# p-value

The p-value is the probability of getting data at least as extreme as yours if the null hypothesis were true. A small p-value means the data would be surprising under H0.

Statistics (university) · Part 06: Hypothesis testing · Card 2 of 9 · Last updated 2026-10-19

## Analogy

If a coin gives 9 heads in 10 flips, the p-value asks how often a fair coin would do something that lopsided.

## Example

**z test for a mean**

H0: mean = 100, sigma = 15, n = 100
Sample mean = 104
SE = 15 / 10 = 1.5
z = 4 / 1.5 = 2.67
Two-sided p = 2 x 0.0038 = 0.0077

## In practice

Researchers report p-values to show how strongly data clashes with the null.

## Practice

### Flashcards

- **Define the p-value.** The chance of data at least this extreme if the null is true.

## Questions people ask

### What does a p-value of 0.03 mean?

If the null hypothesis were true, there would be a 3 percent chance of seeing data at least this extreme. It is not the probability that the null is true. It measures how surprising the data is under the null, nothing more.

### Does a small p-value mean the effect is large?

No. With a huge sample, even a tiny, useless difference can give a very small p-value. A p-value says whether an effect is distinguishable from chance, not whether it matters. Always report the size of the effect and its confidence interval too.

## Related concepts

- [Null and alternative hypotheses](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-6/statistics-university-part-6-concept-1)
- [Significance level and decision](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-6/statistics-university-part-6-concept-3)
- [Type I and Type II errors](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-6/statistics-university-part-6-concept-4)
- [Power of a test](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-6/statistics-university-part-6-concept-5)

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