Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Module: Week 4 of 16 · Fall 2026 · in-person, two 75-minute sessions
Objective covered: Objective 3 — Describe the relationship between two variables.

This file holds two pieces: (A) the Module 4 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. Dates below assume a Tuesday/Thursday session pattern with Week 4 meeting Tue Sep 22 and Thu Sep 24, and end-of-week work due Sunday Sep 27, 11:59 p.m. Adjust the day-of-week and times to match your section.

(A) Module 4 Overview — Start Here

Welcome to Week 4: Exploring Relationships

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 we've described one variable at a time — where data comes from, how to picture it, and how to summarize its center and spread. This week we put two variables side by side and ask how they move together. It's also where we meet the single most misused idea in all of statistics: just because two things rise and fall together does not mean one causes the other. By Friday you'll be able to take any "X is linked to Y" headline and pick it apart.

The week's big question

"When two things move together, what is the data actually telling us — and what is it absolutely not telling us?"

By Friday you'll be able to do three things with any reported relationship: picture it (a scatterplot), measure it (one number, the correlation r), and question it (is it a real cause, or a hidden third variable in disguise?).

By the end of this week, you can…

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

• [ ] Read a scatterplot and describe its direction, form, and strength (remember D-F-S), and spot any outliers.
• [ ] Interpret a correlation r — use its sign for direction and its size (how close to ±1) for strength — and name what r does not tell you (it only sees straight lines, has no units, isn't a percent, and never proves cause).
• [ ] Build and read a two-way table — compute a marginal proportion (÷ the grand total) and a conditional proportion (÷ one group's total) and compare two groups.
• [ ] Name a lurking (confounding) variable in a claimed relationship and explain why correlation isn't causation.

What's due this week, and when

Work these in order — each one gets you ready for the next.

Heads-up on the AI tutorial: you'll use a chatbot to draft, and then you judge its work against what we cover in class. Chatbots routinely slip here — ask one whether "sending fewer firefighters reduces fire damage" (because the two are correlated) and watch whether it catches the lurking variable, the size of the fire. Catching the model is the point.

Late policy reminder: 10% off per day late. If life happens, reach out before the deadline — I'd much rather hear from you early.

How to succeed this week

• Picture before number. Always look at the scatterplot — direction, form, strength — before you trust the correlation. A correlation near 0 can still hide a strong curved relationship; the picture catches what the number misses.
• Memorize the tiny hooks. "D-F-S" for describing a scatterplot. "r is a thermometer for a straight line" — sign for direction, size for tightness, nothing else. And for tables: "Marginal = ÷ grand total; conditional = ÷ one group's total — the word given picks the denominator."
• Don't divide by the wrong total. On a two-way table, "of the students who exercise" means divide by that group's total, not everyone. The phrase after "of" or "given" is your denominator.
• Remember the headline lesson: correlation isn't causation. When two things move together, ask who else is in the room — name a lurking variable, and check whether anything was actually randomly assigned. (Ask me about ice cream and drowning.)
• Treat the chatbot as a smart intern, not an oracle. It drafts; you check. That habit is the whole semester in miniature.

You don't need anything from this week memorized in advance — just bring your curiosity and a willingness to question a headline. Come to class ready to argue about whether ice cream is dangerous. See you Tuesday.

(B) Welcome Announcement — Module 4

Release setting: post on the module's start day (offset = 0 days), i.e., Tue Sep 22, 2026 — not before. If your platform won't preserve the scheduled date on import, post this as a draft labeled "Release: Tue Sep 22."

Subject: Week 4 — does ice cream really cause drowning? 🍦

Hi everyone,

Quick one before class: there's a real, repeatable pattern in the data that says people who eat more ice cream are more likely to drown. The numbers don't lie. So… should we ban ice cream at the beach?

Obviously not — it's summer that drives both the ice cream and the swimming. That gap, between two things moving together and one thing causing the other, is the heart of Week 4, and it's the most misused idea in all of statistics.

This week — Exploring Relationships — we put two variables side by side and learn to do three things with any "X is linked to Y" claim: picture it (a scatterplot), measure it (the correlation r, a single number between −1 and +1), and question it (is it a real cause, or a hidden third variable?). We'll also build two-way tables to compare groups with conditional proportions.

What's due (all close Sun Sep 27, 11:59 p.m., except the discussion's first post):
1. Lecture Tutorial 4 — scatterplots, correlation, two-way tables, and lurking variables, with one approved chatbot (Gemini, Claude, or ChatGPT); submit the share link.
2. Quiz 4 — the week's ideas, auto-graded.
3. Discussion 4 — "Linked, or caused?" — find a real "X linked to Y" headline and reason whether it's causal or a lurking variable; initial post Fri Sep 25, replies by Sun Sep 27.
4. Assignment 4 — "Reading a Relationship" — four problems, coached and graded by your chatbot; submit the report + chat link.

One promise, same as always: this is a course about thinking clearly, not about being a "math person." Lead with the picture and the plain-language idea; the number comes second. After this week, you'll never read a "studies show" headline the same way.

Open the Start Here / Module Overview page first — it lays out everything in order with due dates. Bring your curiosity (and an opinion about whether ice cream is dangerous) to class on Tuesday.

See you soon,
Prof. Rivera