Bootstrapping is a statistical procedure that falls under the broader class of resampling methods). It involves resampling a single dataset to create many simulated samples, which allows for the calculation of standard errors, confidence intervals, and hypothesis testing. Bootstrapping assigns measures of accuracy, such as bias, variance, confidence intervals, and prediction error, to sample estimates). This technique allows estimation of the sampling distribution of almost any statistic using random sampling methods). Bootstrapping estimates the properties of an estimand (such as its variance) by measuring those properties when sampling from an approximating distribution). One standard choice for an approximating distribution is the empirical distribution function of the observed data). Bootstrapping is generally useful for estimating the distribution of a statistic (e.g., mean, variance) without using normality assumptions (as required, e.g., for a z-statistic or a t-statistic) ).

Bootstrapping is used in the following situations):

• When the theoretical distribution of a statistic of interest is complicated or unknown.
• When the sample size is insufficient for straightforward statistical inference.
• When the underlying distribution is well-known, and bootstrapping provides a way to account for the distortions caused by the specific sample that may not be fully representative of the population.

A primary difference between bootstrapping and traditional statistics is how they estimate sampling distributions. Traditional hypothesis testing procedures require equations that estimate sampling distributions using the properties of the sample data, the experimental design, and a test statistic. To obtain valid results, you’ll need to use the proper test statistic and satisfy the assumptions. Bootstrapping, on the other hand, is distribution-independent, providing an indirect method to assess the properties of the distribution underlying the sample and the parameters of interest that are derived from this distribution).