Weekly notes

STAT 45203 · one method page per week

Original instructor-authored notes. Data is synthetic. Open texts are conceptual companions cited by section only (see Open readings & attribution). Ungraded; Blackboard is authoritative for graded work.

Each week’s page follows the same shape: a picture and a worked example first, then the idea in plain language with live-text math, a common mistake to avoid, ungraded practice, and a short bridge to the next week. The through-line is a single question — what is fragile here, and what can we still say?

First half — seeing variability without a formula

  1. Why assumption-light methods? — models, assumptions, and reading a dataset for what is fragile.
  2. Order statistics, ranks, and empirical distributions — quantiles, the median, ranks, and the ECDF as a distribution-free summary.
  3. Permutation logic — what a null hypothesis lets us shuffle, and what it must hold fixed.
  4. Randomization tests — design-based inference and p-values from simulated reassignments.
  5. Bootstrap distributions — resampling with replacement to see how a statistic wobbles.
  6. Bootstrap confidence intervals — percentile intervals, what they assume, and where they fail.
  7. Rank-based one-sample and paired methods — sign and signed-rank tests for one sample and matched pairs. (Midterm this week.)

Second half — ranks, robustness, and comparison

  1. Two-sample rank methods — the rank-sum test and what a location shift does and does not claim.
  2. Categorical and ordinal outcomes — contingency tables, exact logic, and honoring the measurement scale.
  3. Robust summaries and outliers — median, trimmed mean, MAD, and reading influence without deleting data.
  4. Robust regression ideas — why least squares is sensitive, and what a resistant fit changes.
  5. Comparing parametric and nonparametric conclusions — agreement, divergence, and honest reporting.
  6. Simulation study of method behavior — Type I error, power, bias, and coverage as things you can measure.
  7. Applied robust-methods report — the project workshop: turning a comparison into a defensible report.
  8. Final review — synthesis: choosing a method for a purpose.