Notes

The weekly analysis-blueprint spine — question to estimate to conclusion

The notes are the backbone of the course. There is one note per week, and reading the current week’s note before class — and again after — is the single most reliable way to keep up. Every note follows the same shape, so once you learn to read one, you can read them all. That shape is not decoration: it is the course. Each week walks the same six-step analysis blueprint, applied to a new method, so by the end you are not memorizing a box of named tests — you are running one disciplined workflow on whatever data structure lands in front of you.

This is a draft course site: the example datasets are synthetic, the numbers are drafted and provisional, and R is shown but not executed. Read the methods and the reasoning as the course’s own; treat every printed statistic as illustrative until the verification sign-off is complete.

The analysis blueprint — the six questions every note answers

Every method in this course — the paired \(t\), the two-sample \(t\), one-way and two-way ANOVA, ANCOVA, simple and multiple regression, the chi-square test, and logistic regression — is one instance of the same blueprint. When you meet a new method, you are not learning a new ritual; you are filling in the same six steps with new specifics. Hold these six questions in mind on every page:

Question. Are you comparing, explaining, or predicting? The plain-English question comes first; the machinery follows from it.
Structure. What is the unit of analysis? Which variable is the response (\(Y\)) and which are explanatory, grouping, or covariate? What type is the outcome — quantitative, categorical, or binary? And what is the design — paired vs independent, one factor vs two, observational vs experimental?
Method. Which analysis matches that structure — and why this one and not a neighbor? (Why a paired \(t\) and not a two-sample \(t\); why Welch and not pooled; why ANCOVA and not a raw group comparison.)
Assumptions & diagnostics. What does the method assume, and how do you check it — with a plot, a test, a residual, a leverage value?
Estimate & uncertainty. What does the model actually estimate — a mean difference, an effect size, a slope, an odds ratio — reported with a confidence interval, never as a bare p-value?
Conclusion. Is the result statistically significant, practically important, or both? Does the design buy association or causation? What can this analysis not support?

Two disciplines live inside the blueprint and recur on every single page, so watch for them by name:

Report the estimate, not just a verdict. An effect size and an interval — a mean difference of \(6\) points with a 95% CI of \((1.3, 10.7)\) — tells you far more than “significant, \(p = 0.013\).” A lone p-value is never the answer.
Keep three things distinct: statistical significance, practical significance, and causation. A small p-value does not make an effect large, and an observational comparison — where people chose their group — buys you association, not causation, no matter how clean the output looks.

This course is deliberately four things it is not, and the notes resist all four drifts. It is not generic intro statistics (descriptive summaries, the normal model, and a single one-sample t-test are assumed background); not a pure R/software course (the code carries out the fit, but the method’s logic is the message); not a formula-only methods course (the point is to map question → structure → method → estimate → conclusion and to read real output, not to memorize a sampling distribution); and not a disconnected catalog of named tests (every test is one expression of the one blueprint).

How to read a week

Each weekly note is built from the same parts, in the same order. Knowing the anatomy lets you skim for what you need and study with intent — and each part maps onto a step of the blueprint above:

The week question. A single plain-English question the week exists to answer (blueprint step 1). Hold it in mind as you read; everything else is in service of it.
Why this matters and Learning goals. Where the week sits in the arc, and what you should be able to do by the end — “By the end of this week you should be able to…”.
Core vocabulary. The structural words the week leans on — response vs explanatory vs covariate, paired vs independent, main effect vs interaction, log-odds vs odds ratio vs probability — defined where you can find them.
Concept development. The core ideas, built up in a few short sections from intuition toward a precise statement of what the method assumes and what it estimates (blueprint steps 2–5). This is the part to read slowly. The method’s logic is shown first; then the locked numeric instance from the week’s dataset makes it concrete.
Worked examples. Each idea is worked on the recurring Cypress Ridge College Student-Success world — the paired pre/post readiness scores, the Support-vs-Self-guided final exam comparison, final score by instructional format, the Delivery × Background factorial, or the study-hours/pass-fail regression data — with the question and structure stated, the assumptions checked, the computation shown in R, and the estimate reported with its uncertainty and interpreted in sentences. Each concept week also carries one transfer example in a fresh context, so you see the same blueprint move to new data.
A common mistake. The applied-methods error students most often make on this topic — using the wrong design (paired vs independent), ignoring unequal variance, running many comparisons without error-rate control, misreading an interaction, deleting an influential point, calling an observational association causal, reading a bare p-value as the whole story, or interpreting a logit coefficient as a probability — named plainly so you can watch for it in your own work.
Low-stakes self-checks (ungraded). A few practice prompts to test yourself. These are self-check only — no points, no submission.
Reading and source pointer. Where to read more: the relevant Introduction to Modern Statistics (IMS) topic on nearly every week; ModernDive on the computational and reporting weeks; Introductory Statistics for the Life and Biomedical Sciences (ISLBS) on the applied-lab weeks; and Learning Statistics with R (Navarro) named only as an optional pointer — with the reminder that these notes are the course’s own synthesis, grounded in but not copied from the sources.
Evidence and verification status. An honest note that every numeric value in the example datasets is drafted, synthetic (\(\texttt{set.seed(35203)}\)), and not independently checked — R is not executed in this build, and the worked numbers are provisional and not independently verified.
Looking ahead. A sentence or two connecting this week to the next, so the arc stays visible.

Keep the methods glossary, the method chooser (the question → structure → method decision guide), the assumptions and diagnostics guide, and the reporting and interpretation guide open alongside the notes.

The four parts

The fifteen weeks fall into four parts. Each part has a job, and the weeks within it build on one another. The same six-step blueprint runs through all of them; what changes is the data structure — and therefore the method, the estimate, and what you can conclude.

Part I — Questions, structure & estimation (weeks 1–3). Before any test, you learn to read a question, name the data structure, look at the data, and report an estimate with its uncertainty. This is the blueprint in miniature, established once so every later week can lean on it.

Week 1 — Statistical questions, data structure & applied workflow
Week 2 — Exploratory analysis & graphical comparison
Week 3 — Estimation, uncertainty & practical significance (Labor Day falls in this week — Mon Sep 7 has no class, so week 3 runs W/F compressed.)

Part II — Comparing groups (weeks 4–9). The heart of the course: comparing one or many groups, getting the design right (paired vs independent, one factor vs two), checking assumptions, controlling error rates across many comparisons, and reading an interaction before a main effect. The midterm (Fri Oct 9, in class) lands in week 7 and covers weeks 1–7.

Part III — Models, covariates & categorical data (weeks 10–13). From comparing groups to modeling outcomes: regression and the difference between a raw and an adjusted slope, ANCOVA and covariate adjustment, and then categorical and binary outcomes — contingency tables and logistic regression. This is where the confounding → adjustment → association-vs-causation thread is sharpest.

Week 10 — Simple & multiple regression review
Week 11 — ANCOVA & adjustment
Week 12 — Categorical outcomes & contingency tables
Week 13 — Logistic regression for binary outcomes (Fall break, Nov 22–28, falls between weeks 13 and 14 — no classes.)

Part IV — Reporting & synthesis (weeks 14–15). Turning an analysis into an honest, clearly-bounded report, then stepping back to see the whole blueprint at once across the five datasets.

Week 14 — Applied analysis report workshop
Week 15 — Applied methods synthesis & review (Last class is Mon Dec 7; the final-exam window is Dec 9–15, with the exact block posted via Blackboard.)

One coherent synthetic world — the Cypress Ridge College Student-Success Study — runs underneath all four parts, realized as five datasets of different structures (paired, two-group, many-group, two-factor, and a regression/categorical set), so each method is seen exactly where its data structure calls for it. Seeing the same study analyzed five ways is what makes this “models, groups, and categorical data” rather than a test catalog.

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 applied-methods checkpoints, weekly quizzes, homework and analysis memos, applied analysis labs, the midterm, the applied methods project, and the final exam live in Blackboard (the LMS), which is authoritative for due dates, submissions, and grades. If this page and Blackboard ever disagree, follow Blackboard.