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Lesson 45 of 75
Review

Resampling methods

Objective. Use bootstrap and permutation inference.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Resampling methods estimate the sampling distribution of a statistic by repeatedly drawing new samples from observed data rather than relying on theoretical formulas. The bootstrap resamples with replacement from the original dataset many times, computing the statistic of interest each time to build an empirical distribution for standard errors or confidence intervals. Permutation tests instead shuffle group labels to test a null hypothesis of no difference, comparing the observed statistic to the shuffled distribution. For example, bootstrapping a sample mean 1000 times and taking the 2.5th and 97.5th percentiles of the resulting means gives an approximate 95% confidence interval without assuming normality.

Worked example

A bootstrap procedure draws 500 resamples of a dataset's mean to estimate a confidence interval. If the 2.5th percentile is 10.2 and the 97.5th percentile is 14.8, state the width of this bootstrap confidence interval.

5002.510.297.514.8
Bar chart of the values 500, 2.5, 10.2, 97.5, 14.8
  1. 1Interval width = upper bound − lower bound
  2. 2Upper bound = 14.8, lower bound = 10.2
  3. 3Width = 14.8 − 10.2
  4. 4Simplify: 4.6

Answer: 4.6

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Common mistake. Students treat a single bootstrap resample as giving the confidence interval directly; one resample only mimics one hypothetical dataset. The interval requires the spread across thousands of resampled statistics, not one replicate's value.

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