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Bootstrap and Simulation Walkthrough

Few shot

Estimate uncertainty with resampling.

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Teach me to estimate uncertainty by resampling, using my data. Statistic of interest: [STATISTIC]. Data description and size: [DATA_DESCRIPTION]. Language: [LANGUAGE].

Walk through:
1. The idea in plain words and when the bootstrap works poorly (very small samples, extreme statistics such as the maximum, dependent data).
2. A step-by-step algorithm: resample with replacement n values, compute the statistic, repeat 5,000 or more times, take percentiles (2.5 and 97.5) for a percentile interval.
3. Complete code with a fixed random seed, vectorized resampling, and a plot of the bootstrap distribution.
4. A worked example on a tiny dataset of 8 invented numbers, showing three resamples and their means so I see what is happening.
5. How to adapt for the difference between two groups, for a median, and for grouped or paired data (resample whole clusters).
6. A comparison with the formula-based interval and what to conclude if they differ.
7. Checks: does the result change with a different seed or number of repeats?
End with the wording for reporting the interval.

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