Quantifying uncertainty

{A critical literature review and comprehensive simulation study is used to show that (a) non-parametric bootstrap is a viable alternative to commonly taught and used methods in basic estimation tasks (mean, variance, quartiles, correlation). and (b) contrary to recommendations in most related work, double bootstrap performs better than BCa.} Quantifying uncertainty is a fundamental aspect of statistical practice, but it involves a variety of methods, mathematical formulas, and underlying concepts. Could the simpler and more generally applicable non-parametric bootstrap serve as an alternative? This paper addresses this question through a review of related work and a simulation study of one- and two-sided confidence intervals across varying sample sizes, confidence levels, data-generating processes, and statistical functionals. The results suggest that the bootstrap, particularly the double bootstrap, could simplify statistical education and practice without compromising effectiveness.