Statistical Techniques with R: Weight Change Analysis

This repository contains the R code and report for the COMP1814 coursework, which investigates weight changes in mice and rats following a nutritional supplement treatment using simulation, visualization, hypothesis testing, and distribution fitting.

Contents

.
├── main.R                            # Complete R script with data generation, visualization, tests, and fitting
├── Report.pdf                        # Coursework Report 
├── distribution_fits_comparison.pdf  # Plots comparing fitted distributions (Weibull, Lognormal, Gamma)
└── README_R.md                       # This file

Project Overview

In this analysis, we:

1. Generated synthetic data for:

   • Mice weights before/after treatment (Normal distribution)
   • Rats weights before/after treatment (Weibull distribution)

2. Visualized weight distributions using density plots and boxplots.

3. Assessed normality with Q–Q plots and the Shapiro–Wilk test.

4. Performed hypothesis tests:

   • Paired t-test for normally distributed mice data.
   • Wilcoxon signed‑rank test for rats data (non‑normal).

5. Fitted distributions (Weibull, Lognormal, Gamma) to the post‑treatment rats data and compared fits with density, CDF, Q–Q, and P–P plots.

Prerequisites

• R version ≥ 4.0.0

• Installed packages:

  • ggplot2
  • fitdistrplus

You can install missing packages with:

install.packages(c("ggplot2", "fitdistrplus"))

Running the Analysis

1. Open R or RStudio in this project directory.

2. Source the script or run it line by line:

   source("main.R")

3. The script will:

   • Generate and store synthetic datasets in memory.
   • Produce and display density and boxplots for both species.
   • Output results of normality tests and hypothesis tests in the console.
   • Save distribution fitting comparison plots to distribution_fits_comparison.pdf.

Key Results

• Mice paired t-test showed a significant weight increase after treatment (t = –7.29, p < 1e–10).
• Rats Wilcoxon test indicated a significant median change (V = 6503, p ≈ 1.5e–5).
• Among fitted models for rats post‑treatment data, the [best‑fitting distribution] can be judged visually from the PDF plots.

References

• Wickham, H., & Grolemund, G. (2017). R for Data Science. O’Reilly Media.

License

This coursework is distributed under CC BY‑NC‑SA 4.0. Please see the accompanying report for detailed attributions.