Merge branch 'master' of raven.am28.uni-tuebingen.de:scientificComputing

statistics/lecture_statistics.tex

@@ -4,7 +4,6 @@
 \usepackage{pgf}
 %\usepackage{pgf,pgfarrows,pgfnodes,pgfautomata,pgfheaps,pgfshade} 
 %\usepackage{multimedia}
-\usepackage[ngerman]{babel}
 \usepackage[latin1]{inputenc}
 \usepackage{amsmath}
 \usepackage{bm} 
@@ -86,13 +85,13 @@ Bernstein Center T\"ubingen}
 \end{frame} 
 
 \begin{frame} 
-  \frametitle{Plan}
+  \frametitle{plan}
   \setcounter{tocdepth}{1}
   \tableofcontents 
 
 \end{frame} 
 \begin{frame} 
-  \frametitle{Information \"uber Statistik}
+  \frametitle{information}
   \begin{itemize}
   \item Samuels, M. L., Wittmer, J. A., \& Schaffner,
     A. A. (2010). Statistics for the Life Sciences (4th ed.,
@@ -114,41 +113,41 @@ Bernstein Center T\"ubingen}
 % PCA
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section[Präludium]{Präludium}
+\section[Prelude]{Prelude}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 % ----------------------------------------------------------
 \begin{frame} 
-\frametitle{Meine Erwartungen an Masterstudenten}
+\frametitle{my expectations to this course}
 \begin{itemize}
-\item Interesse und Partizipation
-\item Motivation Konzepte zu verstehen und zu hinterfragen
-\item einen hohen wissenschaftlichen Qualitätsstandard
-\item intellektuelle Redlichkeit
-\item ehrliche Kooperation
+\item interest and participation
+\item motivation to understand and question concepts 
+\item high scientific standard
+\item intellectual honesty
+\item sincere cooperation
 \end{itemize}
 \end{frame}
 
 % ----------------------------------------------------------
 \begin{frame} 
-\frametitle{diese Woche wird ...}
+\frametitle{this week will be ...}
 
 \only<1>{
-\framesubtitle{... kein \sout{Spaß} Zuckerschlecken}
+\framesubtitle{... no \sout{fun} piece of cake}
 \begin{center}
   \includegraphics[height=0.7\textheight]{figs/feeding.jpg}
 \end{center}
 }
 
 \only<2>{
-\framesubtitle{... kein \sout{Spaß} Zuckerschlecken}
+\framesubtitle{... no \sout{fun} piece of cake}
 \begin{center}
   \includegraphics[height=0.7\textheight]{figs/nacho-trainer.jpg}
 \end{center}
 }
 
 \only<3>{
-\framesubtitle{... keine Vorlesung (Bitte!)}
+\framesubtitle{... no lecture (please!)}
 \begin{center}
   \includegraphics[height=0.7\textheight]{figs/soccer.jpg}
 \end{center}
@@ -158,138 +157,131 @@ Bernstein Center T\"ubingen}
 
 % ----------------------------------------------------------
 \begin{frame} 
-\frametitle{Was Ihr diese Woche lernen solltet}
+\frametitle{What you should learn this week}
 \begin{itemize}
-\item Eigenschaften guter Plots
-\item Was ist deskriptive/ inferentielle Statistik?
-\item die generelle Struktur statistischer Tests
-\item Was ist/bedeutet ein p-Wert?
-\item Wie bastele ich mir meinen eigenen Test? 
-\item Wie groß muß mein $n$ sein?
-\item Principal Component Analysis (PCA)
+\item What makes good plots?
+\item What is descriptive/inferential statistics?
+\item What is the general structure of a statistical test?
+\item What does a p-value mean?
+\item How can I build my own tests?
+\item How large should my $n$ be?
+\item What is {\em maximum likelihood} and why is it important?
 \end{itemize}
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section[deskriptive Statistik, Fehlerbalken \& Plots]{Day 1 -- Deskriptive
-  Statistik, Fehlerbalken und Plots}
+\section[descriptive statistics, errorbars, and plots]{Day 1 -- descriptive statistics, errorbars, and plots}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\subsection{Arten von Daten}
+\subsection{types of data}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \begin{frame}
-  \frametitle{Datenskalen}
-  \framesubtitle{Welche Datentypen gibt es in der Statistik?}
+  \frametitle{data scales}
+  \framesubtitle{What data types are distinguished in statistics?}
   \Large
-  {\bf Warum sind Datentypen wichtig?}
+  {\bf Why are data types important?}
   \pause
   \begin{itemize}
-  \item Auswahl passender Statistiken
-  \item Auswahl angemessener Plots
-  \item Auswahl von korrekten Tests
+  \item selection of statistics 
+  \item selection of plots
+  \item selection of correct tests
   \end{itemize}
 \end{frame}
 %-------------------------------------------------------------
 
 \begin{frame}
-  \frametitle{Datenskalen}
-  \framesubtitle{Nominalskala (engl. ,,categorial'')}
+  \frametitle{data scales}
+  \framesubtitle{nominal/categorial scale}
   \begin{itemize}
-  \item Eigenschaften wie Zelltyp, Versuchsgruppe
-  \item jede Beobachtung wird eine bestimmten Klasse (Kategorie)
-    zugeordnet
-  \item Die Klassen besitzen keine sinnvolle Ordnung
-  \item  Beispiel: [Zapfen, Stäbchen] vs. [Stäbchen, Zapfen]
+  \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{Datenskalen}
-  \framesubtitle{Ordinalskala (engl. ,,ordinal'')}
+  \frametitle{data scales}
+  \framesubtitle{ordinal scale}
   \begin{itemize}
-  \item Wie Nominalskala, nur ist sinnvolles Ordnen m\"oglich
-  \item {\bf aber:} Unterschiede zwischen den Werten bzw. Klassen
-    nicht vergleichbar (keine Abst\"ande)
-  \item Beispiel: Platzierungen, G\"uteklassen, Ratingskalen
+  \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{Datenskalen}
-  \framesubtitle{Intervallskala (engl. ,,interval'')}
+  \frametitle{data scales}
+  \framesubtitle{interval scale}
   \begin{itemize}
-  \item quantitative/metrische Werte
-  \item Abst\"ande zwischen Werten sind sinnvoll, aber es gibt keine
-    absoluten Nullpunkt
-  \item Beispiel: physikalische Gr\"o{\ss}en wie Temperatur in Grad Celsius
+  \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{Datenskalen}
-  \framesubtitle{Absolut- oder Verh\"altnisskala (engl. ,,ratio)}
+  \frametitle{data scales}
+  \framesubtitle{absolut/ratio scale}
   \begin{itemize}
-  \item wie Intervallskala, aber mit absolutem Nullpunkt
-  \item Beispiel: Temperatur in Kelvin, Einkommen
+  \item like interval scale but with absolute zero
+  \item example: temperature in $^\circ$K
   \end{itemize}
   \pause
-  \begin{emphasize}{Verh\"altnis der Skalen}
+  \begin{emphasize}{relationsships between scales}
     \begin{itemize}
-    \item Skalen besitzen aufsteigenden Informationsgehalt von
-      Nominal- zu Absolutskala
-    \item Konvertierung ,,abw\"arts'' immer m\"oglich
+    \item scales exhibit increasing information content from nominal
+      to absolute
+    \item conversion  ,,downwards'' always possible
     \end{itemize}
   \end{emphasize}
 \end{frame}
 
 %-------------------------------------------------------------
 \begin{frame}
-  \frametitle{Beispiele aus Neuro-/Kognitionswissenschaften}
+  \frametitle{examples from neuroscience and psychology}
   \begin{itemize}
-  \item {\bf Nominalskala:}\pause 
+  \item {\bf nominal:}\pause 
     \begin{itemize}
-    \item Versuchsgruppenzugeh\"origkeit
-    \item Stimulusklasse
-    \item Zelltyp
+    \item treatment group
+    \item stimulus class
+    \item cell type
     \end{itemize}
 
-  \item {\bf Ordinalskala:} \pause 
+  \item {\bf ordinal:} \pause 
     \begin{itemize}
-    \item Ratings
-    \item Krankheitsstadien
-    \item Zust\"ande eines Ionenkanals
+    \item ratings
+    \item clinical stages of a disease
+    \item states of an ion channel
     \end{itemize}
   \item {\bf Absolut-/Ratioskala:}\pause
     \begin{itemize}
-    \item Feuerrate 
-    \item Membranpotential
-    \item Ionenkonzentration
+    \item firing rate
+    \item membrane potential
+    \item ion concentration
     \end{itemize}
   \end{itemize}
 \end{frame}
 %-------------------------------------------------------------
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\subsection{Statistiken}
+\subsection{statistics}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %-------------------------------------------------------------
 \begin{frame}
-  \frametitle{Was ist eine (Test)-Statistik}
-  \begin{definition}{Teststatistik, Pr\"ufwert}
-    \begin{itemize}
-    \item Als {\em Teststatistik} bezeichnet man in der mathematischen
-      Statistik eine Stichprobenfunktion die einer Stichprobe einen
-      Wert zuordnet (z.B. Mittelwert, Median, Standardabweichung,
-      ...).
-
-      \item Als {\em Pr\"ufwert} wird die Realisation einer Teststatistik
-      anhand einer Stichprobe bezeichnet.
-      
-      \source{http://de.wikipedia.org/wiki/Teststatistik}
-    \end{itemize}
+  \frametitle{What is "a statistic"?}
+  \begin{definition}{statistic}
+    A statistic (singular) is a single measure of some attribute of a
+    sample (e.g., its arithmetic mean value). It is calculated by
+    applying a function (statistical algorithm) to the values of the
+    items of the sample, which are known together as a set of data.
+
+    \source{http://en.wikipedia.org/wiki/Statistic}
   \end{definition}
 \end{frame}
 
@@ -297,50 +289,51 @@ Bernstein Center T\"ubingen}
 \begin{frame}
   \frametitle{Beispiele f\"ur Teststatistiken}
   \begin{itemize}
-  \item {\bf Nominalskala:}\pause 
+  \item {\bf nominal:}\pause 
     \begin{itemize}
-    \item Anzahl
-    \item relative H\"aufigkeit
+    \item count
+    \item relative frequency/proportion
     \end{itemize}
 
-  \item {\bf Ordinalskala:} \pause 
+  \item {\bf ordinal:} \pause 
     \begin{itemize}
-    \item Median
-    \item Perzentilen
-    \item Rangkorrelationskoeffizient
+    \item median
+    \item quantile/percentile
+    \item rank correlation 
     \end{itemize}
-  \item {\bf Absolut-/Ratioskala:}\pause
+  \item {\bf absolute/ratio:}\pause
     \begin{itemize}
-    \item Mittelwert
-    \item Varianz/ Standardabweichung
-    \item Pearson Korrelationskoeffizient
+    \item mean
+    \item variance/ standard deviation
+    \item Pearson correlation
     \end{itemize}
   \end{itemize}
 \end{frame}
 
 %-------------------------------------------------------------
 \begin{frame}
-  \frametitle{\"Ubung}
-  \begin{task}{Spearman Rangkorrelationskoeffizient}
+  \frametitle{exercise}
+  \begin{task}{Spearman rank correlation}
     \begin{enumerate}
-    \item Benutze {\tt randi} um zwei 100-dimensionale Vektoren {\tt x,y} mit
-      Zufalls-Integern zwischen $0$ und $10$ zu berechnen. 
-    \item Finde heraus wie man in Matlab den Spearman
-      Rangkorrelationskoeffizient $$\rho = 1- {\frac {6 \sum
-          d_i^2}{n(n^2 - 1)}}$$ berechnet. $d_i = x_i - y_i$ ist die
-      Differenz im Rang der Datenpunkte. 
-    \item Berechne $\rho$ zwischen $x$ und $y$, zwischen $x$ und
-      $y^2$, zwischen $\log(x+1)$ und $y^2$. Berechne auch den
-      \"ublichen (Pearson) Korrelationskoeffizient zwischen diesen
-      Werten. Was kann man beobachten und warum macht das Sinn?
+    \item Use {\tt randi} to generate two  100-dimensional vectors
+      {\tt x,y} of random integers between $0$ and $10$. 
+    \item Find out how to compute the Spearman
+      rank correlation  $$\rho = 1- {\frac {6 \sum
+          d_i^2}{n(n^2 - 1)}}$$ with Matlab. $d_i = x_i - y_i$ is the
+      difference in the rank between the single data points. 
+    \item Compute $\rho$ between $x$ and $y$, between $x$ and
+      $y^2$, between $\log(x+1)$ and $y^2$. 
+    \item Compute the "standard" (Pearson) correlation coefficient
+      between these values. 
+    \item What can you observe and why does it make sense?
     \end{enumerate}
   \end{task}
 \end{frame}
 
 %-------------------------------------------------------------
 \begin{frame}[fragile]
-  \frametitle{\"Ubung - L\"osung}
-  \begin{solution}{Spearman Rangkorrelationskoeffizient}
+  \frametitle{solution}
+  \begin{solution}{Spearman rank correlation }
 \scriptsize
 \begin{lstlisting}
 >>> x = randi(10, 100, 1);
@@ -358,55 +351,185 @@ ans =
 ans =
     0.0551
 \end{lstlisting}
-Der Rangkorrelationskoeffizient \"andert sich nicht bei monotoner
-Transformation der Daten. Daher ist er f\"ur ordinale Daten
-geeignet. Der Pearson Korrelationskoeffizient ist es nicht. 
+The rank correlation does not change under a monotone transformation
+of the data. Therefore, it can be used for ordinal data. The Pearson
+correlation coefficient does not have that property.
   \end{solution}
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Beschreibung und Darstellung von Daten}
+\section{description of data and plotting}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\subsection{Nominalskala}
+\subsection{nominal scale}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %-------------------------------------------------------------
 \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]);
 \end{lstlisting}
 \end{frame}
 
-%-------------------------------------------------------------
+%----------------------------------------------------------
 \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}
@@ -414,15 +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];
@@ -443,6 +566,66 @@ set(gcf, 'PaperPosition',[0.0 0.0 11.7 9.0]);
 \end{lstlisting}
 \end{frame}
 
+%-------------------------------------------------------------
+\begin{frame}[fragile]
+  \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} 
  

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
+
+
+
+
+
+
+
+

statistics/matlab/intervalplots.m

@@ -0,0 +1,16 @@
+close all
+% histogram
+figure()
+x = randn(2000,1);
+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]);