Home Statistical Dictionary P-value

P-value

The probability, assuming the null hypothesis is true, of observing data at least as extreme as what was actually observed.

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In Plain English

Run the experiment assuming there's really no effect. The p-value asks: how surprising would data like mine be under that assumption? A small p-value means your data would be a rare, surprising outcome if the null hypothesis were really true -- which is evidence (not proof) against it.

Definition

For a test statistic $T$ with observed value $t$ , computed under the null hypothesis $H_{0}$ , the p-value is $P (T at least as extreme as t ∣ H_{0} true)$ . It is not the probability that $H_{0}$ is true, and not the probability that the result is due to chance.

Formula

p = P (T \geq t_{o b s} ∣ H_{0})

Notation

T

—Test statistic, treated as a random variable under H0

t_{o b s}

—Observed value of the test statistic from the sample

Properties

A p-value below $α$ leads to rejecting $H_{0}$ , but $α$ itself is a convention, not a law of nature.
A tiny p-value does not imply a large or important effect size -- check the effect size and confidence interval too.
Under a true $H_{0}$ , p-values are uniformly distributed between 0 and 1.

At a Glance

Range0 to 1

Small value meansdata is unusual under H0

Common threshold

α = 0.05

Not equal to

P (H_{0} is true)

Related Terms

Confidence Interval Type I Error

Last updated July 30, 2026← Back to the Dictionary