[bootstrap] finished code for new exercises

bootstrap/exercises/exercises01.tex

@@ -37,7 +37,7 @@ jan.benda@uni-tuebingen.de}
   commentstyle=\itshape\color{darkgray},
   breaklines=true,
   breakautoindent=true,
-  columns=flexible,
+  % columns=flexible,
   frame=single,
   xleftmargin=1em,
   xrightmargin=1em,
@@ -239,7 +239,7 @@ differ in their mean by means of a permutation test.
 \end{parts}
 \begin{solution}
   \lstinputlisting{meandiffpermutation.m}
-  %\lstinputlisting{meandiffplots.m}
+  \lstinputlisting{meandiffplot.m}
   \lstinputlisting{meandiffsignificance.m}
   \includegraphics[width=1\textwidth]{meandiffsignificance}
 \end{solution}

bootstrap/exercises/meandiffpermutation.m

@@ -1,7 +1,7 @@
 function [md, ds, dq] = meandiffpermutation(x, y, nperm, alpha)
 % Permutation test for difference of means of two independent samples.
 %
-% [md, ds] = meandiffpermutation(x, y, nperm, alpha);
+% [md, ds, dq] = meandiffpermutation(x, y, nperm, alpha);
 %
 % Arguments:
 %   x: vector with the samples of the x data set.

bootstrap/exercises/meandiffplot.m

@@ -0,0 +1,40 @@
+function meandiffplot(x, y, md, ds, dq, k, nrows)
+% Plot histogram of data sets and of null hypothesis for differences in mean.
+%
+% meandiffplot(x, y, md, ds, dq, k, rows);
+%
+% Arguments:
+%   x: vector with the samples of the x data set.
+%   y: vector with the samples of the y data set.
+%   md: difference of means of the two data sets.
+%   ds: vector containing the differences of the means of the resampled data sets
+%   dq: minimum difference of the means considered significant.
+%   k: current row for the plot panels.
+%   nrows: number of rows of panels in the figure.
+
+  %% (b) plot histograms:
+  subplot(nrows, 2, k*2-1);
+  bmin = min([x; y]);
+  bmax = max([x; y]);
+  bins = bmin:(bmax-bmin)/20.0:bmax;
+  hist(x, bins, 'facecolor', 'b');
+  hold on
+  hist(y, bins, 'facecolor', 'r');
+  xlabel('x and y')
+  ylabel('counts')
+  hold off
+
+  %% (f) pdf of the differences:
+  [h, b] = hist(ds, 20);
+  h = h/sum(h)/(b(2)-b(1));           % normalization
+
+  %% plot:
+  subplot(nrows, 2, k*2)
+  bar(b, h, 'facecolor', 'b');
+  hold on;
+  bar(b(b>=dq), h(b>=dq), 'facecolor', 'r');
+  plot([md md], [0 4], 'r', 'linewidth', 2);
+  xlabel('Difference of means');
+  ylabel('Probability density of H0');
+  hold off;
+end

bootstrap/exercises/meandiffsignificance.m

@@ -1,48 +1,37 @@
-%% (a) generate data:
 n = 200;
 mx = -40.0;
-my = -40.5;
+nperm = 1000;
+alpha = 0.05;
+
+%% (h) repeat for various means of the y-data set:
+mys = [-40.1, -40.2, -40.5];
+for k=1:length(mys)
+
+  %% (a) generate data:
+  my = mys(k);
   x = randn(n, 1) + mx;
   y = randn(n, 1) + my;
 
-%% (b) plot histograms:
+  %% (d), (e) permutation test:
-subplot(1, 2, 1);
-bmin = min([x; y]);
-bmax = max([x; y]);
-bins = bmin:(bmax-bmin)/20.0:bmax;
-hist(x, bins, 'facecolor', 'b');
-hold on
-hist(y, bins, 'facecolor', 'r');
-xlabel('x and y')
-ylabel('counts')
-hold off
-
-% permutation test:
   [md, ds, dq] = meandiffpermutation(x, y, nperm, alpha);
 
   %% (c) difference of means:
+  fprintf('\nmean x = %.1fmV, mean y = %.1fmV\n', mx, my);
   fprintf('  difference of means = %.2fmV\n', md);
 
-%% (f) pdf of the differences:
-[h, b] = hist(ds, 20);
-h = h/sum(h)/(b(2)-b(1));           % normalization
-
   %% (g) significance:
   fprintf('  difference of means at 5%% significance = %.2fmV\n', dq);
   if md >= dq
-    fprintf('--> difference of means %.2fmV is significant\n', md);
+      fprintf('  --> measured difference of means is significant\n');
   else
-    fprintf('--> %.2fmV is not a significant difference of means\n', md);
+      fprintf('  --> measured difference of means is not significant\n');
+  end
+
+  subplot(length(mys), 2, k*2-1);
+  title(sprintf('mx=%.1fmV, my=%.1fmV', mx, my))
+
+  %% (b), (f) plot histograms of data and pdf of differences:
+  meandiffplot(x, y, md, ds, dq, k, length(mys));
 end
 
-%% plot:
+savefigpdf(gcf, 'meandiffsignificance.pdf', 12, 10);
-subplot(1, 2, 2)
-bar(b, h, 'facecolor', 'b');
-hold on;
-bar(b(b>=dq), h(b>=dq), 'facecolor', 'r');
-plot([md md], [0 4], 'r', 'linewidth', 2);
-xlabel('Difference of means');
-ylabel('Probability density of H0');
-hold off;
-
-savefigpdf(gcf, 'meandiffsignificance.pdf', 12, 6);