Both went up, but not by the same amount
- The idea
- Predict
- See it
- Why
- Check
The idea
“If two numbers moved the same way, they moved by about the same amount.”
Two numbers that both went up look like the same result. Checking how much each one moved is the step people skip.
The short version
The mistake: If two numbers moved the same way, they moved by about the same amount.
What's actually true: Two changes can go the same way and still differ a lot in size. Work out each one before calling them equal.
- Direction says which way a value moved. Size says how much. Work out each change by subtracting before from after, and by dividing after by before.
- When starting values differ, compare ratios or percent change too. Going from 2 to 4 and from 200 to 202 are both +2, but only the first is a doubling.
- Size is evidence too. If unfenced plots stayed near 20, B's much bigger rise suggests deer held B back far more than A. Calling the changes equal throws that away.
On the exam: Both went up? Ask by how much before you call the changes equal.