One-tailed and two-tailed hypothesis

Index: The Book of Statistical Proofs ▷ General Theorems ▷ Frequentist statistics ▷ Statistical hypotheses ▷ One-tailed vs. two-tailed

Definition: Let $H_0$ be a point null hypothesis

\[\label{eq:h0-point} H_0: \; \theta = \theta_0 \;\]

and consider a set alternative hypothesis $H_1$. Then,

$H_1$ is called a left-sided one-tailed hypothesis, if $\theta$ is assumed to be smaller than $\theta_0$:

\[\label{eq:h1-tail1-left} H_1: \; \theta < \theta_0 \; ;\]

$H_1$ is called a right-sided one-tailed hypothesis, if $\theta$ is assumed to be larger than $\theta_0$:

\[\label{eq:h1-tail1-right} H_1: \; \theta > \theta_0 \; ;\]

$H_1$ is called a two-tailed hypothesis, if $\theta$ is assumed to be unequal to $\theta_0$:

\[\label{eq:h1-tail2} H_1: \; \theta \neq \theta_0 \; .\]

Sources:

Wikipedia (2021): "One- and two-tailed tests"; in: Wikipedia, the free encyclopedia, retrieved on 2021-03-31; URL: https://en.wikipedia.org/wiki/One-_and_two-tailed_tests.

Metadata: ID: D138 | shortcut: hyp-tail | author: JoramSoch | date: 2021-03-31, 09:21.