Title: Week 16 Overview — Start Here
Course: Introduction to Statistics (18-Week Generic Edition)

Welcome to Week 16: Chi-Square Tests for Categorical Data

This is your home base for the week. Read it first, then work the checklist below from top to bottom. Everything you need is linked inside the module.

For three weeks you've tested claims about means and proportions — one number at a time. But so much of the world arrives as a whole table of category counts: the color mix in a candy bag, customers by weekday, T-shirt orders by size, pets by housing type. This week you get the one machine that judges an entire table in a single move — the chi-square test — and you'll aim it at the biggest table of the term: the penguins' species-by-island map.

The week's big question

"A company claims a mix; your counts don't quite match it. Is the drift ordinary luck — or is the claim wrong? And when two category tables tangle, are the variables actually linked?"

By the end of the week you'll be able to put any table of counts on trial: build what the claim predicts, measure the drift with one number, and deliver the verdict in careful words.

By the end of this week, you can…

Use this as a checklist. If you can do all five out loud, you're ready for the quiz.

- [ ] Build expected counts — from a claimed distribution (n × claimed proportion) or from independence (row total × column total ÷ grand total).
- [ ] Compute χ² = Σ (O − E)² ⁄ E and its degrees of freedom (k − 1 for goodness-of-fit; (r − 1)(c − 1) for independence — a 3 × 3 table has df 4, not 8).
- [ ] Run a goodness-of-fit test start to finish against the critical-value mini table, checking the conditions first (random data · raw counts · every expected count ≥ 5).
- [ ] Read the contributions — rank categories by (O − E)² ⁄ E, never by the biggest count, to say where a table went off-script.
- [ ] Conclude carefully — "fail to reject = consistent with, never proven," and "a significant association is never a cause."

What to do this week, in order

The table below lists the week's items in working order, with what each is worth and when it's due.

# | Do this | Type | Due
1 | Read Chapter 16 — the module's primary reading (it carries the chi-square critical-value mini table) | Chapter (ungraded prep) | Early in the week
2 | Skim the slides (Deck 16) and the Week 16 lecture outline; browse the Readings & Resources links that interest you | Prep (ungraded) | Alongside class
3 | Lecture Tutorial 16 — work through the week's ideas with your chatbot (mini table included), then submit the share link + Completion Summary | Tutorial · graded (Lecture tutorials, 20% group) | End of Week 16
4 | Practice exercises — quick reps with the AI coach | Practice · ungraded | Before the quiz (recommended)
5 | Data Lab 16 — "Species, Islands, and One Giant Chi-Square" — build the penguins' species × island table from raw data and run a full test of independence (your χ² will land near 300 — and you'll explain why) | Data lab · graded (Data labs, 15% group) | End of Week 16
6 | Quiz 16 — expected counts, χ², df, conditions, contributions, careful conclusions | Quiz · graded (Quizzes, 15% group) · closed to AI | End of Week 16
7 | Discussion 16 — "Rigged, or Random?" — put your own "this is rigged" theory on trial with your chatbot, post the AI summary + chat link, then reply to two classmates | Discussion · graded (Discussions, 15% group) | Initial post two days before week's end; replies by end of Week 16
8 | Assignment 16 — "The Claim vs. the Counts" — four AI-coached problems; submit the report (score on line 1) + chat link | Assignment · graded (Assignments, 25% group) | End of Week 16

Heads-up on the AI work: in this course the chatbot drafts, and you judge. Chatbots reliably fumble chi-square plumbing — they'll answer df = 8 for a 3 × 3 table (it's 4), quote critical values from memory that miss the table, and claim observed zeros break the test (the ≥ 5 rule is about expected counts). Catching the model is the point, and this week's lab makes you do exactly that.

Late policy reminder: 10% off per day late. If life happens, reach out to your instructor before the deadline — early is always easier.

How to succeed this week

- Memorize one formula and one recipe. χ² = Σ (O − E)² ⁄ E — gap, squared, scaled, summed. Recipe: claim → expected counts → conditions → χ² → df → compare → conclude carefully.
- Let the mini table referee. χ² has no universal scale — 6 rejects at df 1 and doesn't at df 3. Every verdict comes from the df-matched critical value (df 1–4 are in Chapter 16), never from a gut feeling about "big."
- Say the two guardrail sentences until they're automatic. "Fail to reject — consistent with the claim, not proven." And "associated, not caused — χ² can convict the table, never the cause."
- Rank by surprise, not size. The biggest observed count is often not the biggest problem — read the contributions, (O − E)² ⁄ E, to find where the table really went off-script.
- Treat the chatbot as a smart intern, not an oracle. It drafts; you check its df, its expected counts, and its critical values against the mini table. That habit is literally graded in the lab.

One more week of new machinery after this — regression — and then the final caps the story. You're one tool away from the complete kit.