RSCH FPX 7864 Assessment 4 ANOVA Application and Interpretation

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• RSCH FPX 7864 Assessment 4 ANOVA Application and Interpretation.

ANOVA Application and Interpretation

Capella University

RSCH-FPX7864

Professor Name

Date

ANOVA Application and Interpretation

Statistical Calculation Analysis of Variance (ANOVA) enables comparison of independent samples of differences in means of more than three groups. Even though helpful, ANOVA is not perfect, e.g., it cannot indicate which groups differ from each other, and there is a need for data that should be normally distributed and with equal variances for all the groups (Alem, 2020). Tukey post-hoc tests were employed to determine mean differences in scores encountered during the study. One-way ANOVA was applied by the study in its assessment of Quiz 3 scores by class sections and in assessing the impact of section alignment upon student performance.

Data Analysis Plan

Variables measured are:

Class Section – Categorical variable (i.e., Section A, Section B).

Quiz 3 (Number of correct answers) – Continuous variable (Quiz 3 scores).

Research Question

Are the Quiz 3 scores of class sections significantly different?

Null Hypothesis (H₀)

The mean Quiz 3 scores of class sections are not significantly different.

Alternate Hypothesis (H₁)

The mean Quiz 3 scores of class sections are significantly different.

Testing Assumptions

Levene’s test is used to determine if groups of the population are equal in variance because ANOVA is a requirement they must satisfy. In testing, the test came back F = 2.898 with df1 = 2 and df2 = 102 and gave back p = 0.060 (F = 2.898, p = 0.060). The derived p-value in the provided data is greater than 0.05, and that holds the null hypothesis as p > 0.05. The test ensures the identical variance distribution between groups, satisfying the homogeneity of variances test requirement criteria. The ANOVA test continues as the requirement for assumption has been met (Zhou et al., 2023). Reliability of ANOVA is guaranteed as there are shared variances among groups that result from the results obtained from Levene’s Test, thus evading possible outcome bias.

The results collected by Quiz 3 reveal extremely high variation in mean values and the statistical rate of spread in different sections of the examination. Section 1 has undergone a mean value of M = 7.237 and a standard deviation of SD 1.153, which shows extremely low variation with uniformity in performance. Section 2, however, had a lower mean of M = 6.333 and a higher standard deviation of SD 1.611, indicating higher variability and lower homogeneity of performance among the students. Section 3 had the highest mean of M = 7.939, with SD 1.560, indicating high overall performance, though the results were varied to some extent. Descriptive statistics indicate heterogeneity in the mean scores pattern and homogeneity between sections. This is a perfect example of all of the groups’ performances during Quiz 3.

The F-test of ANOVA is used to look for group differences in means and group variances. The f-statistic value computed was F(2,102) = 10.951, but its p-value was higher than its significance, lower than 0.001 (p<0.001). Data analysis will deny the null hypothesis since section variables comprise different average scores of quizzes for Quiz 3. Analysis results assured equal variances in sections since the homogeneity of variances assumption was met (Zhou et al., 2023). Exam performance in the context of Quiz 3 is established to indicate the academic performance of pupils at school. The research demonstrates the way institutions must examine group performance metrics as the results feed into the establishment of improved individual student support systems. ANOVA results indicated that there existed a significant difference by class section in terms of Quiz 3 score. The use of a Tukey post-hoc test was conducted in an attempt to notice individual differences among the sections. The result was as stated:

Section 1 vs. Section 2: Section 1 scored on average 0.939 points more than Section 2, SD 0.347. The statistical test had t = 2.23, p = 0.0021, i.e., Section 1 students scored higher than Section 2 students significantly. That implies there will be some variables in Section 1 that are to be credited for scoring more in the quiz than in Section 2

Section 1 vs. 3: The mean difference was -0.667 points with SD = 0.361 between Sections 1 and 3. t = -1.848, p = 0.159 was found, which showed that scores were not different, i.e., Sections 1 and 3 were equally good in the quiz.

Section 2 vs. Section 3: Section 3 outperformed Section 2 with a difference in the means of 1.06 points, and the Section 3 marks were much larger. With SD = 0.347, t = -4.633 and p < 0.001 (t = -1.606, p = 4.633), there was extremely high statistical significance, which revealed the perfection of Section 3’s pedagogy or subject.

Though Sections 1 and 3 were comparable in result, each was superior to Section 2, verifying the value of recording differences on a group-by-group basis in educational measurement for purposes of recording overall patterns of performance.

Statistical Conclusions

In the study, one-way ANOVA was conducted to determine differences in Quiz 3 scores across class sections. Before running ANOVA, Levene’s test had been performed as a test for homogeneity of variances. Results indicated that there was an equal variance assumption and thus made it proper to run ANOVA for purposes of analysis. The ANOVA also yielded a large F-statistic (F(2, 102) = 10.951, p < 0.001), which showed that mean scores in Quiz 3 varied significantly depending on the class section. The result resulted in the rejection of the null hypothesis; thereby, the class section of the class has a significant impact on Quiz 3 performance and is worthy of the use of post-hoc analysis to determine the difference between groups.

To identify precisely where the group differences were, a Tukey post hoc test was conducted, and the result was as follows:

Section 1 vs. Section 2: Section 1 pupils performed higher than Section 2 pupils by 0.939 (p = 0.021). This confirms that there were certain definite factors which occurred only in Section 1, i.e., class dynamics or style of teaching, which could have been the cause of improved performance.

Section 2 vs Section 3: Section 3 was superior to Section 2 with an average difference of -1.606 (p < 0.001) and differed significantly statistically in terms of performance. Section 3, based on the study, can be aided with special teaching methods or a suitable learning environment.

Section 1 and Section 3: There was no significant difference observed between Section 1 and Section 3, with a mean difference of -0.667 (p = 0.159). Both sections are equally effective with environmental factors in order to maintain adequate performance among the students.

Section 1 and Section 3 outperformed Section 2 despite the fact that they shared identical scores. The result was that class section membership influences student quiz scores, hence the likelihood of generating effective study strategies and ultimately consistent student performance by section.

Limitations and Possible Alternatives 

One-way ANOVA is an accurate test of differences in group means, but with some restrictions that make result interpretation challenging. ANOVA statistically does not identify differences between groups. Tukey’s test as a procedure eliminates doubt about ANOVA results to make conclusions (Alem, 2020). This is what the ANOVA requires for calculation between groups, even where there has been interference with the assumption that sample group sizes are not equal. A single, straightforward assumption break will lead to erroneous analysis results. Any other reasons for the differences obtained should be provided since non-analysis-based extraneous variables can influence the outcome (Kang, 2021). Thus, while ANOVA is beneficial to establish overall group differences, proper consideration of limitations athe nd right post hoc testing must be undertaken in incorrect analysis.

Application

A successful myology experiment involves the utilization of resistance and aerobic training, and the two concurrently as an independent variable in training programs of muscles, with three groups. Hypertrophy and strength of muscle are research-dependent variables in measuring differences between quantitative aspects of muscle force production and mass (Hayashida et al., 2024). Myology needs to be learned such that one can understand training protocols that will enable maximum augmentation of the muscle and muscle strengthening gain that will optimize exercise protocols in athletes, ageing, and muscular disease patients (Trombetti et al., 2021). Researchers learn best practices for augmenting the function of the muscles, and even prevention of atrophy in the muscles, and wound healing practices from research on various exercise protocols.

References

• https://doi.org/10.14662/IJARER2020.015
   
• https://doi.org/10.1371/journal.pone.0111810
   
• https://doi.org/10.3352/jeehp.2021.18.17
   
• https://doi.org/10.1007/s00198-015-3236-5