scientificComputing/statistics/lecture/descriptivestatistics.tex

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\title[]{Scientific Computing --- Descriptive Statistics}
\author[]{Jan Benda}
\institute[]{Neuroethology}
\date[]{WS 15/16}
\titlegraphic{\includegraphics[width=0.3\textwidth]{UT_WBMW_Rot_RGB}}

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\begin{frame}
  \frametitle{Content}
  \tableofcontents
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\section{Descriptive statistics}


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\subsection{types of data}

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\begin{frame}
  \frametitle{data scales}
  \framesubtitle{What data types are distinguished in statistics?}
  \Large
  {\bf Why are data types important?}
  \pause
  \begin{itemize}
  \item selection of statistics 
  \item selection of plots
  \item selection of correct tests
  \end{itemize}
\end{frame}
%-------------------------------------------------------------

\begin{frame}
  \frametitle{data scales}
  \framesubtitle{nominal/categorial scale}
  \begin{itemize}
  \item properties like cell type, experimental group (i.e. treatment
    1, treatment 2, control)
  \item each observation/sample is put into one category
  \item there is no reasonable order among the categories
  \item  example: [rods, cones] vs. [cones, rods]
  \end{itemize}
\end{frame}
%-------------------------------------------------------------

\begin{frame}
  \frametitle{data scales}
  \framesubtitle{ordinal scale}
  \begin{itemize}
  \item like nominal scale, but there is an order
  \item {\bf but:} there is no reasonable measure of {\em distance}
    between the classes
  \item examples: ranks, ratings
  \end{itemize}
\end{frame}
%-------------------------------------------------------------

\begin{frame}
  \frametitle{data scales}
  \framesubtitle{interval scale}
  \begin{itemize}
  \item quantitative/metric values
  \item reasonable measure of distance between values but no absolute zero
  \item examples: temperature in $^\circ$C
  \end{itemize}
\end{frame}
%-------------------------------------------------------------

\begin{frame}
  \frametitle{data scales}
  \framesubtitle{absolut/ratio scale}
  \begin{itemize}
  \item like interval scale but with absolute zero
  \item example: temperature in $^\circ$K
  \end{itemize}
  \pause
  %\begin{emphasize}{relationsships between scales}
    \begin{itemize}
    \item scales exhibit increasing information content from nominal
      to absolute
    \item conversion  ,,downwards'' always possible
    \end{itemize}
  %\end{emphasize}
\end{frame}

%-------------------------------------------------------------
\begin{frame}
  \frametitle{examples from neuroscience and psychology}
  \begin{itemize}
  \item {\bf nominal:}\pause 
    \begin{itemize}
    \item treatment group
    \item stimulus class
    \item cell type
    \end{itemize}

  \item {\bf ordinal:} \pause 
    \begin{itemize}
    \item ratings
    \item clinical stages of a disease
    \item states of an ion channel
    \end{itemize}
  \item {\bf Absolut-/Ratioskala:}\pause
    \begin{itemize}
    \item firing rate
    \item membrane potential
    \item ion concentration
    \end{itemize}
  \end{itemize}
\end{frame}


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\subsection{Real-valued data}