Critical regions to construct a null hypothesis test. Inspired by Glen Cowen’s CERN lectures. Also see this graph of a critical region, or these test statistics in hypothesis testing.

Edit and compile if you like:

% Basic drawings % https://www.sharelatex.com/blog/2013/08/27/tikz-series-pt1.html % https://www.tug.org/TUGboat/tb29-1/tb91walczak.pdf \documentclass[border=1pt,tikz]{standalone} \usepackage{tikz} \begin{document} % SET: critical region \begin{tikzpicture}[scale=1.0] \draw[blue!20!black,fill=blue!20,rounded corners=10,thick] (0,0) rectangle (4,2) node[above left] {data space $\Omega$}; \draw[blue!20!black,fill=blue!70!black!70,rounded corners=10,thick,shift={(0.15,0.15)}] (1,0) rectangle (0,1) node[above right] {critical region $\omega$}; \end{tikzpicture} % SET: overlapping critical regions \begin{tikzpicture}[scale=1.0] \draw[blue!20!black,fill=blue!20,rounded corners=10,thick] (0,0) rectangle (4,2) node[above left] {$\Omega$}; \begin{scope}[shift={(0.35,0.05)}] \draw[blue!20!black,fill=blue!70!black!70,rounded corners=10,thick,shift={(0.15,0.15)},scale=0.90] (2,0) rectangle (0,1) node[above left=-5pt] {$\omega_1$}; \draw[blue!20!black,rounded corners=10,thick,shift={(0.30,0.45)},scale=0.90] (2,0) rectangle (0,1) node[right=0pt,above right] {$\omega_2$}; \draw[blue!20!black,rounded corners=10,thick,shift={(0.50,0.30)},scale=0.90] (0,0) rectangle (2,1) node[right=-2pt] {$\omega_3$}; \end{scope} \end{tikzpicture} \end{document}

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