To implement “Bootstrapping Two Medians” method using the “bootstrp” function in MATLAB, you can follow these steps:
- Utilize the "bootstrp" function to generate bootstrap samples for each individual dataset separately. You can read more about "bootstrp" function here: https://www.mathworks.com/help/stats/bootstrp.html
- For each bootstrap sample, try to compute the median using the “median” function. You can read more about it here: https://www.mathworks.com/help/matlab/ref/double.median.html
- Try to Calculate the differences between the medians of the two bootstrap samples.
- Use the differences to compute the confidence interval.
- Check if the confidence interval includes zero. This technique is called “Hypothesis Testing”.
Here's how you could implement this in MATLAB:
% Generating the two samples
x = normrnd(10, 2, [100, 1]);
y = normrnd(12, 3, [100, 1]);
% Bootstrap each sample separately
numBootstraps = 1000;
bootFun = @(data) median(data);
% Generating bootstrap samples and calculate medians
boot_x = bootstrp(numBootstraps, bootFun, x);
boot_y = bootstrp(numBootstraps, bootFun, y);
median_diff = boot_x - boot_y;
alpha = 0.05; % For a 95% confidence interval
CI = prctile(median_diff, [100 * (alpha/2), 100 * (1 - alpha/2)]);
fprintf('Confidence Interval for the difference of medians: [%f, %f]\n', CI(1), CI(2));
% Hypothesis testing
if CI(1) > 0
fprintf('Reject the null hypothesis: there is a significant difference.\n');
elseif CI(2) < 0
fprintf('Reject the null hypothesis: there is a significant difference.\n');
else
fprintf('Fail to reject the null hypothesis: no significant difference.\n');
end
you can read more about "prctile" function here:
Hope it helps!
