analistica/slides/sections/8.md

Results

Compatibility test

Comparing sample properties:

  p = 1 - \text{erf} \left( \frac{t}{\sqrt{2}} \right)\ \with
  t = \frac{|x\ex - x\ob|}{\sqrt{\sigma\ex^2 + \sigma\ob^2}}

• x\ex and x\ob are the expected and observed values
• \sigma\ex and \sigma\ob are their absolute errors

. . .

At 95% confidence level, the values are compatible if:

  p > 0.05

Compatibility test

\setbeamercovered{} \begin{center} \begin{tikzpicture}[>=Stealth] %notes \draw [very thick, gray] (0,0) -- (0,3); \draw [very thick, gray] (-1.45,1.5) -- (1.45,1.5); \draw [very thick, gray] (-1.35,1.3) -- (-1.55,1.7); \draw [very thick, gray] ( 1.35,1.3) -- ( 1.55,1.7); \node at (0,-0.4) {$x\ex$}; \node [right] at (1.7,1.7) {$2 , \sqrt{\sigma\ex^2 + \sigma\ob^2}$}; % axes \draw [very thick, <->] (-5,4) -- (-5,0) -- (5,0); \node [right] at (5,0) {$x$}; % Gaussian \draw [domain=-5:5, smooth, variable=\x, cyclamen, very thick] plot ({\x}, {3exp(-(\x\x/3))}); \pause % area \fill [domain=2:5, smooth, variable=\x, cyclamen!20!white, very thick] (2,0) -- plot ({\x}, {3exp(-(\x\x/3))}) -- (5,0) -- cycle; \fill [domain=-5:-2, smooth, variable=\x, cyclamen!20!white, very thick] (-5,0) -- plot ({\x}, {3exp(-(\x\x/3))}) -- (-2,0) -- cycle; % axes \draw [very thick, <->] (-5,4) -- (-5,0) -- (5,0); % Gaussian \draw [domain=-5:5, smooth, variable=\x, cyclamen, very thick] plot ({\x}, {3exp(-(\x\x/3))}); %notes \draw [thick, cyclamen] (-2,0) -- (-2,0.8); \draw [thick, cyclamen] ( 2,0) -- ( 2,0.8); \node at (2,-0.4) {$x\ob$}; \end{tikzpicture} \end{center} \setbeamercovered{transparent}

L sample results

\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} \ \midrule \multirow{2}{}{1000} & t & 1.549 & 0.072 & 3.790 \ & p & \gre{0.121} & \gre{0.943} & \red{0.000} \ \midrule \multirow{2}{*}{200} & t & 2.508 & 0.418 & 1.547 \ & p & \red{0.012} & \gre{0.676} & \gre{0.122} \ \toprule \end{tabular} \end{center}

M sample results

\begin{center} \begin{tabular}{rcccc} \toprule & & median & mode & fwhm \ \midrule \multirow{2}{}{50000} & t & 669.9 & 0.732 & 1.329 \ & p & \gre{0.000} & \gre{0.464} & \gre{0.184} \ \midrule
\multirow{2}{}{1000} & t & 25.47 & 0.665 & 1.890 \ & p & \gre{0.000} & \gre{0.506} & \gre{0.059} \ \midrule
\multirow{2}{*}{200} & t & 48.12 & 0.028 & 0.388 \ & p & \gre{0.000} & \gre{0.978} & \gre{0.698} \ \toprule \end{tabular} \end{center}

KS samples results

\begin{center} \begin{tabular}{rlll} \toprule & & L sample & M sample \ \midrule \multirow{2}{}{50000} & D & 0.004 & 0.153 \ & p & \gre{0.379} & \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} \ \toprule \end{tabular} \end{center}

Trapani samples results

\begin{center} \begin{tabular}{rlllll} \toprule & & \multicolumn{2}{c}{L sample} & \multicolumn{2}{c}{M sample} \ & & mean & variance & mean & variance \ \midrule \multirow{2}{}{50000} & \Theta & 0.255 & 0.432 & 161.1 & 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} \ \toprule \end{tabular} \end{center}