Advanced statistics: bootstrapping confidence intervals for statistics with "difficult" distributions.

The use of confidence intervals in reporting results of research has increased dramatically and is now required or highly recommended by editors of many scientific journals. Many resources describe methods for computing confidence intervals for statistics with mathematically simple distributions. Computing confidence intervals for descriptive statistics with distributions that are difficult to represent mathematically is more challenging. The bootstrap is a computationally intensive statistical technique that allows the researcher to make inferences from data without making strong distributional assumptions about the data or the statistic being calculated. This allows the researcher to estimate confidence intervals for statistics that do not have simple sampling distributions (e.g., the median). The purposes of this article are to describe the concept of bootstrapping, to demonstrate how to estimate confidence intervals for the median and the Spearman rank correlation coefficient for non-normally-distributed data from a recent clinical study using two commonly used statistical software packages (SAS and Stata), and to discuss specific limitations of the bootstrap.