Null Hypothesis

The default assumption a study tries to challenge — usually that there is no effect or no difference.

Visual intuition

ordinary under model

surprise zone

observed

A small p-value lands far into the surprise zone

The null hypothesis paints the 'ordinary' lane: what results look like when nothing but chance is at work.

Example

Testing a coin for fairness, the null hypothesis is 'heads comes up 50% of the time'; observing 61 heads in 100 flips is unusual enough under that assumption (p ≈ 0.04) that you would reject it.

How It Works

Statistics plays devil's advocate. Before crediting a new drug, you assume it does nothing — the null hypothesis — and ask how surprising your data would be in that boring world. Only when the data would be genuinely rare under 'nothing is going on' (a small ) do you reject the null. Failing to reject is not proof of no effect; it just means the data did not clear the bar.

Concepts

P-Values

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

Data Tricks

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.