Definition: Alternative hypothesis
Index:
The Book of Statistical Proofs ▷
General Theorems ▷
Frequentist statistics ▷
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Alternative hypothesis
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Metadata: ID: D126 | shortcut: h1 | author: JoramSoch | date: 2021-03-12, 10:36.
Definition: Let $H_0$ be a null hypothesis of a statistical hypothesis test. Then, the corresponding alternative hypothesis, denoted as $H_1$, is either the negation of $H_0$ or an interesting sub-case in the negation of $H_0$, depending on context. The test is designed to assess the strength of evidence against $H_0$ and possibly reject it in favor of $H_1$. Usually, $H_1$ is a statement that a particular parameter is non-zero, that there is an effect of a particular treatment or that there is a difference between particular conditions.
More precisely, let $m$ be a generative model describing measured data $y$ using model parameters $\theta \in \Theta$. Then, null and alternative hypothesis are formally specified as
\[\label{eq:h0} \begin{split} H_0&: \; \theta \in \Theta_0 \quad \text{where} \quad \Theta_0 \subset \Theta \\ H_1&: \; \theta \in \Theta_1 \quad \text{where} \quad \Theta_1 = \Theta \setminus \Theta_0 \; . \end{split}\]- Wikipedia (2021): "Exclusion of the null hypothesis"; in: Wikipedia, the free encyclopedia, retrieved on 2021-03-12; URL: https://en.wikipedia.org/wiki/Exclusion_of_the_null_hypothesis#Basic_definitions.
Metadata: ID: D126 | shortcut: h1 | author: JoramSoch | date: 2021-03-12, 10:36.