PSY FPX 7864 Assessment 3 ANOVA Application and Interpretation

Student Name

Capella University

PSY FPX 7864 Quantitative Design and Analysis

Prof. Name

Date

Introduction & Data File Overview

The present study employs Analysis of Variance (ANOVA) to scrutinize disparities across multiple groups. The research focuses on discerning distinctions among sections and quiz 3 variables within a sample of 105 students. The independent variable comprises the student’s section, while quiz 3 scores serve as the dependent variable. The section variable is categorical, possibly subdivided into subgroups, while quiz 3 scores are continuous. The sample size (N) encompasses 105 individuals.

The research inquiry posits: Are there notable variances among mean scores of different sections on Quiz 3? The null hypothesis suggests no disparities, whereas the alternative hypothesis indicates significant differences between section and quiz 3 scores. ANOVA is utilized to test these assertions, under the assumptions that Y follows a normal distribution or remains consistent across all factor levels (Author, Year).

PSY FPX 7864 Assessment 3 ANOVA Application and Interpretation

Test of Normality

To assess normality, the Shapiro-Wilk test is conducted, yielding a p-value of 0.000. A p-value below 0.05 in Shapiro-Wilk suggests non-normal distribution. Therefore, based on this data, the null hypothesis is rejected, indicating the absence of normal distribution (Author, Year).

Results and Analysis

Descriptive Statistics

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

ANOVA

A one-way ANOVA test is conducted to discern the significance of differences among the sections. The degrees of freedom are 2 between sections and 102 within groups. The F-value of 10.951 suggests 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 (Author, Year).

Comparisons

This table illustrates 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 irrespective of the section. Post hoc analysis reveals that section 3 performance significantly surpasses the other two sections.

Conclusion

ANOVA identifies substantial differences among the sections, thereby invalidating the null hypothesis and affirming the alternative hypothesis. Although ANOVA facilitates comparison across multiple variables and is user-friendly, it lacks a mechanism for determining the most significant variable (Author, Year).

PSY FPX 7864 Assessment 3 ANOVA Application and Interpretation

Application

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