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RSCH FPX 7864 Assessment 4 ANOVA Application and Interpretation

Name

Capella University

RSCH FPX 7864 Quantitative Design and Analysis

Prof. Name

Date

Outline for Data Analysis

A single-factor analysis of variance (ANOVA) was performed to examine grades. The study looked at two variables: Section, which denotes various class sections, and Quiz 3, which indicates the number of correctly answered questions. Here, Section is the independent categorical variable, and the Quiz 3 scores are the dependent continuous variable.

Research Inquiry

The purpose of the study is to determine if there is a statistically significant difference in the average scores of different student groups on Quiz 3.

The null hypothesis states that the average scores of different student subgroups on Quiz 3 are not significantly different. On the other hand, the alternative hypothesis indicates that there is a significant difference in the mean scores between the student groups.

Evaluating Presumptions

Verification of Assumptions

Assessing the Equality of Variances (Levene’s Test)
Test
F
df1
df2
p

Levene’s

2.898

2.000

102.000

0.060

The Levene’s test produced a test statistic (F) of 2.898 with degrees of freedom (df) of 2 and 102, and a p-value of 0.060. When the p-value is equal to or less than the typical significance threshold (usually 0.05), it means rejecting the null hypothesis of equal variances, indicating a breach in the assumption of homogeneity. However, since the p-value obtained is above 0.05 (0.060), we cannot reject the null hypothesis, indicating that the assumption of homogeneity remains valid.

Outcome & Analysis

Descriptives
Section
N
Mean
SD
SE
Coefficient of variation

Section 1

3

7.273

1.153

0.201

0.159

Section 2

3

6.333

1.611

0.258

0.254

Section 3

3

7.939

1.560

0.272

0.196

ANOVA – Quiz 3

 
Cases
Sum of Squares
df
Mean Square
F
p

Section

 

47.042

2

23.521

10.951

< .001

Residuals

 

219.091

102

2.148

  

Post Hoc Tests

Standard Post Hoc Comparisons – Section
Comparison
Mean Difference
SE
t
p (Tukey)

1 vs 2

0.939

0.347

2.710

0.021

1 vs 3

-0.667

0.361

-1.848

0.159

2 vs 3

-1.606

0.347

-4.633

< .001

Note. P-value adjusted for comparing a family of 3.

RSCH FPX 7864 Assessment 4 ANOVA Application and Interpretation

The table provides a detailed breakdown of the average scores attained by different student sections in Quiz 3. Statistical analysis using ANOVA showed a noteworthy variance in the mean scores across the sections (F (2,102) =10.951, p< .001). Nevertheless, further examinations through post hoc tests demonstrated no notable distinction (p > 0.05) between the scores of Section 1 and Section 3.

Application

In applied behavior analysis (ABA), ANOVA serves as a useful tool for assessing how various independent factors relate to one dependent variable, allowing for comparisons across multiple factors simultaneously. For instance, it can be utilized to assess strategies for reducing aggressive behavior among individuals, with the strategies being the independent variables and aggressive behavior being the dependent variable. Understanding how different treatment approaches influence aggressive behavior is crucial in improving patients’ quality of life and their interactions with others.

References

Andrade, C. (2019). The P value and statistical significance: misunderstandings, explanations, challenges, and alternatives. Indian Journal of Psychological Medicine, 41(3), 210–215. https://doi.org/10.4103/ijpsym.ijpsym_193_19

RSCH FPX 7864 Assessment 4 ANOVA Application and Interpretation

Midway, S. R., Robertson, M., Flinn, S., & Kaller, M. D. (2020). Comparing multiple comparisons: practical guidance for choosing the best multiple comparisons test. PeerJ, 8, e10387. https://doi.org/10.7717/peerj.10387



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