Notes

The 15-week note sequence for Statistical Inference

This page is the index to the course’s weekly notes. It explains how a week note is put together, then lists all 15 weeks grouped into the five parts of the course arc, each with a one-line theme.

How a weekly note is built

Every weekly note follows the same anatomy, so that once you know the shape you can navigate any week efficiently. Concept weeks and derivation weeks share most of this shape; derivation weeks add two extra pieces described below.

• The week question. Each note opens by naming, in one or two sentences, the specific question the week answers. This keeps the mathematical machinery tied to a reason for learning it.
• Concept development. The heart of the note: the ideas are built up in stages (multiple ### subsections), moving from intuition toward precise definitions and, where relevant, notation.
• Worked examples. Every week works at least one example symbolically first, then numerically. Worked examples draw on two recurring settings:
  • the recurring “MAC Study” slice — a single running synthetic case (a research team studying use of UA Little Rock’s Math Assistance Center) that is revisited and extended week over week, so the same numbers grow more meaningful as more machinery is added to them; and
  • a transfer example — a second, freshly synthetic case in a different everyday context, so you can check that you can apply the week’s idea somewhere other than the MAC Study. Transfer-example data are always original numbers, clearly flagged as synthetic.
• A common mistake. Every note names at least one misconception or misuse that is common at this stage of learning inference (for example, misreading a p-value or a confidence interval), so the correct interpretation is contrasted directly against the wrong one.
• Low-stakes self-checks (ungraded). Short prompts you can use to test your own understanding before moving on. These are practice only — never graded, never scored, never submitted.
• Reading and source pointer. A pointer to the relevant topic in the course’s primary source (MIT OCW 18.05), and, in the weeks where it is the genuinely-used co-source or an optional lighter alternative, a named pointer to ModernDive or OpenIntro IMS as well.
• Looking ahead. A short bridge to what next week builds on top of this one.

Every note also carries a Public vs. graded section near the end, marking the note as public, ungraded study material, with graded work living in Blackboard — see the boundary note at the bottom of this page for the full statement.

Derivation weeks

Four weeks — Week 4, Week 6, Week 9, and Week 12 — are derivation weeks. Alongside the anatomy above, a derivation week carries one additional piece:

• a notation table (a Symbol | Meaning table) that collects the symbols the derivation needs, so the algebra that follows can be read symbol-by-symbol without ambiguity.

The 15 weeks, grouped into five parts

The course arc runs in five parts, each building on the last. Within a part, weeks are listed in order.

Part I — Foundations of inference (Weeks 1–3)

• Week 1 — What statistical inference is — how a population parameter (μ, π) differs from a sample statistic (x̄, p̂), and why inference exists to bridge them.
• Week 2 — Sampling distributions and simulation — what happens to x̄ across repeated samples, built up by simulation.
• Week 3 — Estimators and standard errors — what makes an estimator good, and how a standard error quantifies its sampling variability.

Part II — Estimation theory (Weeks 4–6)

• Week 4 — Bias, variance, and mean squared error — derivation week: decomposing an estimator’s error into bias and variance.
• Week 5 — Likelihood — how plausible different parameter values are, given the data actually observed.
• Week 6 — Maximum likelihood estimation — derivation week: finding the parameter value that makes the observed data most likely.

Part III — Confidence and testing (Weeks 7–9)

• Week 7 — Confidence intervals (+ midterm) — building and correctly interpreting an interval estimate of a parameter.
• Week 8 — Hypothesis tests and p-values — testing a claim about a parameter against the data, and reading a p-value correctly.
• Week 9 — Error rates, power, and decisions — derivation week: Type I/II error, statistical power, and the trade-offs behind a testing decision.

Part IV — Simulation-based and Bayesian inference (Weeks 10–12)

• Week 10 — Bootstrap inference — building a confidence interval by resampling the data itself, without a normal-theory formula.
• Week 11 — Randomization and permutation tests — testing a comparison by reshuffling group labels rather than assuming a sampling distribution.
• Week 12 — Bayesian inference — derivation week: updating a prior belief into a posterior using observed data.

Part V — Synthesis and application (Weeks 13–15)

• Week 13 — Comparing inferential frameworks — placing frequentist, likelihood-based, bootstrap/permutation, and Bayesian answers to the same question side by side.
• Week 14 — Inference project workshop — a workshop session for choosing and applying at least two inferential methods to a new question.
• Week 15 — Final review and synthesis — a one-day synthesis of the whole MAC Study thread across the term.

Public vs. graded

These notes, the examples, and the practice here are public and ungraded — study material only. No graded prompts, answer keys, rubrics, point values, or due dates appear on this site. Graded inference checkpoints, quizzes, homework, labs, the midterm, the project, and the final live in Blackboard (the LMS), which is authoritative for due dates, submissions, and grades. If this page and Blackboard ever disagree, follow Blackboard.