Math 1 · Unit 10 · Lesson 5

Association Is Not Causation

Two quantities can move together without one causing the other. Association means there is a pattern, correlation measures how strong the straight-line pattern is, and causation means one thing actually makes the other happen. Sometimes the pattern is pure coincidence. Sometimes a hidden third quantity, a lurking variable, drives both. To show that one thing causes another you need a carefully designed experiment with randomly assigned groups, not just a strong r.

About 40 minutes A pattern is not a reason

The big idea

Even a perfect pattern does not prove that one thing causes the other. Association means two quantities move together, correlation measures how strong the straight-line pattern is, and causation means one actually makes the other happen. A pattern can be pure coincidence, like the length of the Spelling Bee's winning word and deaths from venomous spiders. Or a lurking variable, a hidden third quantity, can drive both: money behind owning more cars and living longer, hot sunny weather behind ice cream sales and sunburns. So before claiming a cause, ask whether it could be chance, whether something hidden could explain both, and whether there is a real, sensible way one thing makes the other happen. To actually show cause you need a carefully designed experiment, with people put into groups at random and only one thing changed. A strong r is not enough.

The parts of this lesson

Each part is its own short page. Go in order, or pick the one you need.

1The Words We UseThe vocabulary for this lesson, in one place.Start here 2A pattern is not a reasonThe last idea in this unit is a warning about what a good fit can and cannot tell you. 3Lurking variables, and how cause is really shownCoincidence is one reason. 4Cause, or just connected?For each story, decide whether it is reasonable to say the first thing causes the second, or whether they... 5Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with association, correlation, and causation, coincidence and lurking variables with the examples, the four questions to ask, and how an experiment shows cause. Plus a worksheet with an answer key and a short lesson plan.

Study guide (PDF) Worksheet and answer key (PDF) Lesson plan (PDF)

Where this goes next

Previous lesson: Exponential RegressionWhen the data multiplies. Next lesson: Distance, the Pythagorean Theorem on the GridUnit 11 begins: the grid comes back for geometry, starting with how long a segment is. Back to the Math 1 mapEvery Math 1 lesson, in course order. Tell us what you thoughtA few quick questions about this lesson. It takes a minute, and it is how the lesson gets better.

NC Math 1 standards in this lesson: NC.M1.S-ID.9 (distinguish between association and causation), NC.M1.S-ID.8 (interpret the correlation coefficient).