# RSCH FPX 7864 Assignment 4 ANOVA Application and Interpretation

## Data Analysis Plan

RSCH FPX 7864 Assignment 4 ANOVA Application and Interpretation

Grades are the basis for these grades.jasp data from a JASP database where an ANOVA was performed on a single factor. Additionally, it is used to test for statistical significance when comparing the averages of two or more unrelated groups (Siegel & Wagner, 2022). Only the fact that at least two groups are distinct is revealed, not which groups are statistically distinct. The assessment dataset’s goal is to investigate two factors: quiz 3 and section. Quiz 3 is a continuous dependent variable, whereas the section is a categorical independent variable. We want to know whether there is a statistically significant disparity in the mean scores of different student subgroups on Quiz 3, and this is the guiding research question. There is no statistically significant difference in the mean results of the various student subgroups on Quiz 3; this is the null hypothesis for the study. According to the alternative hypothesis, one group of students will have a substantially different mean score on Quiz 3 than the other groups of students.

## Testing Assumptions

RSCH FPX 7864 Assignment 4 ANOVA Application and Interpretation

The Levene’s test is used to test the homogeneity of variance. In our study, the null hypothesis states that the population variances are equal, and this test will be used to prove whether the null hypothesis holds. The p-value from the above test is. 06, which is greater than .05, indicating that p >.05. We fail to reject the null hypothesis because the p-value is greater than .05, so we conclude that homogeneity is not violated.

## Results and Interpretation

The average of the Quiz 3 for every section of students is found to be firm, as shown in the table above.

## RSCH FPX 7864 Assignment 4 ANOVA Application and Interpretation

Average results on Quiz 3 were assigned to three groups using the one-way ANOVA table. In accord with the data in the table above, we may conclude that the null hypothesis of no difference in the means of the three groups of students on Quiz 3 is rejected: F (2, 102) =10.95, p <.001.

## RSCH FPX 7864 Assignment 4 ANOVA Application and Interpretation

Tukey’s HSD was used to conduct a post hoc comparison, and the results indicated that there is a statistically significant difference between section 1 and section 2, p < .05, hence the null hypothesis was rejected. Failure to reject the null hypothesis due to a lack of statistical significance between section 1 and section 3, p > .05. The null hypothesis is rejected because there is a statistically significant difference between sections 2 and 3, p < .05.

## Statistical Conclusions

RSCH FPX 7864 Assignment 4 ANOVA Application and Interpretation

The ANOVA analysis of variance can be used to compare more than two groups with a single test. Meier (2022) states that when using one-way ANOVA, there is a higher chance of making a Type I mistake (falsely rejecting a valid null hypothesis) if several pairwise comparisons are performed on the same data. However, the omnibus test does have the benefit of shielding researchers from exaggerated Type I errors. The problem is that a positive omnibus test doesn’t say which group means something is different, just that there is a difference “somewhere” between them. The statistical analysis shows that there is a significant difference between the third and second quizzes across the three groups of students, as shown by the one-way ANOVA. Using an ANOVA to compare the means of more than two groups might have its restrictions. The p-value, for instance, can only suggest that one set of data is substantially different (Johnson, 2022). In this scenario, the post hoc exam is required to demonstrate the differences in performance on Quiz 3 between the groups of students. When the p-value is smaller than .05, this shows that there is enough evidence to reject the null hypothesis. The post hoc test shows that F is significant and this illustrates that there is enough evidence to reject the null hypothesis and conclude that there is at least one pair of sections that differs in quiz3 mean score. We fail to reject the null hypothesis due to a lack of statistical significance between section 1 and section 3, since p > .05.

## Application

RSCH FPX 7864 Assignment 4 ANOVA Application and Interpretation

Multiple factors may be tested in an ANOVA, which is an analysis of variance test. Multiple tiers of independent variables are possible. In my field of work, which includes psychology, for example, an experiment with treatment and control groups has one component, treatment, but two levels, treatment and control. The ANOVA method may be used if there are more than two distinct groups to compare. Using the two-factor ANOVA, researchers may determine whether or not there are significant variations in means owing to treatment, by sex, or the interaction of treatment and sex. There is no difference between the execution of a one-factor ANOVA and that of a higher-order ANOVA. The analysis of variance (ANOVA) is a useful tool for evaluating potential vendors. When there are more than two groups to compare, we turn to ANOVA, or Analysis of Variance, to see whether there are significant variations in mean scores.

## RSCH FPX 7864 Assignment 4 ANOVA Application and Interpretation

### References

Johnson, R. W. (2022). Alternate forms of the one-way ANOVA F and Kruskal–Wallis test statistics. Journal of Statistics and Data Science Education30(1), 82-85.

https://doi.org/10.1080/26939169.2021.2025177

Meier, L. (2022). Incomplete block designs. ANOVA and Mixed Models, 165-178.

https://doi.org/10.1201/9781003146216-8

Siegel, A. F., & Wagner, M. R. (2022). Anova. Practical Business Statistics, 485-510.