User Guide for Shiny App: Academic, Work and Life Analysis

Author

Affiliation

510119533

The University of Sydney

1 Overview

This Shiny app provides a statistical analysis of survey data exploring the relationship among academic, life and work.

Users can perform normality tests, independence tests between categorical variables, and hypothesis testing using the Wilcoxon rank-sum and permutation tests.

The app allows you to:

Analyze the normality of numerical variables.
Test the independence of categorical variables.
Compare numerical variables between two groups (e.g., WAM levels or target grades) using the Wilcoxon rank-sum and permutation tests.

2 Key Features

2.1 Normality Tests (Numerical Variables Analysis)

Motivation: To determine if numerical variables follow a normal distribution, which is a key assumption for many statistical tests.
Boxplots: Visualize the distribution of a selected numerical variable grouped by a categorical variable.
Q-Q Plots: Assess how closely data follows a normal distribution by comparing observed and theoretical quantiles.
Goodness of Fit Tests: Use chi-square tests, Monte Carlo simulations, and Shapiro-Wilk tests to check for normality.

2.1.1 How to Use:

Choose a numerical variable and a categorical variable to view the distribution via boxplots and Q-Q plots.
Click “Show Overall Data” to view the overall distribution across all categories.

2.2 Independence Tests Between Categorical Variables

Motivation: Test whether two categorical variables are independent of each other, which helps explore relationships like exercise habits and academic performance.
Chi-Square Test for Independence: Calculates whether the observed frequency of categories matches the expected frequency under the assumption of independence.

2.2.1 How to Use:

Select two categorical variables to test for independence.
The results will be displayed along with a summary of the categorical variables.

2.3 Wilcoxon Rank-Sum Test & Permutation Test

Motivation: Investigate whether students have(or aiming for) high grades differ in their lifestyle habits or other categories, compared to students with less high grades (targets).
Wilcoxon Rank-Sum Test: A non-parametric test comparing the ranks of two groups (e.g., “Distinction and Above” vs. “Below Distinction”) for a numerical variable.
Permutation Test: Provides an additional check by randomly shuffling group labels to generate the null distribution and calculate the p-value.

2.3.1 How to Use:

Select a grouping variable (e.g., WAM level or Target Group) and a numerical variable (e.g., weekly exercise hours).
The app will display a boxplot and run both the Wilcoxon rank-sum test and the permutation test.
Review the p-values to determine if the groups differ significantly.

3 How to Navigate the App

3.2 Main Panels

Each section of the app has dedicated panels that display the results of statistical tests, plots (boxplots and Q-Q plots), and summaries.

3.3 Input Controls

Categorical Selection: Select categorical variables such as target grade or wam level.
Numerical Variable Selection: Select numerical variables such as weekly exercise hours or study hours.

4 Limitations

Small Sample Size: Statistical power may be affected if the sample size is too small.
Survey Bias: Self-reported data might be subject to biases, such as recall or social desirability biases.
Simplified Groupings: The app groups target grades and WAM levels into two broad categories (e.g., “Distinction and Above” vs. “Below Distinction”), potentially losing finer details.

5 Capabilities and Limitations

5.1 Capabilities:

Perform standard normality tests for numerical variables.
Test independence between categorical variables using chi-square tests.
Conduct non-parametric Wilcoxon rank-sum tests and permutation tests to compare numerical variables across groups.
Present data visually through interactive boxplots and Q-Q plots.

5.2 Limitations:

Assumptions: Certain tests assume independence of observations and that the distributions of the numerical variables are similar across groups. Violations of these assumptions may affect the results.
Binning: The categorization of WAM levels and target grades might simplify the analysis but can also obscure subtler differences.
Biases in Survey Data: As with all survey data, biases related to response accuracy and interpretation may exist.

6 How to Interpret Results

6.1 Normality Tests:

If the p-value (especially from the Shapiro-Wilk test) is less than 0.05, the data significantly deviates from normality.
If the p-value is greater than 0.05, there is no strong evidence against normality.

6.2 Independence Tests:

If a p-value less than 0.05 in the chi-square test, it would suggest that the two categorical variables are not independent.
If a p-value greater than 0.05 in the chi-square test, it would suggest that the two categorical variables are independent.

6.3 Wilcoxon Rank-Sum and Permutation Tests:

If the p-values are less than 0.05, this suggests a significant difference in the numerical variable between the groups.
If the p-values from both tests are greater than 0.05, there is no significant difference between the groups.

7 Conclusion

This app provides a comprehensive platform for analyzing survey data related to student life, work and academic performance.

By offering visualizations, normality testing, and hypothesis testing, it allows users to explore relationships among various factors.

--- title: "User Guide for Shiny App: Academic, Work and Life Analysis" author: "510119533" institute: "The University of Sydney" #date: "`r format(Sys.time(), '%d %B, %Y %H:%M')`" bibliography: [refs/bibliography.bibtex, refs/Packages.bib,refs/citations.bib ] csl: apa.csl format: html: embed-resources: true # Creates a single HTML file as output code-fold: true # Code folding; allows you to show/hide code chunks code-tools: true # Includes a menu to download the code file table-of-contents: true # (Optional) Creates a table of contents! number-sections: true # (Optional) Puts numbers next to heading/subheadings --- # Overview This Shiny app provides a statistical analysis of survey data exploring the relationship among academic, life and work. Users can perform normality tests, independence tests between categorical variables, and hypothesis testing using the Wilcoxon rank-sum and permutation tests. The app allows you to: - Analyze the normality of numerical variables. - Test the independence of categorical variables. - Compare numerical variables between two groups (e.g., WAM levels or target grades) using the Wilcoxon rank-sum and permutation tests. # Key Features ## Normality Tests (Numerical Variables Analysis) - **Motivation**: To determine if numerical variables follow a normal distribution, which is a key assumption for many statistical tests. - **Boxplots**: Visualize the distribution of a selected numerical variable grouped by a categorical variable. - **Q-Q Plots**: Assess how closely data follows a normal distribution by comparing observed and theoretical quantiles. - **Goodness of Fit Tests**: Use chi-square tests, Monte Carlo simulations, and Shapiro-Wilk tests to check for normality. ### How to Use: - Choose a numerical variable and a categorical variable to view the distribution via boxplots and Q-Q plots. - Click “Show Overall Data” to view the overall distribution across all categories. ## Independence Tests Between Categorical Variables - **Motivation**: Test whether two categorical variables are independent of each other, which helps explore relationships like exercise habits and academic performance. - **Chi-Square Test for Independence**: Calculates whether the observed frequency of categories matches the expected frequency under the assumption of independence. ### How to Use: - Select two categorical variables to test for independence. - The results will be displayed along with a summary of the categorical variables. ## Wilcoxon Rank-Sum Test & Permutation Test - **Motivation**: Investigate whether students have(or aiming for) high grades differ in their lifestyle habits or other categories, compared to students with less high grades (targets). - **Wilcoxon Rank-Sum Test**: A non-parametric test comparing the ranks of two groups (e.g., “Distinction and Above” vs. “Below Distinction”) for a numerical variable. - **Permutation Test**: Provides an additional check by randomly shuffling group labels to generate the null distribution and calculate the p-value. ### How to Use: - Select a grouping variable (e.g., WAM level or Target Group) and a numerical variable (e.g., weekly exercise hours). - The app will display a boxplot and run both the Wilcoxon rank-sum test and the permutation test. - Review the p-values to determine if the groups differ significantly. # How to Navigate the App ## Sidebar - **About**: Provides background information about the app. - **Numerical Variables Analysis**: Allows you to test the normality of numerical variables. - **Independence Test**: Tests the relationship between two categorical variables. - **Wilcoxon Rank-Sum Test**: Compares numerical variables between two groups based on academic performance. ## Main Panels Each section of the app has dedicated panels that display the results of statistical tests, plots (boxplots and Q-Q plots), and summaries. ## Input Controls - **Categorical Selection**: Select categorical variables such as target grade or wam level. - **Numerical Variable Selection**: Select numerical variables such as weekly exercise hours or study hours. # Limitations - **Small Sample Size**: Statistical power may be affected if the sample size is too small. - **Survey Bias**: Self-reported data might be subject to biases, such as recall or social desirability biases. - **Simplified Groupings**: The app groups target grades and WAM levels into two broad categories (e.g., "Distinction and Above" vs. "Below Distinction"), potentially losing finer details. # Capabilities and Limitations ## Capabilities: - Perform standard normality tests for numerical variables. - Test independence between categorical variables using chi-square tests. - Conduct non-parametric Wilcoxon rank-sum tests and permutation tests to compare numerical variables across groups. - Present data visually through interactive boxplots and Q-Q plots. ## Limitations: - **Assumptions**: Certain tests assume independence of observations and that the distributions of the numerical variables are similar across groups. Violations of these assumptions may affect the results. - **Binning**: The categorization of WAM levels and target grades might simplify the analysis but can also obscure subtler differences. - **Biases in Survey Data**: As with all survey data, biases related to response accuracy and interpretation may exist. # How to Interpret Results ## Normality Tests: - If the p-value (especially from the Shapiro-Wilk test) is **less than 0.05**, the data significantly deviates from normality. - If the p-value is **greater than 0.05**, there is no strong evidence against normality. ## Independence Tests: - If a **p-value less than 0.05** in the chi-square test, it would suggest that the two categorical variables are not independent. - If a **p-value greater than 0.05** in the chi-square test, it would suggest that the two categorical variables are independent. ## Wilcoxon Rank-Sum and Permutation Tests: - If the p-values are **less than 0.05**, this suggests a significant difference in the numerical variable between the groups. - If the p-values from both tests are **greater than 0.05**, there is no significant difference between the groups. # Conclusion This app provides a comprehensive platform for analyzing survey data related to student life, work and academic performance. By offering visualizations, normality testing, and hypothesis testing, it allows users to explore relationships among various factors.