Index: The Book of Statistical ProofsGeneral TheoremsFrequentist statisticsStatistical 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 \; .
 
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Metadata: ID: D138 | shortcut: hyp-tail | author: JoramSoch | date: 2021-03-31, 09:21.