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[bootstrap] improved code

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This commit is contained in:
Jan Benda 2020-12-07 22:37:36 +01:00
parent e1c6c32db0
commit 430bdfb7fd
4 changed files with 34 additions and 33 deletions
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19
bootstrap/code/bootstrapsem.m
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@ -1,10 +1,10 @@
nsamples = 100; nsamples = 100;
nresamples = 1000; nresamples = 1000;
% draw a SRS (simple random sample, "Stichprobe") from the population: % draw a simple random sample ("Stichprobe") from the population:
x = randn( 1, nsamples ); x = randn(1, nsamples);
fprintf('%-30s %-5s %-5s %-5s\n', '', 'mean', 'stdev', 'sem' ) fprintf('%-30s %-5s %-5s %-5s\n', '', 'mean', 'stdev', 'sem')
fprintf('%30s %5.2f %5.2f %5.2f\n', 'single SRS', mean( x ), std( x ), std( x )/sqrt(nsamples) ) fprintf('%30s %5.2f %5.2f %5.2f\n', 'single SRS', mean(x), std(x), std(x)/sqrt(nsamples))
% bootstrap the mean: % bootstrap the mean:
mus = zeros(nresamples,1); % vector for storing the means mus = zeros(nresamples,1); % vector for storing the means
@ -13,12 +13,13 @@ for i = 1:nresamples % loop for generating the bootstraps
xr = x(inx); % resample the original SRS xr = x(inx); % resample the original SRS
mus(i) = mean(xr); % compute statistic of the resampled SRS mus(i) = mean(xr); % compute statistic of the resampled SRS
end end
fprintf('%30s %5.2f %5.2f -\n', 'bootstrapped distribution', mean( mus ), std( mus ) ) fprintf('%30s %5.2f %5.2f -\n', 'bootstrapped distribution', mean(mus), std(mus))
% many SRS (we can do that with the random number generator, but not in real life!): % many SRS (we can do that with the random number generator,
% but not in real life!):
musrs = zeros(nresamples,1); % vector for the means of each SRS musrs = zeros(nresamples,1); % vector for the means of each SRS
for i = 1:nresamples for i = 1:nresamples
x = randn( 1, nsamples ); % draw a new SRS x = randn(1, nsamples); % draw a new SRS
musrs(i) = mean( x ); % compute its mean musrs(i) = mean(x); % compute its mean
end end
fprintf('%30s %5.2f %5.2f -\n', 'sampling distribution', mean( musrs ), std( musrs ) ) fprintf('%30s %5.2f %5.2f -\n', 'sampling distribution', mean(musrs), std(musrs))

8
bootstrap/code/correlationsignificance.m
View File

@ -6,7 +6,7 @@ y = randn(n, 1) + a*x;
% correlation coefficient: % correlation coefficient:
rd = corr(x, y); rd = corr(x, y);
fprintf('correlation coefficient of data r = %.2f\n', rd ); fprintf('correlation coefficient of data r = %.2f\n', rd);
% distribution of null hypothesis by permutation: % distribution of null hypothesis by permutation:
nperm = 1000; nperm = 1000;
@ -16,12 +16,12 @@ for i=1:nperm
yr=y(randperm(length(y))); % shuffle y yr=y(randperm(length(y))); % shuffle y
rs(i) = corr(xr, yr); rs(i) = corr(xr, yr);
end end
[h,b] = hist(rs, 20 ); [h,b] = hist(rs, 20);
h = h/sum(h)/(b(2)-b(1)); % normalization h = h/sum(h)/(b(2)-b(1)); % normalization
% significance: % significance:
rq = quantile(rs, 0.95); rq = quantile(rs, 0.95);
fprintf('correlation coefficient of null hypothesis at 5%% significance = %.2f\n', rq ); fprintf('correlation coefficient of null hypothesis at 5%% significance = %.2f\n', rq);
if rd >= rq if rd >= rq
fprintf('--> correlation r=%.2f is significant\n', rd); fprintf('--> correlation r=%.2f is significant\n', rd);
else else
@ -32,7 +32,7 @@ end
bar(b, h, 'facecolor', 'b'); bar(b, h, 'facecolor', 'b');
hold on; hold on;
bar(b(b>=rq), h(b>=rq), 'facecolor', 'r'); bar(b(b>=rq), h(b>=rq), 'facecolor', 'r');
plot( [rd rd], [0 4], 'r', 'linewidth', 2 ); plot([rd rd], [0 4], 'r', 'linewidth', 2);
xlabel('Correlation coefficient'); xlabel('Correlation coefficient');
ylabel('Probability density of H0'); ylabel('Probability density of H0');
hold off; hold off;