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} %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 [below] at (0,-0.7) {$x\ex$}; \node [above right] at (1.5,1.5) {$2 , \sqrt{\sigma\ex^2 + \sigma\ob^2}$}; % 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))}); \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,-0.7) {$x\ob$}; \end{tikzpicture} \end{center} \setbeamercovered{transparent}

Compatibility results:

Median:

:::: {.columns} ::: {.column width=50%}

• t = 0.761
• $p = 0.446$ :::

::: {.column width=50%}

$$
\hence \text{Compatible!}

::: ::::

\vspace{10pt}

. . .

Mode:

:::: {.columns} ::: {.column width=50%}

• t = 1.012
• $p = 0.311$ :::

::: {.column width=50%}

$$
\hence \text{Compatible!}

::: ::::

\vspace{10pt}

. . .

FWHM:

:::: {.columns} ::: {.column width=50%}

• t=1.338
• $p=0.181$ :::

::: {.column width=50%}

$$
\hence \text{Compatible!}

::: ::::

Compatibility results:

Median:

:::: {.columns} ::: {.column width=50%}

• t = 669.940
• $p = 0.000$ :::

::: {.column width=50%}

$$
\hence \text{Not compatible!}

::: ::::

\vspace{10pt}

. . .

Mode:

:::: {.columns} ::: {.column width=50%}

• t = 0.732
• $p = 0.464$ :::

::: {.column width=50%}

$$
\hence \text{Compatible!}

::: ::::

\vspace{10pt}

. . .

FWHM:

:::: {.columns} ::: {.column width=50%}

• t = 1.329
• $p = 0.184$ :::

::: {.column width=50%}

$$
\hence \text{Compatible!}

::: ::::

KS results

Samples results

N = 50000 sampled points

. . .

Landau sample:

:::: {.columns} ::: {.column width=50%}

• D = 0.004
• $p = 0.379$ :::

::: {.column width=50%}

$$
\hence \text{Compatible!}

::: ::::

\vspace{10pt}

. . .

Moyal sample:

:::: {.columns} ::: {.column width=50%}

• D = 0.153
• $p = 0.000$ :::

::: {.column width=50%}

$$
\hence \text{Not compatible!}

::: ::::

Trapani results

Samples results

. . .

Landau sample:

:::: {.columns} ::: {.column width=33%}

$$
\mu_1
\begin{cases}
  \Theta = 0.255 \\
  p = 0.614
\end{cases}

:::

::: {.column width=33% .c}

$$
\mu_2
\begin{cases}
  \Theta = 0.432 \\
  p = 0.511
\end{cases}

:::

::: {.column width=33% .c}

$$
\hence \text{Infinite!}

::: ::::

. . .

\vspace{20pt}

Moyal sample:

:::: {.columns} ::: {.column width=33%}

$$
\mu_1
\begin{cases}
  \Theta^2 = 106 \\
  p = 0.000
\end{cases}

:::

::: {.column width=33%}

$$
\mu_2
\begin{cases}
  \Theta^2 = 162 \\
  p = 0.000
\end{cases}

:::

::: {.column width=33% .c}

$$
\hence \text{Finite!}

::: ::::