day 2 done

statistics/assignments/day2.tex

@@ -0,0 +1,46 @@
+\documentclass[addpoints,10pt]{exam}
+\usepackage{url}
+\usepackage{color}
+\usepackage{hyperref}
+
+\pagestyle{headandfoot}
+\runningheadrule
+\firstpageheadrule
+
+\firstpageheader{Scientific Computing}{afternoon assignment day 02}{10/21/2014}
+%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
+\firstpagefooter{}{}{}
+\runningfooter{}{}{}
+\pointsinmargin
+\bracketedpoints
+
+%\printanswers
+\shadedsolutions
+
+
+\begin{document}
+%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
+\sffamily
+%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{questions}
+  \question Download example002 from yesterday (brain weights). 
+  \begin{parts}
+    \part Simulate a null distribution via permutation.
+    \part Determine whether you can reject ``means are equal'' on a
+    5\% significance level using the simulated null distribution.
+    \part Check whether the means are different with a two sample
+    t-test in matlab ({\tt ttest2}).
+    \part Plot the data appropriately and generate a single slide that
+    contains the plot and short discussion of the test that respects
+    the nature statistical checklist (ignore all question whether the
+    assumptions of the test are satisfied).
+    \part Upload the slide and the code to Ilias. Deadline is 19h00.
+  \end{parts}
+\end{questions}
+
+
+
+
+
+\end{document}

statistics/examples/example002.tex

@@ -1,3 +1,3 @@
-Brain Weight In 1888, P. Topinard published data on the brain weights
+Brain Weight: In 1888, P. Topinard published data on the brain weights
 of hundreds of French men and women. Brain weights are given in
 gram. 

statistics/lecture_statistics01.tex

@@ -22,14 +22,19 @@
   % \useoutertheme{miniframes}
 }
 
-\AtBeginSection[]
+\AtBeginSubsection[]
 {
   \begin{frame}<beamer>
     \begin{center}
       \Huge \insertsectionhead
     \end{center}
+    \tableofcontents[ 
+    currentsubsection, 
+    hideothersubsections, 
+    sectionstyle=show/hide, 
+    subsectionstyle=show/shaded, 
+] 
     % \frametitle{\insertsectionhead}
-    % \tableofcontents[currentsection,hideothersubsections]
   \end{frame}
 }
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
@@ -84,25 +89,7 @@ Bernstein Center T\"ubingen}
 
 \end{frame} 
 
-\begin{frame} 
-  \frametitle{plan}
-  \setcounter{tocdepth}{1}
-  \tableofcontents 
 
-\end{frame} 
-\begin{frame} 
-  \frametitle{information}
-  \begin{itemize}
-  \item Samuels, M. L., Wittmer, J. A., \& Schaffner,
-    A. A. (2010). Statistics for the Life Sciences (4th ed.,
-    p. 668). Prentice Hall.
-  \item Zar, J. H. (1999). Biostatistical Analysis. (D. Lynch,
-    Ed.)Prentice Hall New Jersey (4th ed., Vol. 4th, p. 663). Prentice
-    Hall. doi:10.1037/0012764
-  \item \url{http://stats.stackexchange.com}
-  \end{itemize}
-\end{frame} 
- 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % errorbars (error bar paper)
 % confidence intervals (sources of error)
@@ -170,8 +157,7 @@ Bernstein Center T\"ubingen}
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section[descriptive statistics, errorbars, and plots]{Day 1 --
-  descriptive statistics and plots}
+\section{Day 1 -- descriptive statistics and plots}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \subsection{types of data}
@@ -523,7 +509,7 @@ correlation coefficient does not have that property.
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\subsection{nominal scale}
+\subsection{plotting data}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 %-------------------------------------------------------------

statistics/matlab/bootstrap_mean.m

@@ -0,0 +1,13 @@
+load thymusglandweights.dat
+x = thymusglandweights(1:50);
+
+m = 500;
+n = length(x);
+
+mu = zeros(m,1);
+for i = 1:m
+    mu(i) = mean(x(randi(n,n,1)));
+end
+fprintf("bootstrap standard error: %.4f\n", std(mu));
+fprintf("standard error: %.4f\n", std(x)/sqrt(n));
+

statistics/matlab/ci_mean.m

@@ -0,0 +1,19 @@
+load thymusglandweights.dat
+
+n = 80;
+x = thymusglandweights(1:n);
+
+m = 5000;
+me = zeros(m,1);
+for i = 1:m
+    me(i) = median(x(randi(n,n,1)));
+end
+
+t025 = tinv(0.025, n-1);
+t975 = tinv(0.975, n-1);
+
+se = std(x)/sqrt(n);
+
+fprintf('bootstrap quantiles: %.4f, %.4f \n', quantile(me,0.025), quantile(me,0.975));
+fprintf('analytical quantile: %.4f, %.4f \n', mean(x)+t025*se, mean(x)+t975*se);
+

statistics/matlab/ci_media.m

@@ -0,0 +1,17 @@
+load thymusglandweights.dat
+x = thymusglandweights(1:50);
+
+m = 500;
+n = length(x);
+x = sort(x);
+me = zeros(m,1);
+for i = 1:m
+    me(i) = median(x(randi(n,n,1)));
+end
+
+a1 = binoinv(0.025,n,.5)-1;
+a2 = binoinv(1-0.025,n,.5);
+
+fprintf('bootstrap quantiles: %.4f, %.4f \n', quantile(me,0.025), quantile(me,1-0.025));
+fprintf('analytical quantile: %.4f, %.4f \n', x(a1),x(a2));
+

statistics/matlab/tests.m

@@ -0,0 +1,38 @@
+close all
+clear all
+load thymusglandweights.dat
+
+literature_mean = 34.3;
+
+x = thymusglandweights;
+n = length(x);
+y = x - mean(x) + literature_mean;
+
+m = 2000;
+me = zeros(m,1);
+for i = 1:m
+    me(i) = median(y(randi(n,n,1)));
+end
+
+hist(me, 50);
+hold on
+mu = mean(x);
+plot([mu,mu],[0,200],'--r','LineWidth',3);
+xlabel('thymus gland weights [g]');
+ylabel('frequency');
+title('bootstrapped null distribution');
+hold off
+
+% 5% significance boundaries
+low = quantile(me,0.025);
+high =  quantile(me,0.975);
+disp(['the 5% boundaries are: ', num2str(low), ' ', num2str(high)]);
+
+hold on
+plot([low,low],[0,200],'--g','LineWidth',3);
+plot([high,high],[0,200],'--g','LineWidth',3);
+hold off
+
+pval = mean(abs(me-literature_mean) > abs(mu - literature_mean))
+
+legend('Null distribution','measured mean','5% significance boundaries')