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Bootstrapping vs. the CLT

Difference​

Bootstrapping

  • Goal: to estimate the distribution of a sample statistic (e.g. the sample mean).
  • Given just a single sample

The Central Limit Theorem

  • Goal: to describe the distribution of the sample mean (or sum)
  • It depends on information about the population (i.e. the population mean and population SD). However, since the sample mean and SD are likely to be close to the population mean and SD, we can use them as approximations in the CLT!

As a result, we can approximate the distribution of the sample mean, given just a single sample, without ever having to bootstrap! In other words, the CLT is a shortcut to bootstrapping!