New bootstrap exercises

statistics/code/bootstrapsem.m

@@ -0,0 +1,23 @@
+nsamples = 1000
+resample = 500
+
+  x = randn( nsamples, 1 );
+sem = std(x)/sqrt(nsamples);
+
+mu = zeros( resample, 1 );
+for i = 1:resample
+  % resample:
+  xr = x(randi(nsamples, nsamples, 1));
+  % compute statistics on sample:
+  mu(i) = mean(xr);
+end
+bootsem = std( mu );
+
+hold on
+hist( x, 20 );
+hist( mu, 20 );
+hold off
+
+disp(['bootstrap standard error: ', num2str(bootsem)]);
+disp(['standard error: ', num2str(sem)]);
+

statistics/code/bootstraptymus.m

@@ -0,0 +1,24 @@
+resample = 500
+
+load( 'thymusglandweights.dat' );
+x = thymusglandweights;
+nsamples = length( x );
+sem = std(x)/sqrt(nsamples);
+
+mu = zeros( resample, 1 );
+for i = 1:resample
+  % resample:
+  xr = x(randi(nsamples, nsamples, 1));
+  % compute statistics on sample:
+  mu(i) = mean(xr);
+end
+bootsem = std( mu );
+
+hold on
+hist( x, 20 );
+hist( mu, 20 );
+hold off
+
+disp(['bootstrap standard error: ', num2str(bootsem)]);
+disp(['standard error: ', num2str(sem)]);
+

statistics/code/boxwhisker.m

@@ -0,0 +1,3 @@
+x = randn(40, 10);
+boxplot(x, 'whisker', 100.0 );
+

statistics/code/correlations.m

@@ -0,0 +1,14 @@
+n = 1000
+x = randn( n, 1 );
+y = randn( n, 1 ) + 0.2*x;
+r = corr(x,y)
+
+  nsamples = 500;
+  rs = zeros( nsamples, 1 );
+for i = 1:nsamples
+	  xs = x(randi(n,n,1));
+ys = x(randi(n,n,1));
+	  rs(i) = corr(xs,ys);
+end
+
+hist( rs, 20 )

statistics/code/tdistribution.m

@@ -0,0 +1,32 @@
+n = 100000
+x=randn(n, 1);
+
+nsamples = 3;
+nmeans = 10000;
+means = zeros( nmeans, 1 );
+sdevs = zeros( nmeans, 1 );
+students = zeros( nmeans, 1 );
+for i=1:nmeans
+  sample = x(randi(n, nsamples, 1));
+  means(i) = mean(sample);
+  sdevs(i) = std(sample);
+  students(i) = mean(sample)/std(sample)*sqrt(nsamples);
+end
+sdev = 1.0
+msdev = std(means)
+
+%  scatter( means, sdevs )
+
+hold on;
+dxg=0.01;
+xmax = 10.0
+xmin = -xmax
+xg = [xmin:dxg:xmax];
+pg = exp(-0.5*(xg/sdev).^2)/sqrt(2.0*pi)/sdev;
+hold on
+plot(xg, pg, 'r', 'linewidth', 4)
+
+bins = xmin:0.1:xmax;
+hist(means, bins, 1.0/(bins(2)-bins(1)) );
+hold off;
+