Research methods · The numbers
Absolute vs relative risk
Try this first
A headline says a pill cuts heart-attack risk by 50%. Before reading on: is that an enormous benefit, or could it be almost nothing? What is the one number you'd need before you could even tell?
Out of 100 people like you, suppose 2 would have a heart attack over the next five years. A pill comes along that drops it to 1 in 100. That is a 50% cut — one of the two events is gone, half of them. It is also a change of exactly one person in a hundred. The other 99 are unaffected either way: they were never going to have the event, or they have it regardless. Same fact, two honest descriptions — and they feel wildly different. "Cut in half" sounds like a reason to act today. "One in a hundred" sounds like a coin-flip you might skip. The trick is that a marketer gets to choose which sentence you hear.
The one idea
A relative number ("50% lower") is meaningless until you know the base rate it's cutting from. Always demand the absolute change in plain people-per-hundred. The number needed to treat (NNT) makes it human — how many people take the pill for one to benefit — and your own benefit scales with your baseline risk, not the headline's.
See the whole hundred
Relative risk hides the crowd that never changes. Draw all 100 people and the trick stops working: the left grid is life without the pill, the right is life with it. The only difference is one square.
Three numbers, one finding
Every relative claim can be unpacked into three figures that sound far less dramatic and far more useful. Here is the heart-attack pill, all three ways:
| Measure | Value | What it answers |
|---|---|---|
| Relative risk reduction | 50% | Of the events, what share is gone? (1 of 2) |
| Absolute risk reduction | 1 point (2% → 1%) | How much did my own risk drop? |
| Number needed to treat | 100 | How many take it for one to benefit? |
NNT is just 1 ÷ absolute reduction. A 1-point drop (0.01) gives 1 ÷ 0.01 = 100: a hundred people swallow the pill, with its cost and side effects, so that one of them avoids an event. The same 50% relative cut applied to a base rate of 20% would mean 20% → 10% — a 10-point absolute drop and an NNT of 10. Identical headline, ten times the real benefit. The relative number never told you which world you were in.
Work one, then finish one
Worked: A statin trial reports it "lowers major cardiac events by 50%," and the base rate in the trial was 2% over the study. Unpack it. Relative reduction: 50%. Absolute reduction: 2% → 1%, so 1 percentage point. NNT: 1 ÷ 0.01 = 100 — treat 100 such people to prevent one event. None of that is a reason to refuse the pill; for a cheap, safe drug an NNT of 100 can be well worth it. It is a reason to refuse the headline's framing and judge the trade on the absolute numbers.
Your turn: A label warns that "processed meat raises colorectal-cancer risk by 18%." Lifetime risk of colorectal cancer runs around 5%. Translate the scare into absolute terms — roughly what does the 18% buy you? (18% of a 5% base rate is about 0.9 of a point, so roughly 5% → about 6% lifetime — about one extra case per 100 heavy processed-meat eaters, not 18 extra per 100.)
Why this matters
Relative risk is the favorite move of the people on both ends of your feed. A scare headline says a habit "raises your risk 40%" and you brace for catastrophe; a supplement brand says its capsule "cuts inflammation markers 30%" and you reach for your wallet. Both lean on the same gap: the relative number sounds enormous while the absolute change can be a rounding error — or genuinely large. You cannot tell from the percentage alone. The next time you're deciding whether to start a medication, drop a food, or buy a bottle, ask the boring question the framing was built to skip: what's the base rate, and how many people like me change outcomes — one in ten, or one in a thousand? Often the honest answer is small enough that the decision turns entirely on cost and side effects, which is exactly where it should have started.
Recall check · no peeking
- State the difference between a relative risk reduction and an absolute risk reduction, using the 2%→1% example.
- What does "number needed to treat" mean, and how do you get it from the absolute reduction?
- Why does the base rate decide whether a "50% lower" claim is a big deal or nearly nothing?
Explain it back
In one plain sentence, tell a friend why "this cuts your risk in half" can be a tiny real change in their actual life.