RSCH FPX 7864 Assessment 4

RSCH FPX 7864 Assessment 4 ANOVA Application and Interpretation Data Analysis Plan The statistical method known as analysis of variance (ANOVA) can be used to compare and test differences between two or more means. The ANOVA test is considered vital for using comparative as well as experimental research designs (Koli, 2024). In the following assessment, the results for correct answers within Quiz 3 are assessed for correct frequency, which shows if there is any divergence. Section and Quiz 3 A variable that a student is assigned to, and is a type of variable, is the classroom group, which is the variable section. Quiz 3, however, is a continuous variable and measures students’ performance as determined by the number of correct answers given. Research Question Is there a statistically significant difference in Quiz 3 scores among students from different classroom sections? Null Hypothesis (Ho) There is no statistically significant difference in Quiz 3 scores among students from different classroom sections. Alternative Hypothesis (HA) There are statistically significant differences in Quiz 3 scores among students from different classroom sections. Testing Assumptions Levene’s test was used to ascertain whether the assumption of homogeneity was met. The test is a conventional practice in checking the equal variance assumption in analysis. Assumption of homogeneity means that the variance is the same for all groups. By performing Levene’s test, following a conventional analysis in checking homogeneity in analysis of variance, F(2, 102) = 2.690, p = 0.073, where df1 = 2 and df2 = 102 were yielded. The p-value is already large, which means that there is not enough evidence to reject the null hypothesis, so homogeneity is achieved. Based on the evidence, Levene’s test result was not significant, meaning the assumption of homogeneity of variances in ANOVA was valid, and it is appropriate to interpret the differences in group means (Najafi & Nasiri, 2023). However, violation of assumptions has little effect on results in the analysis of variance but can impact precision and/or statistical power. Results and Interpretation The values for mean (M) and standard deviation (SD) for Quiz 3 outcomes are presented below for all groups, organized according to the section variable. Section 1: M = 7.242, SD= 1.173 Section 2: M = 6.179, SD= 1.537 Section 3: M = 7.545, SD= 1.734 The analysis of the scores from Quiz 3 in the classrooms using one-way ANOVA revealed significant differences in the mean scores of the three sections of the classrooms. The highest average score was obtained by students in Section 3 (M = 7.545, SD = 1.734) followed by students in Section 1 and in Section 2 which obtained a mean of 7.242 and 1.173 and a mean of 7.325 and 1.275, respectively. The mean of the scores of students in Section 2 was 6.179 with a std deviation of 1.537, which was the lowest. A one-way ANOVA indicated that F(2, 102) = 8.354, p < .001, which means that the performance on Quiz 3 was indeed statistically significantly different among the classroom sections. The fact is very strong evidence in favor of the alternative hypothesis that there were meaningful differences in Quiz 3 scores among sections. The value of the F statistic indicates that the variance among group means was significantly greater than the variance within the groups. The correlation indicated is fairly high between classroom sections and quiz scores. Combined with the results of one-way ANOVA, the researcher was able to make a statement that there were meaningful differences among group means, which means that the classification of groups was correlated with variability in the outcome measure (Hazar & Hazar, 2025). Moreover, the very small p-value indicates that the noted variations in Quiz 3 scores across the sections are very unlikely to be the product of chance. Therefore, the null hypothesis was rejected and the alternative hypothesis accepted as the findings indicated that there was a significant difference in the performance of Quiz 3 between the classroom sections. Other comparisons might be achieved by post hoc analysis with Tukey’s HSD, comparing the difference in Quiz 3 scores for any of these three sections. A p-value of < 0.05 was achieved by comparing the data in Section 1 and Section 2. So there is a significant difference between the Quiz 3 scores of Section 1 and Section 2. While the mean scores in Section 1 seemed high when compared with the mean scores in Section 2, it did not reach a 7.242 score. Furthermore, there was a comparison of Sections two and three. The obtained p-value was: 0.001, < 0.05, which means that the difference is statistically significant. The mean differences among the sections were determined, and it was found that Section 3 had the best mean. A comparison was, however, made between Section 1 and Section 3, and a high p-value was achieved. The value was well beyond the 0.05 value. Therefore, there is no statistically significant difference in cutoffs, and the cutoff in Section Three is slightly higher. The obtained values in the comparison include a t-statistic value of 2.993 in comparing Section 1 and Section 2, and -3.846 in comparing Section two with Section 3. Results indicated that there were meaningful differences between academic outcomes in specific sections of the classroom, suggesting that section-level resources, including instruction, peer relationships, and classroom climate, could be important factors to consider when examining academic outcomes (Rosen & Kelly, 2023). Overall, the data indicate that there were no significant. Sections 1 and 3 on Quiz 3, but that Section 2 had significantly lower performance compared to the other sections. Statistical Conclusions The performance of the different sections on Quiz 3 scores was evaluated using a one-way analysis of variance (ANOVA) statistical test. The results were statistically significant, F (2, 102) = 8.354, p < .001, indicating a significant difference in performance of the different sections of the classroom in Quiz 3. The null hypothesis was rejected. Also, the results revealed (F = 2.690, p = .073) that the data had equal variances as the results of Levene’s test were not significant.