PSY FPX 7864 Assessment 3 ANOVA Application and Interpretation
Phillip April 23, 2024 No Comments

PSY FPX 7864 Assessment 3 ANOVA Application and Interpretation

PSY FPX 7864 Assessment 3 ANOVA Application and Interpretation


Capella university

PSY FPX 7864 Quantitative Design and Analysis

Prof. Name


Introduction & Data File Overview

The Analysis of Variance (ANOVA) method is utilized to test distinctions across multiple groups. This study aims to discern disparities among sections and quiz 3 variables within a cohort of 105 students. The independent variable is the student’s section, while quiz 3 scores serve as the dependent variable. The section variable is categorical, potentially divided into subgroups, whereas quiz 3 scores are continuous. The total sample size, or N size, comprises 105 individuals.

The research inquiry is as follows: Is there a notable variance among mean scores of different sections on Quiz 3? The null hypothesis posits no disparities, while the alternative hypothesis suggests significant differences between section and quiz 3 scores. ANOVA will be employed to test these assertions, contingent upon the assumptions that Y follows a normal distribution or that y remains consistent across all factor levels.

Test of Normality

Normality within the dataset is assessed using the Shapiro-Wilk test, yielding a p-value of 0.000. A p-value below 0.05 in Shapiro-Wilk indicates non-normal distribution or dissimilarities. Thus, based on this data, the null hypothesis is refuted, signifying absence of normal distribution.

Results and Analysis

Descriptive Statistics

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

The table below presents data for all three sections. Mean scores are displayed in the third column, with section one averaging 7.27, section 2 averaging 6.33, and section 3 averaging 7.94. Standard deviation is also depicted in column 4.





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


The subsequent table illustrates a one-way ANOVA test, discerning 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 distinctions among the sections. Furthermore, the p-value of 0.000 contradicts the null hypothesis. The effect size, at 0.246, is relatively large.

PSY FPX 7864 Assessment 3 ANOVA Application and Interpretation


Sum of Squares


Mean Square



Section 47.042 2 23.521 10.951 < .001
Residuals 219.091 102 2.148


This table demonstrates 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 surpassing 0.05 denote significant disparities regardless of section. Post hoc analysis reveals that section 3 performance significantly surpasses the other two sections.


Mean Difference



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


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


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

PSY FPX 7864 Assessment 3 ANOVA Application and Interpretation