One Number, and Everything It Cannot Carry

You'll learnwhat r measures and the range it lives in, why the sign is direction and the size is strength, the properties that decide most questions — unitless, symmetric, not the slope, not resistant — the curved patterns it cannot see, and why no value of r turns an association into a cause.

The correlation coefficient squeezes a whole scatterplot into one number, and everything it cannot carry is where the errors live. This page runs the properties instead of reciting them: it converts hours to minutes and shows r not moving while the slope shrinks by a factor of 60; it ranks a tight fall above a loose rise because strength is the size; it adds one point to a formless cloud and watches r jump from 0.09 to 0.71; it fits a straight line to a cloud built from a curve and still gets 0.925. Then the big one — ice cream sales and beach rescues run together at 0.91, and when the page holds temperature fixed the association is gone. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · WHAT r IS · PROPERTIES · BLIND SPOTS · CAUSATION · v2

r survives a unit change, the slope does not; one point lifts it to 0.71

Before you start

What you're looking at

The eight students' cloud, and then a series of clouds each built to exercise one property of r — or one thing r cannot do.

The question

What does the one number actually carry, and what gets smuggled in when it is read as more?

Step 1 / 12