plotting basically done

statistics/lecture_statistics.tex

@@ -42,7 +42,7 @@
 Bernstein Center T\"ubingen}
 
 \institute[Scientific Computing]{}
- \date{11/27/2013}
+ \date{10/20/2014}
 %\logo{\pgfuseimage{logo}}
 
 \subject{Lectures}
@@ -359,9 +359,7 @@ correlation coefficient does not have that property.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{description of data and plotting}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\subsection{nominal scale}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{what makes a good plot}
 %-------------------------------------------------------------
 \begin{frame}[fragile]
   \frametitle{}
@@ -470,6 +468,8 @@ correlation coefficient does not have that property.
   \end{itemize}
   \mycite{Allen et al. 2012, Neuron}
 \end{frame}
+
+\subsection{bad examples}
 %-------------------------------------------------------------
 \begin{frame}[fragile]
   \frametitle{suboptimal example}
@@ -481,17 +481,50 @@ correlation coefficient does not have that property.
 
 %-------------------------------------------------------------
 \begin{frame}[fragile]
-  \frametitle{different axes}
+  \frametitle{suboptimal example}
+      \begin{center}
+        \includegraphics[width=.5\linewidth]{figs/badbarright.png}
+      \end{center}
+      \source{http://en.wikipedia.org/wiki/Misleading\_graph}
 \end{frame}
+
+%-------------------------------------------------------------
+\begin{frame}[fragile]
+  \frametitle{suboptimal example}
+      \begin{center}
+        \includegraphics[width=.4\linewidth]{figs/yaxisscalingleft.png}
+        \hspace{.5cm}
+        \includegraphics[width=.4\linewidth]{figs/yaxisscalingright.png}
+      \end{center}
+      \source{http://en.wikipedia.org/wiki/Misleading\_graph}
+\end{frame}
+
+%-------------------------------------------------------------
+\begin{frame}[fragile]
+  \frametitle{suboptimal example}
+      \begin{center}
+        \includegraphics[width=.4\linewidth]{figs/badscatterleft.png}
+        \hspace{.5cm}
+        \includegraphics[width=.4\linewidth]{figs/badscatterright.png}
+      \end{center}
+      \source{http://en.wikipedia.org/wiki/Misleading\_graph}
+\end{frame}
+
+
 %-------------------------------------------------------------
 
 \begin{frame}
-  \frametitle{Bad bar plot}
+  \frametitle{suboptimal example}
   \begin{center}
     \includegraphics[width=.8\linewidth]{figs/badbarplot}
   \end{center}
   \source{www.enfovis.com}
 \end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{nominal scale}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
 %-------------------------------------------------------------
 \begin{frame}[fragile]
   \frametitle{plotting nominal data}
@@ -536,7 +569,7 @@ set(gcf, 'PaperPosition',[0.0 0.0 11.7 9.0]);
 \end{frame}
 %-------------------------------------------------------------
 \begin{frame}[fragile]
-  \frametitle{Darstellung nominaler Daten}
+  \frametitle{plotting nominal data}
   \framesubtitle{exercise}
   \begin{task}{pie chart}
     Plot the same data ($n_{py}=50$, $n_{in}=90$) as a pie chart in Matlab.
@@ -544,7 +577,7 @@ set(gcf, 'PaperPosition',[0.0 0.0 11.7 9.0]);
 \end{frame}
 %-------------------------------------------------------------
 \begin{frame}[fragile]
-  \frametitle{Darstellung nominaler Daten}
+  \frametitle{plotting nominal data}
   \framesubtitle{pie chart for relative frequency}
       \scriptsize
 \begin{lstlisting}
@@ -614,18 +647,152 @@ ylabel('Count')
 %-------------------------------------------------------------
 \begin{frame}[fragile]
   \frametitle{plotting interval/ratio/absolute data}
-  \framesubtitle{other ways}
-  There are other ways to plot a sample $x_1, ..., x_n$ of
-  interval/ratio/absolute scale data. E.g. 
+  \framesubtitle{bar plot}
+  There are several ways to plot a sample $x_1, ..., x_n$ of interval/ratio/absolute
+  scale with a bar plot
+  \begin{center}
+    \includegraphics[width=.6\linewidth]{figs/barplots.png}
+  \end{center}
+\end{frame}
+
+%-------------------------------------------------------------
+\begin{frame}[fragile,fragile]
+  \frametitle{plotting interval/ratio/absolute data}
+  \framesubtitle{bar plot}
+\scriptsize
+\begin{lstlisting}
+% bar plot
+x = rand(10,1);
+gray = [.5,.5,.5];
+
+bar(1, mean(x), 'EdgeColor','w','FaceColor', gray);
+hold on
+
+bar(2, mean(x), 'EdgeColor','w','FaceColor', gray);
+plot(0*x + 2, x, 'ok');
+
+bar(3, mean(x), 'EdgeColor','w','FaceColor', gray);
+errorbar(3, mean(x), std(x), 'ok');
+
+bar(4, mean(x), 'EdgeColor','w','FaceColor', gray);
+errorbar(4, mean(x), std(x)/sqrt(length(x)), 'ok');
+set(gca, 'xtick',[])
+ylabel('uniformly distributed random data in [0,1]')
+box('off')
+title('different forms of bar plots')
+hold off
+\end{lstlisting}
+\end{frame}
+
+%-------------------------------------------------------------
+\begin{frame}[fragile,fragile]
+  \frametitle{plotting interval/ratio/absolute data}
+  \framesubtitle{bar plot and measure of central tendency and spread}
+
   \begin{itemize}
-  \item box plot 
-  \item bar plot
-  \item smoothed histogram
-  \item ...
+  \item A bar plot collapses real data onto a single number and some
+    measure of spread. This number is usually a {\em measure of central
+    tendency}, i.e. a typical/central value for the probability
+  distribution of the data.\pause
+  \item What measures of central tendency can you think of?\pause
+    \begin{itemize}
+    \item mean
+    \item median
+    \item geometric mean (the nth root of the product of the data values)
+    \item weighted mean
+    \item midrange (mean of the maximum and minimum values of a data set)
+    \end{itemize}\pause
+  \item Additionally, the bar plot is equipped with a measure of {\em
+      spread} or {\em dispersion}. What measure of spread can you think of?\pause
+    \begin{itemize}
+    \item standard deviation
+    \item range (maximum minus minimum of a dataset)
+    \item inter-quartile range 
+    \end{itemize}
   \end{itemize}
-  We will look at them while plotting mixed data in the following.
 \end{frame}
 
+%-------------------------------------------------------------
+\begin{frame}[fragile,fragile]
+  \frametitle{plotting interval/ratio/absolute data}
+  \framesubtitle{measure of central tendency and spread}
+  \Large
+  \begin{center}
+    \bf The part of statistics that summarizes data in a small number
+    of values is called {\em descriptive statistics}.
+  \end{center}
+\end{frame}
+
+%-------------------------------------------------------------
+\begin{frame}[fragile]
+  \frametitle{plotting interval/ratio/absolute data}
+  \framesubtitle{boxplot}
+  \begin{minipage}{1.0\linewidth}
+    \begin{minipage}{0.5\linewidth}
+      \begin{center}
+        \includegraphics[width=\linewidth]{figs/boxplot.png}
+      \end{center}
+    \end{minipage}
+    \begin{minipage}{0.5\linewidth}
+      Who knows what the elements mean?\pause
+      \begin{itemize}
+      \item the box depicts the inter-quartile range
+      \item the line denotes the median
+      \item the whiskers denote the extreme value of the data not
+        considered outliers
+      \item outliers are plotted separately 
+      \end{itemize}
+      \begin{task}{Outliers}
+        \begin{itemize}
+        \item Find out how an outlier is defined in a matlab boxplot.
+        \item Can you remove an outlier from the dataset?
+        \end{itemize}
+      \end{task}
+    \end{minipage}
+  \end{minipage}
+\end{frame}
+
+%-------------------------------------------------------------
+\begin{frame}[fragile]
+  \frametitle{plotting interval/ratio/absolute data}
+  \framesubtitle{violinplot}
+      \begin{center}
+        \includegraphics[width=.8\linewidth]{figs/violinplots.png}
+      \end{center}
+      \begin{itemize}
+      \item Violinplots depict the distribution of the data by a
+        smoothed histogram. 
+      \item Additional information (data points, median,
+        inter-quartile range) are plotted inside. 
+      \end{itemize}
+\end{frame}
+
+%-------------------------------------------------------------
+\begin{frame}[fragile]
+  \frametitle{plotting combinations of scales}
+  What could we use for a combination of categorial/nominal and
+  interval/ratio/absolute?
+  \pause
+  \begin{center}
+    \includegraphics[width=.5\linewidth]{figs/factorplot.png}
+  \end{center}
+  Each category is a single bar. 
+\end{frame}
+
+%-------------------------------------------------------------
+\begin{frame}[fragile]
+  \frametitle{plotting combinations of scales}
+  What could we use for a combination of interval/ratio/absolute and
+  interval/ratio/absolute, e.g. $(x_1, y_1), ..., (x_n,y_n)$?  \pause
+  \begin{center}
+    \includegraphics[width=.8\linewidth]{figs/paireddata.png}
+  \end{center}
+  Scatter plot or paired bar chart. Scatter plot can also be used for
+  ordinal vs. ordinal data (why not the bar chart?). 
+\end{frame}
+
+
+
 
 \end{document} 
  

statistics/matlab/intervalplots.m

@@ -14,3 +14,42 @@ ylabel('Count')
 set(gcf, 'PaperUnits', 'centimeters');
 set(gcf, 'PaperSize', [11.7 9.0]);
 set(gcf, 'PaperPosition',[0.0 0.0 11.7 9.0]);
+
+% bar plot
+figure
+x = rand(10,1);
+gray = [.5,.5,.5];
+
+bar(1, mean(x), 'EdgeColor','w','FaceColor', gray);
+hold on
+
+bar(2, mean(x), 'EdgeColor','w','FaceColor', gray);
+plot(0*x + 2, x, 'ok');
+
+bar(3, mean(x), 'EdgeColor','w','FaceColor', gray);
+errorbar(3, mean(x), std(x), 'ok');
+
+bar(4, mean(x), 'EdgeColor','w','FaceColor', gray);
+errorbar(4, mean(x), std(x)/sqrt(length(x)), 'ok');
+set(gca, 'xtick',[])
+ylabel('uniformly distributed random data in [0,1]')
+box('off')
+title('different forms of bar plots')
+set(gcf, 'PaperUnits', 'centimeters');
+set(gcf, 'PaperSize', [11.7 9.0]);
+set(gcf, 'PaperPosition',[0.0 0.0 11.7 9.0]);
+hold off
+
+% box plot
+figure
+x = rand(10,1);
+x(10) = 3;
+boxplot(x)
+set(gca, 'xtick',[])
+ylabel('data')
+box('off')
+title('box plot')
+set(gcf, 'PaperUnits', 'centimeters');
+set(gcf, 'PaperSize', [11.7 9.0]);
+set(gcf, 'PaperPosition',[0.0 0.0 11.7 9.0]);
+hold off