Math Says Yes

Glossary term

P-value

How surprising the observed data would be if a chosen null model were true.

Visual intuition

ordinary under model

surprise zone

observed

A small p-value lands far into the surprise zone

The surprise zone contains results at least as unusual as the observed result under the null model.

Example

A small p-value says the data would be unusual under the null model; it does not prove the alternative explanation.

How It Works

A p-value is not the that the claim is true or false. It measures surprise under a model, often a model of no difference or no effect.

Concepts

A p-value is the probability of seeing data at least this extreme if a specific null model were true. It is not the probability that the claim is false, not the chance the result was random, and not a measure of how large or important the effect is.

Lessons

A bell curve with a small highlighted tail separated from the main curve.

Small P Is Not Proof

A small p-value says the data would be surprising under a null model, not that the claim is probably true or important.

Related Facts

4 min · medium

A small p-value label beside a null model curve with the tail highlighted.

A p-value is not the chance your result is wrong

A p-value is a check for surprise: it asks how often a result this extreme would appear if there were really no effect. It does not tell you the chance your result is wrong.

5 min · medium

A horizontal range bar with a center dot on the left, and a dashed threshold line with a marker crossing it on the right.

P-value vs confidence interval: what each one tells you

A p-value asks whether the data look surprising under a null model. A confidence interval asks which effect sizes remain plausible.