Title: Week 4 Overview — Start Here
Course: Introduction to Statistics (18-Week Generic Edition)

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.

# | Do this | Type | Due
1 | Read Chapter 4 — the module's primary reading | Chapter (ungraded prep) | Early in the week
2 | Skim the slides (Deck 4) and the Week 4 lecture outline; browse the Readings & Resources links that interest you | Prep (ungraded) | Alongside class
3 | Lecture Tutorial 4 — work through the week's ideas with your chatbot, then submit the share link + Completion Summary | Tutorial · graded (Lecture tutorials, 20% group) | End of Week 4
4 | Practice exercises — quick reps with the AI coach | Practice · ungraded | Before the quiz (recommended)
5 | Data Lab 4 — "Flippers, Grams & Islands" — the penguins return: scatterplot flipper vs. body mass, compute r with =CORREL(), build the species × island two-way table | Data lab · graded (Data labs, 15% group) | End of Week 4
6 | Quiz 4 — scatterplots, r, two-way tables, association vs. causation | Quiz · graded (Quizzes, 15% group) · closed to AI | End of Week 4
7 | Discussion 4 — "The Scroll-and-Sleep Question" — argue all three explanations for the screens-and-sleep link 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 4
8 | Assignment 4 — "Measure the Link, Doubt the Arrow" — four AI-coached problems; submit the report (score on line 1) + chat link | Assignment · graded (Assignments, 25% group) | End of Week 4

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.