Course: Introduction to Statistics (18-week generic edition)
Module: Week 16 of 18 · planned around two ~75-minute sessions
Objective covered: Objective 9 — Use chi-square procedures to test claims about categorical data: goodness-of-fit and independence.

This file holds two pieces: (A) the Module 16 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. All timing is relative — "start of Week 16," "end of Week 16" — and maps onto real dates when the adopting instructor sets the term calendar.

(A) Module 16 Overview — Start Here

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.

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.

(B) Welcome Announcement — Module 16

Release setting: drips at the start of Week 16 (offset = 0 days from module start) — not before. If your platform won't preserve the scheduled release on import, post it as a draft labeled "Release: start of Week 16."

Subject: Week 16 — every "this is rigged" argument, settled with one number

Hi everyone,

Quick gut-check: is there something you're privately sure is rigged? The candy bag that shorts your favorite color, the vending machine that eats your coins, the weekday your bus always lets you down? This week you get the tool that settles exactly those arguments — the chi-square test, the machine that judges a whole table of category counts at once.

This week — Chi-Square Tests for Categorical Data — we tackle the big question: when your counts don't match a claim, is that ordinary luck or real evidence? Last week you tested proportions one at a time; now entire tables go on trial — a claimed candy mix, a store's weekday traffic, pets by housing type — using one statistic, χ², and the critical-value table in Chapter 16.

Three things not to miss:
1. Chapter 16 is your primary reading — it carries the week's critical-value mini table, so start there; every other item leans on it.
2. Data Lab 16 brings back our penguins one more time before the finale: you'll build the species × island table from the raw data and run a full test of independence on it. Your chi-square will land near 300 — the biggest of the term — and the best part is explaining what it does and doesn't prove. Due at the end of Week 16.
3. Discussion 16 ("Rigged, or Random?") wants your initial post two days before the week ends — bring your own rigged theory and put it on trial.

Plus the usuals: Lecture Tutorial 16 (your chatbot becomes a chi-square tutor — share link + summary), Quiz 16 (closed to AI), and Assignment 16 ("The Claim vs. the Counts", AI-coached with retries).

One heads-up carried over from last week's momentum: after this, only regression remains — then the cumulative final (a low-stakes checkpoint; its whole prep bundle lives in the Week 18 module). You are one tool away from the complete kit.

Open the Start Here / Module Overview page first — it lays out everything in order with due points. Bring a "rigged" theory you're willing to test.

See you in the course!