Index: The Book of Statistical Proofs ▷ General Theorems ▷ Frequentist statistics ▷ Hypothesis testing ▷ Alternative hypothesis

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

\[\label{eq:h0} \begin{split} H_0&: \; \theta \in \Theta_0 \quad \text{where} \quad \Theta_0 \subset \Theta \\ H_1&: \; \theta \in \Theta_1 \quad \text{where} \quad \Theta_1 = \Theta \setminus \Theta_0 \; . \end{split}\]
 
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Metadata: ID: D126 | shortcut: h1 | author: JoramSoch | date: 2021-03-12, 10:36.