450 lines
13 KiB
TeX
Executable File
450 lines
13 KiB
TeX
Executable File
\documentclass{beamer}
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\usepackage{xcolor}
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\usepackage{listings}
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\usepackage{pgf}
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%\usepackage{pgf,pgfarrows,pgfnodes,pgfautomata,pgfheaps,pgfshade}
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%\usepackage{multimedia}
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\usepackage[ngerman]{babel}
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\usepackage[latin1]{inputenc}
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\usepackage{amsmath}
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\usepackage{bm}
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\usepackage[T1]{fontenc}
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\usepackage{hyperref}
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\usepackage{ulem}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\mode<presentation>
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{
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\usetheme{Singapore}
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\setbeamercovered{opaque}
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\usecolortheme{tuebingen}
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\setbeamertemplate{navigation symbols}{}
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\usefonttheme{default}
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\useoutertheme{infolines}
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% \useoutertheme{miniframes}
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}
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\AtBeginSection[]
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{
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\begin{frame}<beamer>
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\begin{center}
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\Huge \insertsectionhead
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\end{center}
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% \frametitle{\insertsectionhead}
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% \tableofcontents[currentsection,hideothersubsections]
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\end{frame}
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}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
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\setbeamertemplate{blocks}[rounded][shadow=true]
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\title[]{Scientific Computing -- Statistics}
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\author[Statistics]{Fabian Sinz\\Dept. Neuroethology,
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University T\"ubingen\\
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Bernstein Center T\"ubingen}
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\institute[Scientific Computing]{}
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\date{11/27/2013}
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%\logo{\pgfuseimage{logo}}
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\subject{Lectures}
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%%%%%%%%%% configuration for code
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\lstset{
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basicstyle=\ttfamily,
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numbers=left,
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showstringspaces=false,
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language=Matlab,
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commentstyle=\itshape\color{darkgray},
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keywordstyle=\color{blue},
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stringstyle=\color{green},
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backgroundcolor=\color{blue!10},
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breaklines=true,
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breakautoindent=true,
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columns=flexible,
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frame=single,
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captionpos=b,
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xleftmargin=1em,
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xrightmargin=1em,
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aboveskip=10pt
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}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\newcommand{\mycite}[1]{
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\begin{flushright}
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\tiny \color{black!80} #1
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\end{flushright}
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}
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\input{../latex/environments.tex}
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\makeatother
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\begin{document}
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\begin{frame}
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\titlepage
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\end{frame}
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\begin{frame}
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\frametitle{Plan}
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\setcounter{tocdepth}{1}
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\tableofcontents
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\end{frame}
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\begin{frame}
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\frametitle{Information \"uber Statistik}
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\begin{itemize}
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\item Samuels, M. L., Wittmer, J. A., \& Schaffner,
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A. A. (2010). Statistics for the Life Sciences (4th ed.,
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p. 668). Prentice Hall.
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\item Zar, J. H. (1999). Biostatistical Analysis. (D. Lynch,
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Ed.)Prentice Hall New Jersey (4th ed., Vol. 4th, p. 663). Prentice
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Hall. doi:10.1037/0012764
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\item \url{http://stats.stackexchange.com}
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\end{itemize}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% errorbars (error bar paper)
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% confidence intervals (sources of error)
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% plotting (the right plot for the right data, Dan plotting paper)
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% statistical test structure (bootstrapping, resampling, permutation)
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% Don'ts: repeated testing, exclude data points
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% study design
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% PCA
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section[Pr<50>ludium]{Pr<EFBFBD>ludium}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% ----------------------------------------------------------
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\begin{frame}
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\frametitle{Meine Erwartungen an Masterstudenten}
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\begin{itemize}
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\item Interesse und Partizipation
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\item Motivation Konzepte zu verstehen und zu hinterfragen
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\item einen hohen wissenschaftlichen Qualit<69>tsstandard
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\item intellektuelle Redlichkeit
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\item ehrliche Kooperation
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\end{itemize}
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\end{frame}
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% ----------------------------------------------------------
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\begin{frame}
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\frametitle{diese Woche wird ...}
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\only<1>{
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\framesubtitle{... kein \sout{Spa<EFBFBD>} Zuckerschlecken}
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\begin{center}
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\includegraphics[height=0.7\textheight]{figs/feeding.jpg}
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\end{center}
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}
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\only<2>{
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\framesubtitle{... kein \sout{Spa<EFBFBD>} Zuckerschlecken}
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\begin{center}
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\includegraphics[height=0.7\textheight]{figs/nacho-trainer.jpg}
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\end{center}
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}
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\only<3>{
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\framesubtitle{... keine Vorlesung (Bitte!)}
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\begin{center}
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\includegraphics[height=0.7\textheight]{figs/soccer.jpg}
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\end{center}
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}
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\end{frame}
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% ----------------------------------------------------------
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\begin{frame}
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\frametitle{Was Ihr diese Woche lernen solltet}
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\begin{itemize}
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\item Eigenschaften guter Plots
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\item Was ist deskriptive/ inferentielle Statistik?
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\item die generelle Struktur statistischer Tests
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\item Was ist/bedeutet ein p-Wert?
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\item Wie bastele ich mir meinen eigenen Test?
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\item Wie gro<72> mu<6D> mein $n$ sein?
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\item Principal Component Analysis (PCA)
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\end{itemize}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section[deskriptive Statistik, Fehlerbalken \& Plots]{Day 1 -- Deskriptive
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Statistik, Fehlerbalken und Plots}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Arten von Daten}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
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\frametitle{Datenskalen}
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\framesubtitle{Welche Datentypen gibt es in der Statistik?}
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\Large
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{\bf Warum sind Datentypen wichtig?}
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\pause
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\begin{itemize}
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\item Auswahl passender Statistiken
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\item Auswahl angemessener Plots
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\item Auswahl von korrekten Tests
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\end{itemize}
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\end{frame}
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%-------------------------------------------------------------
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\begin{frame}
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\frametitle{Datenskalen}
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\framesubtitle{Nominalskala (engl. ,,categorial'')}
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\begin{itemize}
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\item Eigenschaften wie Zelltyp, Versuchsgruppe
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\item jede Beobachtung wird eine bestimmten Klasse (Kategorie)
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zugeordnet
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\item Die Klassen besitzen keine sinnvolle Ordnung
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\item Beispiel: [Zapfen, St<53>bchen] vs. [St<53>bchen, Zapfen]
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\end{itemize}
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\end{frame}
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%-------------------------------------------------------------
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\begin{frame}
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\frametitle{Datenskalen}
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\framesubtitle{Ordinalskala (engl. ,,ordinal'')}
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\begin{itemize}
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\item Wie Nominalskala, nur ist sinnvolles Ordnen m\"oglich
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\item {\bf aber:} Unterschiede zwischen den Werten bzw. Klassen
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nicht vergleichbar (keine Abst\"ande)
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\item Beispiel: Platzierungen, G\"uteklassen, Ratingskalen
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\end{itemize}
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\end{frame}
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%-------------------------------------------------------------
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\begin{frame}
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\frametitle{Datenskalen}
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\framesubtitle{Intervallskala (engl. ,,interval'')}
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\begin{itemize}
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\item quantitative/metrische Werte
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\item Abst\"ande zwischen Werten sind sinnvoll, aber es gibt keine
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absoluten Nullpunkt
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\item Beispiel: physikalische Gr\"o{\ss}en wie Temperatur in Grad Celsius
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\end{itemize}
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\end{frame}
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%-------------------------------------------------------------
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\begin{frame}
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\frametitle{Datenskalen}
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\framesubtitle{Absolut- oder Verh\"altnisskala (engl. ,,ratio)}
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\begin{itemize}
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\item wie Intervallskala, aber mit absolutem Nullpunkt
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\item Beispiel: Temperatur in Kelvin, Einkommen
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\end{itemize}
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\pause
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\begin{emphasize}{Verh\"altnis der Skalen}
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\begin{itemize}
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\item Skalen besitzen aufsteigenden Informationsgehalt von
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Nominal- zu Absolutskala
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\item Konvertierung ,,abw\"arts'' immer m\"oglich
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\end{itemize}
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\end{emphasize}
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\end{frame}
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%-------------------------------------------------------------
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\begin{frame}
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\frametitle{Beispiele aus Neuro-/Kognitionswissenschaften}
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\begin{itemize}
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\item {\bf Nominalskala:}\pause
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\begin{itemize}
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\item Versuchsgruppenzugeh\"origkeit
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\item Stimulusklasse
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\item Zelltyp
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\end{itemize}
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\item {\bf Ordinalskala:} \pause
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\begin{itemize}
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\item Ratings
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\item Krankheitsstadien
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\item Zust\"ande eines Ionenkanals
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\end{itemize}
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\item {\bf Absolut-/Ratioskala:}\pause
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\begin{itemize}
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\item Feuerrate
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\item Membranpotential
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\item Ionenkonzentration
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\end{itemize}
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\end{itemize}
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\end{frame}
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%-------------------------------------------------------------
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Statistiken}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%-------------------------------------------------------------
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\begin{frame}
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\frametitle{Was ist eine (Test)-Statistik}
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\begin{definition}{Teststatistik, Pr\"ufwert}
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\begin{itemize}
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\item Als {\em Teststatistik} bezeichnet man in der mathematischen
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Statistik eine Stichprobenfunktion die einer Stichprobe einen
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Wert zuordnet (z.B. Mittelwert, Median, Standardabweichung,
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...).
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\item Als {\em Pr\"ufwert} wird die Realisation einer Teststatistik
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anhand einer Stichprobe bezeichnet.
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\source{http://de.wikipedia.org/wiki/Teststatistik}
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\end{itemize}
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\end{definition}
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\end{frame}
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%-------------------------------------------------------------
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\begin{frame}
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\frametitle{Beispiele f\"ur Teststatistiken}
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\begin{itemize}
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\item {\bf Nominalskala:}\pause
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\begin{itemize}
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\item Anzahl
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\item relative H\"aufigkeit
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\end{itemize}
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\item {\bf Ordinalskala:} \pause
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\begin{itemize}
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\item Median
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\item Perzentilen
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\item Rangkorrelationskoeffizient
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\end{itemize}
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\item {\bf Absolut-/Ratioskala:}\pause
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\begin{itemize}
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\item Mittelwert
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\item Varianz/ Standardabweichung
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\item Pearson Korrelationskoeffizient
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\end{itemize}
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\end{itemize}
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\end{frame}
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%-------------------------------------------------------------
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\begin{frame}
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\frametitle{\"Ubung}
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\begin{task}{Spearman Rangkorrelationskoeffizient}
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\begin{enumerate}
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\item Benutze {\tt randi} um zwei 100-dimensionale Vektoren {\tt x,y} mit
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Zufalls-Integern zwischen $0$ und $10$ zu berechnen.
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\item Finde heraus wie man in Matlab den Spearman
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Rangkorrelationskoeffizient $$\rho = 1- {\frac {6 \sum
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d_i^2}{n(n^2 - 1)}}$$ berechnet. $d_i = x_i - y_i$ ist die
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Differenz im Rang der Datenpunkte.
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\item Berechne $\rho$ zwischen $x$ und $y$, zwischen $x$ und
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$y^2$, zwischen $\log(x+1)$ und $y^2$. Berechne auch den
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\"ublichen (Pearson) Korrelationskoeffizient zwischen diesen
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Werten. Was kann man beobachten und warum macht das Sinn?
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\end{enumerate}
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\end{task}
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\end{frame}
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%-------------------------------------------------------------
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\begin{frame}[fragile]
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\frametitle{\"Ubung - L\"osung}
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\begin{solution}{Spearman Rangkorrelationskoeffizient}
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\scriptsize
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\begin{lstlisting}
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>>> x = randi(10, 100, 1);
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>>> y = randi(10, 100, 1);
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>>> corr(x,y,'type','Spearman')
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ans =
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0.1220
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>>> corr(x,y.^2,'type','Spearman')
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ans =
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0.1220
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>>> corr(x,y,'type','Pearson')
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ans =
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0.1074
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>>> corr(x,y.^2,'type','Pearson')
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ans =
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0.0551
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\end{lstlisting}
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Der Rangkorrelationskoeffizient \"andert sich nicht bei monotoner
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Transformation der Daten. Daher ist er f\"ur ordinale Daten
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geeignet. Der Pearson Korrelationskoeffizient ist es nicht.
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\end{solution}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Beschreibung und Darstellung von Daten}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Nominalskala}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%-------------------------------------------------------------
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\begin{frame}[fragile]
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\frametitle{Darstellung nominaler Daten}
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\framesubtitle{Bar-Plot f\"ur Anzahl/ rel. H\"aufigkeit}
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\begin{center}
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\includegraphics[width=.8\linewidth]{figs/nominaldataplot}
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\end{center}
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\end{frame}
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%-------------------------------------------------------------
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\begin{frame}[fragile]
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\frametitle{Darstellung nominaler Daten}
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\framesubtitle{Bar-Plot f\"ur Anzahl/ rel. H\"aufigkeit}
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\scriptsize
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\begin{lstlisting}
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% eigentlicher Plot
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bar([1,2], [50, 90], 'facecolor', 'k')
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% Achsenbeschriftung
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ylabel('cell count')
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xlabel('cell type')
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% Kosmetik
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xlim([0.5,2.5])
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ylim([0, 100])
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box('off')
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set(gca,'XTick',1:2,'XTickLabel',{'pyramidal','interneuron'},'FontSize',20)
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% Settings fuers Abspeichern
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set(gcf, 'PaperUnits', 'centimeters');
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set(gcf, 'PaperSize', [11.7 9.0]);
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set(gcf, 'PaperPosition',[0.0 0.0 11.7 9.0]);
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\end{lstlisting}
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\end{frame}
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%-------------------------------------------------------------
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\begin{frame}[fragile]
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\frametitle{Darstellung nominaler Daten}
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\framesubtitle{Pie-Chart f\"ur Anzahl/ rel. H\"aufigkeit}
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\begin{center}
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\includegraphics[width=.8\linewidth]{figs/nominaldataplot2}
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\end{center}
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\end{frame}
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%-------------------------------------------------------------
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\begin{frame}[fragile]
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\frametitle{Darstellung nominaler Daten}
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\framesubtitle{\"Ubung}
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\begin{task}{Pie-Chart}
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Plotte dieselben Daten ($n_{py}=50$, $n_{in}=90$) als Pie-Chart in Matlab.
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\end{task}
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\end{frame}
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%-------------------------------------------------------------
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\begin{frame}[fragile]
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\frametitle{Darstellung nominaler Daten}
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\framesubtitle{Pie-Chart f\"ur Anzahl/ rel. H\"aufigkeit}
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\scriptsize
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\begin{lstlisting}
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data = [50, 90];
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h = pie(data, [1,0], {'pyramidal (n=50)', 'interneuron (n=90)'})
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hText = findobj(h,'Type','text') % text object handles
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set(h(1), 'FaceColor', [.2,.2,.2]);
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set(h(2), 'Rotation', 45);
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set(h(3), 'FaceColor', [.8,.8,.8]);
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set(h(4), 'Rotation', 45);
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title('cell count')
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set(gca,'XTick',1:2,'XTickLabel',{'pyramidal', 'interneuron'})
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box('off')
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set(gcf, 'PaperUnits', 'centimeters');
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set(gcf, 'PaperSize', [11.7 9.0]);
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set(gcf, 'PaperPosition',[0.0 0.0 11.7 9.0]);
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\end{lstlisting}
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\end{frame}
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\end{document}
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