Expanded bootstrap chapter and improved latex header

bootstrap/code/bootstrapsem.out

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+>> bootstrapsem
+                                mean   stdev  sem  
+                    single SRS  -0.13   0.97   0.10
+     bootstrapped distribution  -0.13   0.10  -
+         sampling distribution  -0.00   0.10  -

bootstrap/code/correlationsignificance.m

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+% generate correlated data:
+n=200;
+a=0.2;
+x = randn(n, 1);
+y = randn(n, 1) + a*x;
+
+% correlation coefficient:
+rd = corr(x, y);
+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
+    rs(i) = corr(xr, yr);
+end
+[h,b] = hist(rs, 20 );
+h = h/sum(h)/(b(2)-b(1));  % normalization
+
+% significance:
+rq = quantile(rs, 0.95);
+fprintf('correlation coefficient of null hypothesis at 5%% significance = %.2f\n', rq );
+if rd >= rq
+    fprintf('--> correlation r=%.2f is significant\n', rd);
+else
+    fprintf('--> r=%.2f is not a significant correlation\n', rd);
+end
+
+% plot:
+bar(b, h, 'facecolor', 'b');
+hold on;
+bar(b(b>=rq), h(b>=rq), 'facecolor', 'r');
+plot( [rd rd], [0 4], 'r', 'linewidth', 2 );
+xlabel('Correlation coefficient');
+ylabel('Probability density of H0');
+hold off;

bootstrap/code/correlationsignificance.out

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+>> correlationsignificance
+correlation coefficient of data r = 0.23
+correlation coefficient of null hypothesis at 5% significance = 0.12
+--> correlation r=0.23 is significant