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\title[]{Scientific Computing --- Descriptive Statistics}
\author[]{Jan Benda}
\institute[]{Neuroethology}
\date[]{WS 15/16}
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\section{Descriptive statistics}


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\subsection{Statistics of ratio data}

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\begin{frame}
  \frametitle{Statistics of ratio data}
  \begin{itemize}
  \item Location, central tendency
    \begin{itemize}
    \item arithmetic mean
    \item median
    \item mode
    \end{itemize}

  \item Spread, dispersion
    \begin{itemize}
    \item variance
    \item standard deviation
    \item interquartile range
    \item coefficient of variation
    \item minimum, maximum
    \end{itemize}

  \item Shape
    \begin{itemize}
    \item skewnees
    \item kurtosis
    \end{itemize}

  \item Dependence
    \begin{itemize}
    \item Pearson correlation coefficient
    \item Spearman's rank correlation coefficient
    \end{itemize}

  \end{itemize}
\end{frame}

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\subsection{Data types}

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\begin{frame}
  \frametitle{Data types: nominal scale}
  \begin{itemize}
  \item Binary
    \begin{itemize}
    \item ``yes/no'',
    \item ``true/false'',
    \item ``success/failure'', etc.
    \end{itemize}
  \item Categorial
    \begin{itemize}
    \item cell type (``rod/cone/horizontal cell/bipolar cell/ganglion cell''),
    \item blood type (``A/B/AB/0''),
    \item parts of speech (``noun/veerb/preposition/article/...''),
    \item taxonomic groups (``Coleoptera/Lepidoptera/Diptera/Hymenoptera''), etc.
    \end{itemize}
  \item Each observation/measurement/sample is put into one category
  \item There is no reasonable order among the categories.\\
    example: [rods, cones] vs. [cones, rods]
  \pause
  \item Statistics: mode, i.e. the most common item
  \end{itemize}
\end{frame}

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\begin{frame}
  \frametitle{Data types: ordinal scale}
  \begin{itemize}
  \item Like nominal scale, but with an order
  \item Examples: ranks, ratings
    \begin{itemize}
    \item ``bad/ok/good'',
    \item ``cold/warm/hot'',
    \item ``young/old'', etc.
    \end{itemize}
  \item {\bf But:} there is no reasonable measure of {\em distance}
    between the classes
  \pause
  \item Statistics: mode, median
  \end{itemize}
\end{frame}

%-------------------------------------------------------------
\begin{frame}
  \frametitle{Data types: interval scale}
  \begin{itemize}
  \item Quantitative/metric values
  \item Reasonable measure of distance between values, but no absolute zero
  \item Examples: 
    \begin{itemize}
    \item Temperature in $^\circ$C ($20^\circ$C is not twice as hot as $10^\circ$C)
    \item Direction measured in degrees from magnetic or true north
    \end{itemize}
  \pause
  \item Statistics:
    \begin{itemize}
    \item Central tendency: mode, median, arithmetic mean
    \item Dispersion: range, standard deviation
    \end{itemize}
  \end{itemize}
\end{frame}

%-------------------------------------------------------------
\begin{frame}
  \frametitle{Data types: absolute/ratio scale}
  \begin{itemize}
  \item Like interval scale, but with absolute origin/zero
  \item Examples: 
    \begin{itemize}
    \item Temperature in $^\circ$K
    \item Length, mass, duration, electric charge, ...
    \item Plane angle, etc.
    \item Count (e.g. number of spikes in response to a stimulus)
    \end{itemize}
  \pause
  \item Statistics:
    \begin{itemize}
    \item Central tendency: mode, median, arithmetic, geometric, harmonic mean
    \item Dispersion: range, standard deviation
    \item Coefficient of variation (ratio standard deviation/mean)
    \item All other statistical measures
    \end{itemize}
  \end{itemize}
\end{frame}

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\begin{frame}
  \frametitle{Data types}
  \begin{itemize}
  \item Data type selects
    \begin{itemize}
    \item statistics 
    \item type of plots (bar graph versus x-y plot)
    \item correct tests
    \end{itemize}
  \item Scales exhibit increasing information content from nominal
    to absolute.\\
    Conversion  ,,downwards'' is always possible
  \item For example: size measured in meter (ratio scale) $\rightarrow$
    categories ``small/medium/large'' (ordinal scale)
  \end{itemize}
\end{frame}

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\begin{frame}
  \frametitle{Examples from neuroscience}
  \begin{itemize}

  \item {\bf absolute:}\pause
    \begin{itemize}
    \item size of neuron/brain
    \item length of axon
    \item ion concentration
    \item membrane potential
    \item firing rate
    \end{itemize}

  \item {\bf interval:}\pause
    \begin{itemize}
    \item edge orientation
    \end{itemize}

  \item {\bf ordinal:} \pause 
    \begin{itemize}
    \item stages of a disease
    \item ratings
    \end{itemize}

  \item {\bf nominal:}\pause 
    \begin{itemize}
    \item cell type
    \item odor
    \item states of an ion channel
    \end{itemize}

  \end{itemize}
\end{frame}


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