wangx53_final_draft.Rmd

---
title: "Data Analytics Research Individual Final Project Report"
author: "Evangeline Wang"
date: "Fall 2024"
output:
  pdf_document:
    toc: yes
    toc_depth: '3'
  html_notebook: default
  html_document:
    toc: yes
    toc_depth: 3
    toc_float: yes
    number_sections: yes
    theme: united
---

# DAR Project and Group Members

* Project name: MARS 
* Project team members: 
  - Xuanting Wang (Primary Contributor)

# 0.0 Preliminaries

This report includes the analysis and findings on Martian sample composition patterns using data from the Perseverance rover’s PIXL and LIBS instruments. Required R packages include:

* `ggplot2`
* `tidyverse`
* `ggtern`
* Additional packages are installed and loaded as necessary.

```{r, include=FALSE}
# Install required packages if not already installed
packages <- c("ggplot2", "tidyverse", "dplyr", "ggtern")
for (pkg in packages) {
  if (!require(pkg, character.only = TRUE)) {
    install.packages(pkg, dependencies = TRUE)
    library(pkg, character.only = TRUE)
  }
}
```

# 1.0 Project Introduction

This project investigates the chemical composition of Martian samples across campaigns using PIXL and LIBS datasets. Key objectives include:

- Identifying patterns in cation group compositions (Si-Al, Fe-Mg, Ca-Na-K).
- Assessing variations across campaigns using statistical analysis.
- Comparing insights derived from PIXL and LIBS data.

Data analysis involved methods such as ANOVA, post-hoc tests, and logistic regression for campaign classification based on cation group compositions.

# 2.0 Organization of Report

This report is organized as follows:

- **Section 3.0:** PIXL Data Analysis – Findings and visualizations.
- **Section 4.0:** LIBS Data Analysis – Results and comparisons.
- **Section 5.0:** Conclusions, limitations, and future directions.
- **Section 6.0:** Appendix – Supplementary materials.

# 3.0 PIXL Data Analysis

## 3.1 Data and Methods

PIXL datasets were processed to calculate the cation group sums:

- **Si-Al:** Sum of \( SiO_2 \) and \( Al_2O_3 \).
- **Fe-Mg:** Sum of \( FeO-T \) and \( MgO \).
- **Ca-Na-K:** Sum of \( CaO \), \( Na_2O \), and \( K_2O \).

Samples were classified based on the largest cation group proportion. Statistical methods included:

- ANOVA for campaign-based differences.
- Dunn’s post-hoc tests for pairwise comparisons.
- Logistic regression for campaign classification.

## 3.2 Findings

1. **Classification Results:**
   - **Si-Al rich:** Majority of samples (11).
   - **Fe-Mg rich:** Fewer samples (5).
   - **Ca-Na-K rich:** Minimal samples.

2. **Statistical Results:**
   - ANOVA indicated significant differences in Si-Al (p = 0.0014) and Ca-Na-K (p = 0.0136) across campaigns.
   - Fe-Mg showed marginal significance (p = 0.0791).

3. **Post-hoc Test Results:**
   - Significant differences in Si-Al and Ca-Na-K between Crater Floor and Delta Front.

4. **Logistic Regression:**
   - Limited predictive power for campaign classification using cation compositions.

## 3.3 Visualizations

- **Ternary Plot:** Proportional distribution of cation groups.
- **Density Plots:** Distribution patterns of Si-Al, Fe-Mg, and Ca-Na-K.
- **Box Plots:** Campaign-specific variations in cation concentrations.

# 4.0 LIBS Data Analysis

## 4.1 Data and Methods

LIBS data followed the same processing pipeline as PIXL. The analysis included:

- Campaign-based classification.
- Statistical tests (ANOVA and Dunn’s test).
- Comparisons between LIBS and PIXL results.

## 4.2 Findings

1. **Classification Results:**
   - Si-Al rich (majority), Fe-Mg rich, and Ca-Na-K rich distributions mirrored PIXL trends.

2. **Statistical Results:**
   - Significant variations were observed in all cation groups (p < 0.0001) across campaigns.

3. **Post-hoc Test Results:**
   - Clear differences between Campaign 3 and the other campaigns.

4. **Logistic Regression:**
   - Fe-Mg showed some predictive strength in distinguishing campaigns.

## 4.3 Visualizations

- **Ternary Plot:** Similar trends as PIXL.
- **Box Plots:** Campaign-specific distributions.

# 5.0 Conclusions, Limitations, and Future Work

## 5.1 Conclusions

- Both datasets showed consistent compositional trends, with Campaign 3 exhibiting distinct patterns.
- Significant differences were noted in Si-Al, Fe-Mg, and Ca-Na-K across campaigns.

## 5.2 Limitations

- Limited predictive power in logistic regression models.
- Variability in sample sizes may affect statistical robustness.

## 5.3 Recommendations

- Incorporate additional datasets (e.g., SHERLOC) for broader insights.
- Explore machine learning models for improved classification accuracy.

# 6.0 Appendix

## Supplementary Figures

- Extended ternary plots, density plots, and box plots.
- Statistical tables summarizing ANOVA and post-hoc results.

## References

1. PIXL and LIBS Data Documentation.
2. R Documentation for ggplot2 and tidyverse.