question: Is the difference between the mean scores of various student groupings on Quiz 3 statistically significant? The study's null hypothesis is that there is no statistically significant difference between the mean scores of the student subgroups on Quiz 3. The alternative hypothesis is that the mean score of one group of students on Quiz 3 will differ significantly from the scores of the other groups of students. Testing Assumptions Assumption Checks Test for Equality of Variances (Levene's) F df1 df2 p 2.898 2.000 102.000 0.060 Levene's test is used to determine whether the variance is homogeneous. This study's null hypothesis establishes whether or not the population variances are equal. Since the p-value is 0.06, which is greater than 0.05, p > 0.05, as a result, we cannot reject the null hypothesis and conclude that homogeneity is not violated. Results & Interpretation 2

Descriptives Descriptives - quiz3 section N Mean SD SE Coefficient of variation 1 3 3 7.273 1.153 0.201 0.159 2 3 9 6.333 1.611 0.258 0.254 3 3 3 7.939 1.560 0.272 0.196 ANOVA - quiz3 Cases Sum of Squares df Mean Square F p section 47.042 2 23.521 10.951 < .001 Residuals 219.091 102 2.148 Note. Type III Sum of Squares Post Hoc Tests Standard Post Hoc Comparisons - section Mean Difference SE t p tukey 1 2 0.939 0.347 2.710 0.021 3 -0.667 0.361 -1.848 0.159 2 3 -1.606 0.347 -4.633 < .001 Note. P-value adjusted for comparing a family of 3 According to the descriptive table, quiz 3 average was firm for each section. Section 1 had a mean ( M = 7.273) and standard deviation ( SD = 1.153). Section 2 had a mean ( M = 6.333) and standard deviation ( SD = 1.611). Section 3 had a mean ( M = 7.939) and standard deviation ( SD = 1.560). 3

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The ANOVA table associated the mean scores from quiz 3 to the three sections of students. The ANOVA table showed a distinctive difference in the mean of quiz 3 compared to the three selections of students, F (2,102) =10.951, p <0.001. The null hypothesis was rejected. The post hoc comparison using the Tukey test shows a significant difference between section 1 and section 2 with p <0.05. The null hypothesis is rejected. There is also a significant difference between section 2 and section 3 with p <0.05, rejecting the null hypothesis. Statistical Conclusions A single test can be used to compare more than two groups using the ANOVA variance analysis. Meier (2022) notes that if multiple pairwise comparisons are made on the same data using one-way ANOVA, there is a greater likelihood of committing a Type I error (erroneously rejecting a legitimate null hypothesis). However, the omnibus test has the advantage of protecting researchers against inflated Type I mistakes. The issue is that a positive omnibus test only indicates a difference "somewhere" between the groups; it does not specify which group means something is different. The one-way ANOVA in the statistical analysis suggests a significant difference between the three student groups' third and second quizzes. There may be limitations when using an ANOVA to compare the means of more than two groups. For example, the p-value can only indicate that one data set is significantly different from the other (Johnson, 2022). The post hoc test is necessary to show how the student groups' performance on Quiz 3 differs from one another. A p -value less than 0.05 indicates that there is insufficient data to support the null hypothesis. The post hoc test reveals that F is significant, demonstrating sufficient data to reject the null hypothesis and conclude that the mean score for quiz 3 varies in 4

at least one pair of parts. Because there is insufficient statistical significance between section 1 and section 3, we are unable to reject the null hypothesis ( p >0.05). Application The fact that the categorical predictor variable might have two or more groups gives ANOVA an advantage over t-tests. This allowance is beneficial in my field of study and can be used to compare different department strategies and the task efficiency of the new business structure. Industry 4.0 is making it necessary for businesses to incorporate robotics, automation, and artificial intelligence. The comparison would be used to see if there is a significant difference in the current output of work compared to the inclusion of machine workers. The independent variable is the current strategies, and the inclusion of machine workers is the dependent variable. The null hypothesis would be that there is a significant difference between current department strategies and the inclusion of machine workers. The alternative hypothesis would be that there is no significant difference between the current department strategies and the inclusion of machine workers. 5

References Johnson, R. W. (2022). Alternate forms of the one-way ANOVA F and Kruskal–Wallis test statistics. Journal of Statistics and Data Science Education , 30 (1), 82-85. Meier, L. (2022). Incomplete block designs. ANOVA and Mixed Models , 165-178. 6

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