Evidence vs Proof: What Quantitative Evidence Can and Cannot Do

The last chapter set out the four questions behind every appraisal. Before you can ask whether a number fits, assumes too much, or leaves something out, you need one distinction that sits underneath all of them: the difference between a number that supports a claim and a number that proves it. Getting this straight is the first move that stops a confident figure from deciding things for you.

Why One Number Rarely Settles a Question

A single statistic can feel like the end of the discussion. “Reported burglaries fell 20%.” “Nine out of ten users renewed.” The figure lands, and the claim behind it seems to follow automatically. But a number arrives with a lot left unsaid: where it came from, what it counted, what it left out, and whether something else could explain it just as well.

Treating one figure as the final word is the most common mistake in reading evidence, and it is the easiest to avoid once you can name it. The fix is not to distrust every number. It is to know how much weight a given number can bear, so you neither wave it away nor let it carry more than it should.

Tell Evidence Apart From Proof

Start with a few plain words you will use for the rest of the course.

The gap between those last two words does most of the work in this chapter. In everyday life, a single number almost never proves a claim. It supports it, a little or a lot, and then leaves room for other explanations you have to weigh yourself.

It helps to picture support and proof not as an on-off switch but as a dial. Evidence turns the dial up or down, raising or lowering how confident you can reasonably be. Strong, varied, carefully collected evidence turns it a long way up. A single figure from one source nudges it partway. Almost nothing in ordinary numeracy turns it all the way to certainty, and expecting it to is how people get misled.

See the Difference at a Glance

The two words describe different jobs a number can do. Laid side by side, the contrast is easy to hold onto.

Most of the numbers you meet live in the left column. The skill is not to promote them to the right column, but to read them honestly for what they are.

Watch It Work: The “Safer Now” Claim

Picture a flyer from a neighborhood group. It reads: “Our area is safer now, reported burglaries fell 20% last year.” One statistic, one confident claim. Before reading on, decide for yourself: does that number prove the neighborhood is safer?

Here is the honest reading. The figure is real evidence, and it points the right way. A 20% drop in reported burglaries is not nothing, and it does raise how believable the “safer now” claim is. So it belongs on the dial, turned up a little.

But it does not prove the claim, for reasons the single number quietly hides:

• It counts reported burglaries, not all burglaries. Fewer reports can mean fewer crimes, or simply that fewer people bothered to report;

• It covers one type of crime. Burglaries could fall while other incidents rise, so “safer” overall does not follow;

• It spans one year. A single year can swing up or down by chance, without any real change in safety;

• It says nothing about the wider picture. If burglaries fell across the whole city, this area is not especially safer; it is simply part of a wider trend.

None of these points make the claim false. They mark the distance between support and proof. The number nudges the dial up; it does not spin it to certainty. What would push it closer to proof is more and varied evidence: several years pointing the same way, several kinds of crime, and a comparison against similar areas, so that fewer competing explanations survive.

That is the whole move. You take a number, grant it the support it genuinely gives, and then, instead of stopping there, you ask what it still leaves open. Every later chapter is a sharper version of that same question.

Let’s Recap!

• A single number almost always supports a claim rather than proving it.

• Support makes a claim more believable; proof settles it beyond reasonable doubt and is rare in everyday numeracy.

• Think of support and proof as a dial of warranted confidence, not an on-off switch.

• Reading evidence honestly means granting what it supports while naming what it still leaves open.

• More and more varied evidence is what moves a claim from merely supported toward proven.

With the difference between support and proof in hand, the next chapter turns to the first of the four questions: does this evidence actually fit the decision you are trying to make?