diff --git a/slides/sections/8.md b/slides/sections/8.md index f320140..2dd6806 100644 --- a/slides/sections/8.md +++ b/slides/sections/8.md @@ -61,19 +61,20 @@ $$ ## L sample results +\vspace{20pt} \begin{center} \begin{tabular}{rcccc} \toprule & & median & mode & fwhm \\ \midrule - \multirow{2}{*}{50000} & $t$ & 0.761 & 1.012 & 1.338 \\ - & $p$ & \gre{0.446} & \gre{0.311} & \gre{0.181} \\ + \multirow{2}{*}{50000} & $t$ & 0.027 & 1.012 & 1.338 \\ + & $p$ & \gre{0.979} & \gre{0.311} & \gre{0.181} \\ \midrule - \multirow{2}{*}{5000} & $t$ & 2.263 & 0.084 & 1.767 \\ - & $p$ & \red{0.023} & \gre{0.933} & \gre{0.077} \\ + \multirow{2}{*}{5000} & $t$ & 0.912 & 0.200 & 3.033 \\ + & $p$ & \gre{0.362} & \gre{0.841} & \red{0.002} \\ \midrule - \multirow{2}{*}{1000} & $t$ & 1.549 & 0.072 & 3.790 \\ - & $p$ & \gre{0.121} & \gre{0.943} & \red{0.000} \\ + \multirow{2}{*}{1000} & $t$ & 1.189 & 0.232 & 0.208 \\ + & $p$ & \gre{0.235} & \gre{0.817} & \gre{0.835} \\ \toprule \end{tabular} \end{center} @@ -81,16 +82,29 @@ $$ \setbeamercovered{} \begin{center} \begin{tikzpicture}[>=Stealth, overlay] - \pause - % Left note - \draw [fill=white] (-5.5,-0.1) rectangle (-1.85,1.1); - \node [above right, align=left] at (-5.5,-0.1) {$m\ex = 1.356...$\\$m\ob = 1.402 \pm 0.020$}; - \draw [cyclamen, ->, very thick] (-3.5,1.1) to [out=90, in=-135] (-1.2, 2); - \pause - % Right note - \draw [fill=white] (2,2.5) rectangle (5.2,3.7); - \node [above right, align=left] at (2,2.5) {$w\ex = 4.02...$\\$w\ob = 5.08 \pm 0.28$}; - \draw [cyclamen, ->, very thick] (4.5, 2.5) to [out=-90, in=0] (3.5, 0.8); + % Rectangles + \draw <2> [gray, very thick] (-1.4,0.3) rectangle (0.4,5.5); + \draw <3> [gray, very thick] (0.4,0.3) rectangle (2,5.5); + \draw <4> [gray, very thick] (2,0.3) rectangle (3.8,5.5); + % Estimations ellipses + \draw <5-> [cyclamen, thick] (2.8,3.57) ellipse (0.8cm and 0.3cm); + \draw <5-> [cyclamen, thick] (2.8,2.18) ellipse (0.8cm and 0.3cm); + \draw <5-> [cyclamen, thick] (2.8,0.8) ellipse (0.8cm and 0.3cm); + % Estimations notes + \draw <6> [fill=white] (-5.5,-0.1) rectangle (0.3,2.3); + \node <6> [above right, align=right] at (-5.5,-0.1) { + $w\ex = 4.02... \hspace{22pt} $\\ + $50000 \hence w\ob = 4.11 \pm 0.07$\\ + $5000 \hence w\ob = 4.40 \pm 0.13$\\ + $1000 \hence w\ob = 3.96 \pm 0.27$}; + % FHWM notes + \draw <7-> [fill=white] (-5.5,2.9) rectangle (-1.4,5.1); + \node <7-> [above right, align=center] at (-5.5,3) { + $f_\varepsilon(x) = \frac{1}{N\varepsilon} \sum_{i = 1}^N + G \left( \frac{x-x_i}{\varepsilon} \right)$\\\\ + $\varepsilon = 0.88 \, S_N + \left( \frac{d + 2}{4}N \right)^{-1/(d + 4)}$}; + \draw <8> [cyclamen, thick] (-4.45,3.45) ellipse (0.4cm and 0.3cm); \end{tikzpicture} \end{center} \setbeamercovered{transparent} @@ -98,26 +112,43 @@ $$ ## M sample results +\vspace{20pt} \begin{center} \begin{tabular}{rcccc} \toprule & & median & mode & fwhm \\ \midrule - \multirow{2}{*}{50000} & $t$ & 669.9 & 0.732 & 1.329 \\ + \multirow{2}{*}{50000} & $t$ & 58.01 & 0.732 & 1.329 \\ & $p$ & \gre{0.000} & \gre{0.464} & \gre{0.184} \\ \midrule - \multirow{2}{*}{5000} & $t$ & 108.6 & 0.683 & 0.588 \\ - & $p$ & \gre{0.000} & \gre{0.495} & \gre{0.556} \\ - \midrule - \multirow{2}{*}{1000} & $t$ & 25.47 & 0.665 & 1.890 \\ - & $p$ & \gre{0.000} & \gre{0.506} & \gre{0.059} \\ + \multirow{2}{*}{5000} & $t$ & 16.80 & 0.014 & 0.215 \\ + & $p$ & \gre{0.000} & \gre{0.989} & \gre{0.830} \\ + \midrule + \multirow{2}{*}{1000} & $t$ & 11.61 & 0.028 & 1.001 \\ + & $p$ & \gre{0.000} & \gre{0.978} & \gre{0.317} \\ \toprule \end{tabular} \end{center} +\setbeamercovered{} +\begin{center} +\begin{tikzpicture}[>=Stealth, overlay] + % Rectangles + \draw <2> [gray, very thick] (-1.4,0.3) rectangle (0.4,5.5); + \draw <3> [gray, very thick] (0.4,0.3) rectangle (2,5.5); + \draw <4,5,6> [gray, very thick] (2,0.3) rectangle (3.8,5.5); + \node <5> at (-2,2.5) {\includegraphics{images/gamo-pdf.pdf}}; + \node <6> at (-2,2.5) {\includegraphics{images/gala-pdf.pdf}}; + \draw <5,6> [thick] (-5.15,0) rectangle (1.22,5.05); +\end{tikzpicture} +\end{center} +\setbeamercovered{transparent} + ## KS samples results +\vspace{10pt} + \begin{center} \begin{tabular}{rccc} \toprule @@ -125,36 +156,62 @@ $$ \midrule \multirow{2}{*}{50000} & $D$ & 0.004 & 0.153 \\ & $p$ & \gre{0.379} & \gre{0.000} \\ - \midrule - \multirow{2}{*}{5000} & $D$ & 0.008 & 0.151 \\ - & $p$ & \gre{0.812} & \gre{0.000} \\ - \midrule - \multirow{2}{*}{1000} & $D$ & 0.020 & 0.162 \\ - & $p$ & \gre{0.794} & \gre{0.000} \\ - \midrule - \multirow{2}{*}{200} & $D$ & 0.086 & 0.226 \\ - & $p$ & \gre{0.100} & \gre{0.000} \\ + \midrule + \multirow{2}{*}{5000} & $D$ & 0.010 & 0.148 \\ + & $p$ & \gre{0.714} & \gre{0.000} \\ + \midrule + \multirow{2}{*}{1000} & $D$ & 0.026 & 0.162 \\ + & $p$ & \gre{0.478} & \gre{0.000} \\ + \midrule + \multirow{2}{*}{200} & $D$ & 0.054 & 0.205 \\ + & $p$ & \gre{0.579} & \gre{0.000} \\ \toprule \end{tabular} \end{center} +\setbeamercovered{} +\begin{center} +\begin{tikzpicture}[>=Stealth, overlay] + % Rectangles + \draw <2> [gray, very thick] (-1,0.3) rectangle (1,6.9); + \draw <3> [gray, very thick] (1,0.3) rectangle (3.3,6.9); + % 200 points ellipse + \draw <4> [gray, very thick] (-3.5,0.3) rectangle (3.5,1.9); +\end{tikzpicture} +\end{center} +\setbeamercovered{transparent} + ## Trapani samples results +\vspace{20pt} \begin{center} \begin{tabular}{rccccc} \toprule & & \multicolumn{2}{c}{L sample} & \multicolumn{2}{c}{M sample} \\ & & $\mu_1$ & $\mu_2$ & $\mu_1$ & $\mu_2$ \\ \midrule - \multirow{2}{*}{50000} & $\Theta$ & 0.255 & 0.432 & 161.1 & 162.5 \\ + \multirow{2}{*}{50000} & $\Theta$ & 0.255 & 0.432 & 106.1 & 162.5 \\ & $p$ & \gre{0.614} & \gre{0.511} & \gre{0.000} & \gre{0.000} \\ - \midrule - \multirow{2}{*}{1000} & $\Theta$ & 0.809 & 0.809 & 10.83 & 5.823 \\ - & $p$ & \gre{0.368} & \gre{0.368} & \gre{0.016} & \gre{0.001} \\ - \midrule - \multirow{2}{*}{200} & $\Theta$ & 0.472 & 0.170 & 2.232 & 2.981 \\ - & $p$ & \gre{0.492} & \gre{0.680} & \red{0.135} & \red{0.084} \\ + \midrule + \multirow{2}{*}{5000} & $\Theta$ & 2.178 & 2.556 & 23.36 & 36.48 \\ + & $p$ & \gre{0.140} & \gre{0.110} & \gre{0.000} & \gre{0.000} \\ + \midrule + \multirow{2}{*}{1000} & $\Theta$ & 0.694 & 0.060 & 5.985 & 7.302 \\ + & $p$ & \gre{0.405} & \gre{0.549} & \gre{0.014} & \gre{0.007} \\ \toprule \end{tabular} \end{center} + +\setbeamercovered{} +\begin{center} +\begin{tikzpicture}[>=Stealth, overlay] + % Rectangles + \draw <2,3> [gray, very thick] (-2,0.3) rectangle (1,6.1); + \draw <4> [gray, very thick] (1,0.3) rectangle (4.2,6.1); + % Estimations ellipses + \draw <3> [cyclamen, thick] (-1.28,2.18) ellipse (0.7cm and 0.3cm); + \draw <3> [cyclamen, thick] (0.29,2.18) ellipse (0.7cm and 0.3cm); +\end{tikzpicture} +\end{center} +\setbeamercovered{transparent}