Test
Definition
Given the test hypotheses scenario introduced above, a test is defined as a mapping from the data outcome space to the set , formally
\phi:&\mathbb{R}^n&\to&\mathbb{R}\\ &y&\mapsto&\phi(y)\;. \end{array}$$ Here, the test value $\phi(y) = 0$ represents the act of not rejecting [[Statistical Test|null hypothesis]], while the test value $\phi(y) = 1$ represents the act of rejecting the [[Statistical Test|null hypothesis]]. The test is considered as a composition between the [[test statistic]] $\gamma$ and the [[decision rule]] $\delta$ and is defined as $\phi=\delta\circ\gamma:\mathbb{R}^n\to\{0,1\}$. ## Reference [[D. Ostwald - The general linear model 20_21|Ost20 pp. 116-117]] .