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diff --git a/statistics/lecture_statistics.tex b/statistics/lecture_statistics.tex
index 36c7c31..3ef58ff 100755
--- a/statistics/lecture_statistics.tex
+++ b/statistics/lecture_statistics.tex
@@ -113,7 +113,7 @@ Bernstein Center T\"ubingen}
% PCA
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section[Pr�ludium]{Prelude}
+\section[Prelude]{Prelude}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% ----------------------------------------------------------
@@ -364,32 +364,162 @@ correlation coefficient does not have that property.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%-------------------------------------------------------------
\begin{frame}[fragile]
- \frametitle{Darstellung nominaler Daten}
- \framesubtitle{Bar-Plot f\"ur Anzahl/ rel. H\"aufigkeit}
+ \frametitle{}
+ \begin{center}
+ \Huge What makes a good plot?
+ \end{center}
+\end{frame}
+
+%-------------------------------------------------------------
+\begin{frame}[fragile]
+ \frametitle{features of a good plot}
+ A good plot
+ \begin{itemize}
+ \item helps the reader to clearly understand your point.\pause
+ \item is not misleading and let's the reader judge the information
+ on her own (different y-axis/length scales in two related plots,
+ "squeezing" via log-plots). \pause
+ \item contains information about the data (a comic might be
+ illustrative, but does not contain information about the
+ data).\pause
+ \item adheres to the principle of {\em ink minimization}.
+ \end{itemize}
+\end{frame}
+
+
+%-------------------------------------------------------------
+\begin{frame}[fragile]
+ \frametitle{features of a good plot}
+ \framesubtitle{design/organization}
+ \begin{itemize}
+ \item Is the display consistent with the model or hypothesis
+ being tested?\pause
+ \item Are there "empty dimensions" in the display that could be
+ removed (A 3D pie chart for 2D categorical data, extraneous colors
+ that do not encode meaningful information)?\pause
+ \item Does the display provide an honest and transparent portrayal
+ of the data (hiding, smoothing, modifying data points should be
+ avoided or explicitly mentioned)?
+ \end{itemize}
+ \mycite{Allen et al. 2012, Neuron}
+\end{frame}
+
+%-------------------------------------------------------------
+\begin{frame}[fragile]
+ \frametitle{features of a good plot}
+ \framesubtitle{axes}
+ \begin{itemize}
+ \item Are axes scales defined as linear, log, or radial?\pause
+ \item Does each axis label describe the variable and its units (use
+ "a.u." for arbitrary units)?\pause
+ \item Are axes limits appropriate for the data (The graphic should
+ not be bounded at zero if the data can take on both positive and
+ negative values.)?\pause
+ \item Is the aspect ratio appropriate for the data (When x and y
+ axes contrast the same variable under different conditions the
+ graphic should be square.)?
+ \end{itemize}
+ \mycite{Allen et al. 2012, Neuron}
+\end{frame}
+%-------------------------------------------------------------
+\begin{frame}[fragile]
+ \frametitle{features of a good plot}
+ \framesubtitle{color mapping}
+ \begin{itemize}
+ \item Is a color bar provided?\pause
+ \item Is the color map sensible for the data type (does the data
+ extend to both $\pm$, does it live in an interval, is it
+ circular)?\pause
+ \item Are contrasting colors consistent with a natural interpretation?
+ \item Can features be discriminated when printed in grayscale?
+ \item Has red/green contrast been avoided to accommodate common
+ forms of colorblindness?
+ \end{itemize}
+ \mycite{Allen et al. 2012, Neuron}
+\end{frame}
+%-------------------------------------------------------------
+\begin{frame}[fragile]
+ \frametitle{features of a good plot}
+ \framesubtitle{uncertainty}
+ \begin{itemize}
+ \item Does the display indicate the uncertainty of estimated parameters?\pause
+ \item Is the type of error surface appropriate for the data?
+ \begin{itemize}
+ \item Use standard deviations to describe variability in the population.\pause
+ \item Use standard errors or confidence intervals to make inferences
+ about parameters estimated from a sample.\pause
+ \item Parametric confidence intervals should only be used if data
+ meet the assumptions of the underlying model.\pause
+ \end{itemize}
+ \item Are the units of uncertainty defined (is it standard error, is
+ it $95\%$ confidence interval)?
+ \end{itemize}
+ \mycite{Allen et al. 2012, Neuron}
+\end{frame}
+%-------------------------------------------------------------
+\begin{frame}[fragile]
+ \frametitle{features of a good plot}
+ \framesubtitle{annotation}
+ \begin{itemize}
+ \item Are all symbols defined, preferably by directly labeling objects?\pause
+ \item Is the directionality of a contrast between conditions obvious?\pause
+ \item Is the number of samples or independent experiments indicated?\pause
+ \item Are statistical procedures and criteria for significance described?\pause
+ \item Are uncommon abbreviations avoided or clearly defined?\pause
+ \item Are abbreviations consistent with those used in the text?
+ \end{itemize}
+ \mycite{Allen et al. 2012, Neuron}
+\end{frame}
+%-------------------------------------------------------------
+\begin{frame}[fragile]
+ \frametitle{suboptimal example}
+ \begin{center}
+ \includegraphics[width=.5\linewidth]{figs/nobelbad}
+ \end{center}
+ \mycite{Hafting et al. 2005, nature}
+\end{frame}
+
+%-------------------------------------------------------------
+\begin{frame}[fragile]
+ \frametitle{different axes}
+\end{frame}
+%-------------------------------------------------------------
+
+\begin{frame}
+ \frametitle{Bad bar plot}
+ \begin{center}
+ \includegraphics[width=.8\linewidth]{figs/badbarplot}
+ \end{center}
+ \source{www.enfovis.com}
+\end{frame}
+%-------------------------------------------------------------
+\begin{frame}[fragile]
+ \frametitle{plotting nominal data}
+ \framesubtitle{bar plot for count and relative frequency}
\begin{center}
\includegraphics[width=.8\linewidth]{figs/nominaldataplot}
\end{center}
\end{frame}
%-------------------------------------------------------------
\begin{frame}[fragile]
- \frametitle{Darstellung nominaler Daten}
- \framesubtitle{Bar-Plot f\"ur Anzahl/ rel. H\"aufigkeit}
+ \frametitle{plotting nominal data}
+ \framesubtitle{bar plot for count and relative frequency}
\scriptsize
\begin{lstlisting}
-% eigentlicher Plot
+% plot
bar([1,2], [50, 90], 'facecolor', 'k')
-% Achsenbeschriftung
+% labels axes
ylabel('cell count')
xlabel('cell type')
-% Kosmetik
+% cosmetics
xlim([0.5,2.5])
ylim([0, 100])
box('off')
set(gca,'XTick',1:2,'XTickLabel',{'pyramidal','interneuron'},'FontSize',20)
-% Settings fuers Abspeichern
+% settings for saving the figure
set(gcf, 'PaperUnits', 'centimeters');
set(gcf, 'PaperSize', [11.7 9.0]);
set(gcf, 'PaperPosition',[0.0 0.0 11.7 9.0]);
@@ -398,8 +528,8 @@ set(gcf, 'PaperPosition',[0.0 0.0 11.7 9.0]);
%----------------------------------------------------------
\begin{frame}[fragile]
- \frametitle{Darstellung nominaler Daten}
- \framesubtitle{Pie-Chart f\"ur Anzahl/ rel. H\"aufigkeit}
+ \frametitle{plotting nominal data}
+ \framesubtitle{pie chart for count and relative frequency}
\begin{center}
\includegraphics[width=.8\linewidth]{figs/nominaldataplot2}
\end{center}
@@ -407,15 +537,15 @@ set(gcf, 'PaperPosition',[0.0 0.0 11.7 9.0]);
%-------------------------------------------------------------
\begin{frame}[fragile]
\frametitle{Darstellung nominaler Daten}
- \framesubtitle{\"Ubung}
- \begin{task}{Pie-Chart}
- Plotte dieselben Daten ($n_{py}=50$, $n_{in}=90$) als Pie-Chart in Matlab.
+ \framesubtitle{exercise}
+ \begin{task}{pie chart}
+ Plot the same data ($n_{py}=50$, $n_{in}=90$) as a pie chart in Matlab.
\end{task}
\end{frame}
%-------------------------------------------------------------
\begin{frame}[fragile]
\frametitle{Darstellung nominaler Daten}
- \framesubtitle{Pie-Chart f\"ur Anzahl/ rel. H\"aufigkeit}
+ \framesubtitle{pie chart for relative frequency}
\scriptsize
\begin{lstlisting}
data = [50, 90];
@@ -438,9 +568,64 @@ set(gcf, 'PaperPosition',[0.0 0.0 11.7 9.0]);
%-------------------------------------------------------------
\begin{frame}[fragile]
- \frametitle{Darstellung von Interval-/Absolutskala Daten}
-
+ \frametitle{plotting interval/ratio/absolute data}
+ \framesubtitle{histogram}
+ \begin{center}
+ \includegraphics[width=.8\linewidth]{figs/histogram}
+ \end{center}
\end{frame}
+%-------------------------------------------------------------
+\begin{frame}[fragile]
+ \frametitle{plotting interval/ratio/absolute data}
+ \framesubtitle{bad choice of bins}
+ \begin{center}
+ \includegraphics[width=.4\linewidth]{figs/histogrambad}
+ \includegraphics[width=.4\linewidth]{figs/histogrambad2}
+ \end{center}
+ \begin{summary}{Rule of thumb}
+ Choose the bins $b\approx n/20$.
+ \end{summary}
+\end{frame}
+%-------------------------------------------------------------
+\begin{frame}[fragile]
+ \frametitle{plotting interval/ratio/absolute data}
+ \framesubtitle{how to do in Matlab}
+ \scriptsize
+\begin{lstlisting}
+x = randn(2000,1); % generate Gaussian data
+
+hist(x, 50); % generate histogram
+
+% set facecolor to gray
+h = findobj(gca, 'Type','patch');
+set(h(1), 'FaceColor',[.2,.2,.2], 'EdgeColor','w', 'linewidth',2)
+
+% plot a white grid over it
+h = gridxy([],get(gca,'ytick'),'color','w','linewidth',2)
+uistack(h, 'top')
+
+% cosmetics
+box('off');
+xlabel('Data')
+ylabel('Count')
+\end{lstlisting}
+\end{frame}
+
+%-------------------------------------------------------------
+\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.
+ \begin{itemize}
+ \item box plot
+ \item bar plot
+ \item smoothed histogram
+ \item ...
+ \end{itemize}
+ We will look at them while plotting mixed data in the following.
+\end{frame}
+
\end{document}
diff --git a/statistics/matlab/gridxy.m b/statistics/matlab/gridxy.m
new file mode 100644
index 0000000..1fbe64a
--- /dev/null
+++ b/statistics/matlab/gridxy.m
@@ -0,0 +1,127 @@
+function hh = gridxy(x,varargin)
+% GRIDXY - Plot grid lines
+% GRIDXY(X) plots vertical grid lines at the positions specified
+% by X. GRIDXY(X,Y) also plots horizontal grid lines at the positions
+% specified by Y. GRIDXY uses the current axes, if any. Lines outside
+% the plot area are plotted but not shown. When X or Y is empty no vertical
+% or horizontal lines are plotted.
+%
+% The lines are plotted as a single graphics object. H = GRIDXY(..) returns
+% a graphics handle to that line object.
+%
+% GRIDXY(..., 'Prop1','Val1','Prop2','Val2', ...) uses the properties
+% and values specified for color, linestyle, etc. Execute GET(H), where H is
+% a line handle, to see a list of line object properties and their current values.
+% Execute SET(H) to see a list of line object properties and legal property values.
+%
+% Examples
+% % some random plot
+% plot(10*rand(100,1), 10*rand(100,1),'bo') ;
+% % horizontal red dashed grid
+% gridxy([1.1 3.2 4.5],'Color','r','Linestyle',':') ;
+% % vertical solid thicker yellowish grid, and store the handle
+% h = gridxy([],[2.1:0.7:5 8],'Color',[0.9 1.0 0.2],'linewidth',3) ;
+%
+% GRIDXY can be used to plot a irregular grid on the axes.
+%
+% See also PLOT, REFLINE, GRID, AXES, REFLINEXY
+
+% NOTE: This function was previously known as XYREFLINE
+
+% for Matlab R13
+% version 2.2 (feb 2008)
+% (c) Jos van der Geest
+% email: jos@jasen.nl
+
+% History
+% Created (1.0) feb 2006
+% 2.0 apr 2007 - renamed from reflinexy to gridxy, reflinexy is now used
+% for plotting intersection between X and Y axes
+% 2.1 apr 2007 - add error check for line properties
+% 2.2 feb 2008 - added set(gca,'layer','top') to put gridlines behind the
+% axis tick marks
+
+error(nargchk(1,Inf,nargin)) ;
+
+% check the arguments
+if ~isnumeric(x),
+ error('Numeric argument expected') ;
+end
+
+if nargin==1,
+ y = [] ;
+ va = [] ;
+else
+ va = varargin ;
+ if ischar(va{1}),
+ % optional arguments are
+ y = [] ;
+ elseif isnumeric(va{1})
+ y = va{1} ;
+ va = va(2:end) ;
+ else
+ error('Invalid second argument') ;
+ end
+ if mod(size(va),2) == 1,
+ error('Property-Value have to be pairs') ;
+ end
+end
+
+% get the axes to plot in
+hca=get(get(0,'currentfigure'),'currentaxes');
+if isempty(hca),
+ warning('No current axes found') ;
+ return ;
+end
+
+% get the current limits of the axis
+% used for limit restoration later on
+xlim = get(hca,'xlim') ;
+ylim = get(hca,'ylim') ;
+
+% setup data for the vertical lines
+xx1 = repmat(x(:).',3,1) ;
+yy1 = repmat([ylim(:) ; nan],1,numel(x)) ;
+
+% setup data for the horizontal lines
+xx2 = repmat([xlim(:) ; nan],1,numel(y)) ;
+yy2 = repmat(y(:).',3,1) ;
+
+
+% create data for a single line object
+xx1 = [xx1 xx2] ;
+if ~isempty(xx1),
+ yy1 = [yy1 yy2] ;
+ % add the line to the current axes
+ np = get(hca,'nextplot') ;
+ set(hca,'nextplot','add') ;
+ h = line('xdata',xx1(:),'ydata',yy1(:)) ;
+ set(hca,'ylim',ylim,'xlim',xlim) ; % reset the limits
+
+ uistack(h,'bottom') ; % push lines to the bottom of the graph
+ set(hca,'nextplot',np,'Layer','top') ; % reset the nextplot state
+
+ if ~isempty(va),
+ try
+ set(h,va{:}) ; % set line properties
+ catch
+ msg = lasterror ;
+ error(msg.message(21:end)) ;
+ end
+ end
+
+else
+ h = [] ;
+end
+
+if nargout==1, % if requested return handle
+ hh = h ;
+end
+
+
+
+
+
+
+
+
diff --git a/statistics/matlab/intervalplots.m b/statistics/matlab/intervalplots.m
index b069918..7b04e92 100644
--- a/statistics/matlab/intervalplots.m
+++ b/statistics/matlab/intervalplots.m
@@ -2,5 +2,15 @@ close all
% histogram
figure()
x = randn(2000,1);
-hist(x, 50, 'gray')
-box('off');
\ No newline at end of file
+hist(x, 50);
+h = findobj(gca, 'Type','patch');
+set(h(1), 'FaceColor',[.2,.2,.2], 'EdgeColor','w', 'linewidth',2)
+grid('off')
+h = gridxy([],get(gca,'ytick'),'color','w','linewidth',2)
+box('off');
+uistack(h, 'top')
+xlabel('Data')
+ylabel('Count')
+set(gcf, 'PaperUnits', 'centimeters');
+set(gcf, 'PaperSize', [11.7 9.0]);
+set(gcf, 'PaperPosition',[0.0 0.0 11.7 9.0]);