← Use statistical methods to make a formal inference

3 Bootstrapping: what it is and why it works

Watch: Bootstrapping: what it is and why it works Opens a YouTube search: pick a video that clicks for you You only have one sample from each population, but you need to know how much the difference between medians would vary if you took the samples again. Bootstrapping simulates that.

The bootstrap procedure

• Take your original sample of size n. Resample n values from it, WITH replacement, so some values appear twice, some not at all. That is one bootstrap sample.
• Do this for both groups, and calculate the difference between the two medians.
• Repeat this whole process ~1000 times, recording the difference each time.
• You now have a bootstrap distribution of the difference between medians.
• Chop off the bottom 5% and top 5%. The middle 90% is your 90% confidence interval.

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Why "with replacement" matters

Resampling without replacement would just give you your original sample back every time, with zero variation. Sampling with replacement is what lets the bootstrap sample differ from the original, and that variation is a stand-in for the sampling variation you would get from re-sampling the real population. ✕

The conceptual trap

Bootstrapping does not tell you about the accuracy of the original sampling. If your sample was biased (say, only volunteers), the bootstrap faithfully reproduces that bias. It quantifies sampling variation, not sampling quality.

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