Definition:Unbiased Hypothesis Test

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 $\delta$.

Let $\delta$ be such that the probability that $T$ takes a value in $C$ when $H_1$ is true is always greater than $\alpha$.

Then $\delta$ is known as an unbiased hypothesis test.

Also see

• Results about hypothesis testing 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): unbiased hypothesis test
• 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): unbiased hypothesis test