Definition:P-Value

Definition

Let $\delta$ be a hypothesis test.

Let $H_0$ and $H_1$ be the null hypothesis and alternative hypothesis of $\delta$ respectively.

Let $T$ be the test statistic which is being used to determine whether $H_0$ or $H_1$ holds.

Let $C$ be the critical region of $\delta$.

Let $\alpha$ be the significance level of $\delta$.

The $p$-value of $\delta$ is the probability that $T$ takes a value greater than or equal to a calculated value when $H_0$ is true.

Also known as

If a $p$-value is less than a given significance level $\alpha$, the term exact significance level is often used for $p$-value.

Also see

• Definition:Exact $p$-Value

• Results about $p$-values can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): hypothesis testing
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): $p$-value
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): hypothesis testing
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): $p$-value