What is a design matrix | Lecture 10 class notes | by Trevor Caughlin in Spring 2026, EEB622.

This project applied exploratory data analysis and visualization techniques to investigate whether federal IIJA funding distribution reveals political bias by examining total funding, per capita allocation, and population-funding ratios across all 50 states. Using dumbbell plots, diverging bar charts, choropleth maps, and scatter plots, the analysis layers multiple perspectives to guide the viewer through a data-driven narrative — from broad national patterns to state-level exceptions. The visualizations demonstrated that per capita funding favors smaller, predominantly Red states, suggesting that formula-based allocation and infrastructure need outweigh political affiliation in determining federal funding distribution.

Class Assignment 5

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This analysis uses NHANES data to examine bone mineral density (BMD) through one-way ANOVA and correlation methods. Part 1 tests whether BMD differs across five ethnic groups, including assumption checks, effect size calculation, and post-hoc comparisons. Results show significant ethnic differences (p < 0.001), with Non-Hispanic Black individuals having higher BMD. Part 2 explores correlations between BMD and potential predictors (age, BMI, calcium, vitamin D, physical activity) using transformed variables. BMI shows the strongest association with BMD (r = 0.425), while age shows a negative relationship (r = -0.232). Part 3 reflects on methodological choices, assumption challenges, and R programming skills developed during the analysis. Methods: R with tidyverse, ggplot2, broom, and car packages.