PSY FPX 7864 Assessment 3

Introduction & Data File Overview

The Analysis of Variance (ANOVA) method is applied to test the differences among greater than one group. The intent of this research is to determine differences among sections and quiz 3 variables among a sample of 105 students. The independent variable is the student’s section, and quiz 3 scores are the dependent variable. The variable section is categorical, perhaps divided into subgroups, whereas quiz 3 scores are continuous. The total sample size, or N size, is made up of 105 participants.

The research question is: Are mean scores of different sections significantly different for Quiz 3? The null hypothesis is no differences, and the alternative hypothesis is differences between quiz 3 scores and section scores. ANOVA will be used to test these claims under the assumptions that Y is normally distributed or Y is constant for all levels of factors.

PSY FPX 7864 Assessment 3:Test of Normality

Normality of the dataset is measured via the Shapiro-Wilk test, and the p-value is found to be 0.000. A p-value of less than 0.05 in Shapiro-Wilk indicates non-normal distribution or differences. Based on this information, therefore, the null hypothesis is rejected, meaning lack of normal distribution.

Results and Analysis

Skewness of the data is 0.00, meaning normal distribution, whereas that of kurtosis is -1.419, below the expected range.

The table below presents information for all three sections. Mean scores are indicated in the third column, where section one is an average of 7.27, section 2 an average of 6.33, and section 3 an average of 7.94. Standard deviation is also indicated in column 4. 

ANOVA

The table below displays a one-way ANOVA test, distinguishing between the significance of differences among the sections. Between-groups degrees of freedom are 2, and within-groups degrees of freedom are 102. The F-value of 10.951 supports there being significant differences between the sections. Also, the p-value of 0.000 against the null hypothesis. The effect size, at 0.246, is large. 

Comparisons

This table depicts the mean difference of every section. Sections 1 and 2 especially depict a mean difference of 0.939, while sections 1 and 3 depict a mean difference of -0.667. All values greater than 0.05 establish significant differences regardless of section. Post hoc analysis indicates that Section 3 performance significantly surpasses the other two sections. 

Conclusion

ANOVA finds a significant difference among the sections. The null hypothesis is rejected in favor of the alternative hypothesis. ANOVA facilitates comparison between more than two variables and is simple to use, but it lacks provision to find out the most influential variable.

Application

This test is found to be effective in numerous real-life scenarios, such as education, as is the situation with this study. It can also be used to optimize results within the healthcare industry, such as with drug therapy and treatment procedures.