Course: Introduction to Statistics (18-week generic edition)
Module: Week 4 of 18 · planned around two ~75-minute sessions
Objective covered: Objective 3 — Describe and interpret relationships between two variables using scatterplots, correlation, and two-way tables.

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. All timing is relative — "start of Week 4," "end of Week 4" — and maps onto real dates when the adopting instructor sets the term calendar.

(A) Module 4 Overview — Start Here

Welcome to Week 4: Relationships Between Two Variables

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 handled one variable at a time — where it comes from, what its picture looks like, its center and spread. This week the course does what your brain already does constantly: it puts two variables side by side. Taller people, bigger shoes? Older car, lower price? More scrolling, worse sleep? Every one of those hunches is a claim about a relationship — and this week you learn to draw it, measure it, table it, and (most importantly) resist the urge to call it a cause.

The week's big question

"When one thing moves, does the other move too — and how do we measure that link without getting fooled into calling it a cause?"

By the end of the week you'll be able to take any claimed link between two things — a scatterplot, a correlation, a table, a headline — and answer three questions: What does the relationship look like? How strong is it? Is it a cause?

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 — name the explanatory (x) and response (y) variables, then describe Direction, Form, Strength — and check for Stragglers.
• [ ] Interpret the correlation coefficient r — sign = direction, size = strength — and recite its rules: between −1 and +1, no units, unmoved by axis-swaps or unit changes, straight-lines-only, and not resistant to outliers.
• [ ] Work a two-way table — compute a marginal distribution (out of everyone) and a conditional distribution (out of one group), and compare conditionals to spot an association.
• [ ] Refuse an unearned arrow — give the three possible explanations for any association and name a plausible lurking variable.

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. This week's machine mistakes are famous: chatbots divide by the wrong total in two-way tables (the joint 40/200 or wrong-group 40/70 instead of the conditional 40/80) and read r = −0.94 as "a 94% drop" (r is not a percent of anything). Catching exactly these errors is graded in the lab.

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

• Describe scatterplots in a fixed order. Direction, Form, Strength — then check for Stragglers. A description is a sentence in context, not a bare number.
• Read r in two moves. Sign = direction, size = strength. So −0.9 beats +0.5 on strength, and r ≈ 0 only rules out straight-line patterns — an arch can hide there.
• Let the denominator do the thinking. Marginal = out of everyone; conditional = out of the "among ___" group. Find the group first; its total is your denominator.
• Compare conditionals to catch an association. Different conditional percents across groups = associated. Equal(ish) = not.
• Keep Week 1's line handy — upgraded. Correlation is a handshake, not a push — and before you believe a push, hunt the third hand. Three explanations exist for every association; observational data can't pick among them.

You measured one variable; now you can measure a link. Come to the first session ready to argue about whether your phone ruins your sleep — or just attends the ruin.

(B) Welcome Announcement — Module 4

Release setting: drips at the start of Week 4 (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 4."

Subject: Welcome to Week 4 — two variables at a time

Hi everyone,

Nice work last week — you can now take any single column of data and tell its whole story: shape, center, spread, and the outliers that distort it. This week, the natural next question: what happens when two columns move together?

This week — Relationships Between Two Variables — we tackle the big question: When one thing moves, does the other move too — and how do we measure that link without calling it a cause? You'll read scatterplots like sentences (direction, form, strength), compress a whole cloud of dots into one number (the correlation r), untangle two kinds of percent inside two-way tables — and learn why even a gorgeous correlation never proves an arrow.

Three things not to miss:
1. Chapter 4 is your primary reading — start there; the cocoa-stand and aquarium examples in it come back everywhere this week.
2. Data Lab 4 brings the penguins back for their best act yet: flipper length vs. body mass in a real scatterplot, your first =CORREL(), and a species-by-island table with a lurking variable hiding in plain sight. Due at the end of Week 4.
3. Discussion 4 asks whether your screen time causes your worst sleep — or the other way around, or neither. Your initial post is due two days before the week ends, so classmates have time to reply.

One heads-up: this is the week the course's favorite slogan — correlation is a handshake, not a push — stops being a slogan and becomes a skill. By the end of the week you'll spot the third hand behind a headline in seconds.

Open the Start Here / Module Overview page first — it lays out everything in order with due points. Bring a hunch about two things that move together; we'll measure it.

See you in the course!