Definition: Null hypothesis
Index: The Book of Statistical Proofs ▷ General Theorems ▷ Frequentist statistics ▷ Hypothesis testing ▷ Null hypothesis
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Metadata: ID: D125 | shortcut: h0 | author: JoramSoch | date: 2021-03-12, 10:25.
Definition: The statement which is tested in a statistical hypothesis test is called the “null hypothesis”, denoted as $H_0$. The test is designed to assess the strength of evidence against $H_0$ and possibly reject it. The opposite of $H_0$ is called the “alternative hypothesis”. Usually, $H_0$ is a statement that a particular parameter is zero, that there is no effect of a particular treatment or that there is no difference between particular conditions.
More precisely, let $m$ be a generative model describing measured data $y$ using model parameters $\theta \in \Theta$. Then, a null hypothesis is formally specified as
\[\label{eq:h0} H_0: \; \theta \in \Theta_0 \quad \text{where} \quad \Theta_0 \subset \Theta \; .\]- 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: D125 | shortcut: h0 | author: JoramSoch | date: 2021-03-12, 10:25.