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