From 9c462f6070c206c867953b86e36f72447507aa87 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Tue, 12 Dec 2017 11:29:38 +0100 Subject: [PATCH] added bootstrap of correlation coefficient --- bootstrap/exercises/correlationbootstrap.m | 37 ++++++++++++++ bootstrap/exercises/correlationbootstrap.pdf | Bin 0 -> 4688 bytes .../exercises/correlationsignificance.pdf | Bin 59661 -> 59541 bytes bootstrap/exercises/exercises01.tex | 48 +++++++++++++----- 4 files changed, 73 insertions(+), 12 deletions(-) create mode 100644 bootstrap/exercises/correlationbootstrap.m create mode 100644 bootstrap/exercises/correlationbootstrap.pdf diff --git a/bootstrap/exercises/correlationbootstrap.m b/bootstrap/exercises/correlationbootstrap.m new file mode 100644 index 0000000..5abb951 --- /dev/null +++ b/bootstrap/exercises/correlationbootstrap.m @@ -0,0 +1,37 @@ +%% (a) bootstrap: +nperm = 1000; +rb = zeros(nperm,1); +for i=1:nperm + % indices for resampling the data: + inx = randi(length(x), length(x), 1); + % resampled data pairs: + xb=x(inx); + yb=y(inx); + rb(i) = corr(xb, yb); +end + +%% (b) pdf of the correlation coefficients: +[hb,bb] = hist(rb, 20 ); +hb = hb/sum(hb)/(bb(2)-bb(1)); % normalization + +%% (c) significance: +rbq = quantile(rb, 0.05); +fprintf('correlation coefficient at 5%% significance = %.2f\n', rbq ); +if rbq > 0.0 + fprintf('--> correlation r=%.2f is significant\n', rd); +else + fprintf('--> r=%.2f is not a significant correlation\n', rd); +end + +%% plot: +hold on; +bar(b, h, 'facecolor', [0.5 0.5 0.5]); +bar(bb, hb, 'facecolor', 'b'); +bar(bb(bb<=rbq), hb(bb<=rbq), 'facecolor', 'r'); +plot( [rd rd], [0 4], 'r', 'linewidth', 2 ); +xlim([-0.25 0.75]) +xlabel('Correlation coefficient'); +ylabel('Probability density'); +hold off; + +savefigpdf( gcf, 'correlationbootstrap.pdf', 12, 6 ); diff --git a/bootstrap/exercises/correlationbootstrap.pdf b/bootstrap/exercises/correlationbootstrap.pdf new file mode 100644 index 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