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PSY FPX 7864 Assessment 3 ANOVA Application and Interpretation

Name

Capella University

PSY FPX 7864 Quantitative Design and Analysis

Prof. Name

Date

Introduction & Data File Overview

The Analysis of Variance (ANOVA) method is employed to examine differences across multiple groups. This study aims to identify disparities among sections and Quiz 3 scores within a cohort of 105 students. The independent variable is the student’s section, while the dependent variable is the Quiz 3 score. The section variable is categorical and divided into subgroups, whereas Quiz 3 scores are continuous. The total sample size, or N size, comprises 105 students.

The research question is: Is there a significant difference among the mean scores of different sections on Quiz 3? The null hypothesis posits no significant differences, whereas the alternative hypothesis suggests substantial differences between section and Quiz 3 scores. ANOVA will be utilized to test these hypotheses, assuming that Y follows a normal distribution or that Y is consistent across all factor levels.

Test of Normality

Normality within the dataset is assessed using the Shapiro-Wilk test, which yields a p-value of 0.000. A p-value below 0.05 in the Shapiro-Wilk test indicates a non-normal distribution or differences. Therefore, based on this data, the null hypothesis is rejected, indicating a lack of normal distribution.

Results and Analysis

Descriptive Statistics

The skewness of the dataset is 0.00, suggesting a normal distribution, while the kurtosis is -1.419, which is beyond the expected range.

 
N
Mean
SD
SE
Coefficient of Variation
Section 137.2731.1530.2010.159
Section 236.3331.6110.2580.254
Section 337.9391.5600.2720.196

The table above presents data for all three sections. Mean scores are shown in the third column, with Section 1 averaging 7.27, Section 2 averaging 6.33, and Section 3 averaging 7.94. Standard deviation is also depicted in column 4.

ANOVA

The table below illustrates a one-way ANOVA test, identifying the significance of differences among the sections. Degrees of freedom are 2 between sections and 102 within groups. The F-value of 10.951 indicates significant differences among the sections. Moreover, the p-value of 0.000 rejects the null hypothesis. The effect size, at 0.246, is relatively large.

PSY FPX 7864 Assessment 3 ANOVA Application and Interpretation

 
Cases
Sum of Squares
df
Mean Square
F
p
Section 47.042223.52110.951< .001
Residuals 219.0911022.148 

Comparisons

The table below shows the mean difference between each section. Notably, Sections 1 and 2 exhibit a mean difference of 0.939, while Sections 1 and 3 show a mean difference of -0.667. All values exceeding 0.05 indicate significant differences regardless of section. Post hoc analysis reveals that Section 3’s performance significantly surpasses the other two sections.

Comparison
Mean Difference
SE
t
p (Tukey)
1 vs 20.9390.3472.7100.021
1 vs 3-0.6670.361-1.8480.159
2 vs 3-1.6060.347-4.633< .001

Conclusion

ANOVA identifies substantial differences among the sections. The null hypothesis is rejected, affirming the alternative hypothesis. While ANOVA facilitates comparison across multiple variables and is user-friendly, it lacks a mechanism for identifying the most significant variable.

Application

This test is useful in various real-life scenarios, including education, as demonstrated in this study. Additionally, it can aid in optimizing outcomes in healthcare settings, such as medication therapies and treatment methodologies.

PSY FPX 7864 Assessment 3 ANOVA Application and Interpretation

References
  • Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.). SAGE Publications Ltd.
  • Howell, D. C. (2012). Statistical Methods for Psychology (8th ed.). Wadsworth.
  • McDonald, J. H. (2014). Handbook of Biological Statistics (3rd ed.). Sparky House Publishing.

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