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Fabian Sinz 2014-10-11 18:25:31 +02:00
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statistics/lecture_statistics.tex
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@ -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[Präludium]{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);
@ -358,16 +351,16 @@ 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]
@ -403,7 +396,7 @@ 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}
@ -443,6 +436,11 @@ set(gcf, 'PaperPosition',[0.0 0.0 11.7 9.0]);
\end{lstlisting}
\end{frame}
%-------------------------------------------------------------
\begin{frame}[fragile]
\frametitle{Darstellung von Interval-/Absolutskala Daten}
\end{frame}
\end{document}