Point and set hypothesis

Index: The Book of Statistical Proofs ▷ General Theorems ▷ Frequentist statistics ▷ Statistical hypotheses ▷ Point/exact vs. set/inexact

Definition: Let $H$ be a statistical hypothesis. Then,

$H$ is called a point hypothesis or exact hypothesis, if it specifies an exact parameter value:

\[\label{eq:hyp-point} H: \; \theta = \theta^{*} \; ;\]

$H$ is called a set hypothesis or inexact hypothesis, if it specifies a set of possible values with more than one element for the parameter value (e.g. a range or an interval):

\[\label{eq:hyp-non-point} H: \; \theta \in \Theta^{*} \; .\]

Sources:

Wikipedia (2021): "Exclusion of the null hypothesis"; in: Wikipedia, the free encyclopedia, retrieved on 2021-03-19; URL: https://en.wikipedia.org/wiki/Exclusion_of_the_null_hypothesis#Terminology.

Metadata: ID: D129 | shortcut: hyp-point | author: JoramSoch | date: 2021-03-19, 14:28.