[bootstrap] added difference of mean

bootstrap/code/correlationsignificance.m

@@ -1,6 +1,6 @@
 % generate correlated data:
-n=200;
-a=0.2;
+n = 200;
+a = 0.2;
 x = randn(n, 1);
 y = randn(n, 1) + a*x;
 
@@ -11,13 +11,13 @@ fprintf('correlation coefficient of data r = %.2f\n', rd);
 % distribution of null hypothesis by permutation:
 nperm = 1000;
 rs = zeros(nperm,1);
-for i=1:nperm
-    xr=x(randperm(length(x)));  % shuffle x
-    yr=y(randperm(length(y)));  % shuffle y
+for i = 1:nperm
+    xr = x(randperm(length(x)));  % shuffle x
+    yr = y(randperm(length(y)));  % shuffle y
     rs(i) = corr(xr, yr);
 end
-[h,b] = hist(rs, 20);
-h = h/sum(h)/(b(2)-b(1));       % normalization
+[h, b] = hist(rs, 20);
+h = h/sum(h)/(b(2)-b(1));         % normalization
 
 % significance:
 rq = quantile(rs, 0.95);

bootstrap/code/meandiffsignificance.m

@@ -0,0 +1,40 @@
+% generate two data sets:
+n = 200;
+d = 0.2;
+x = randn(n, 1);
+y = randn(n, 1) + d;
+
+% difference of sample means:
+md = mean(y) - mean(x);
+fprintf('difference of means of data d = %.2f\n', md);
+
+% distribution of null hypothesis by permutation:
+nperm = 1000;
+xy = [x; y];                         % x and y data in one column vector
+ds = zeros(nperm,1);
+for i = 1:nperm
+    xyr = xy(randperm(length(xy)));  % shuffle data
+    xr = xyr(1:length(x));           % random x-data
+    yr = xyr(length(x)+1:end);       % random y-data
+    ds(i) = mean(yr) - mean(xr);     % difference of means
+end
+[h, b] = hist(ds, 20);
+h = h/sum(h)/(b(2)-b(1));       % normalization
+
+% significance:
+dq = quantile(ds, 0.95);
+fprintf('difference of means of null hypothesis at 5%% significance = %.2f\n', dq);
+if md >= dq
+    fprintf('--> difference of means d=%.2f is significant\n', md);
+else
+    fprintf('--> d=%.2f is not a significant difference of means\n', md);
+end
+
+% plot:
+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;

bootstrap/code/meandiffsignificance.out

@@ -0,0 +1,4 @@
+>> meandiffsignificance
+difference of means of data d = 0.18
+difference of means of null hypothesis at 5% significance = 0.17
+--> difference of means d=0.18 is significant