THE BOOTSTRAP approach replaces all the formulae and tables for "distributions" -- such as the "normal curve" which has made so many students suffer through elementary "stats" courses in college -- and replaces those conventional methods with experimental "Monte Carlo" manipulations of the observed data. This is how cardplayers estimated the probabilities of various hands during the centuries before the development of deductive mathematical probability and statistics. This system relies on repeated resampling of a set of data and requires no comparison outside the observed sample -- hence "bootstrap."
The classical approach, by contrast, develops an equation for each problem, based on a set of axioms and using a variety of advanced mathematical techniques. The researcher who wishes only to deal with a practical statistical task must then select an appropriate equation. But unless you understand how the equations are derived -- and not one non-mathematician in a boatload can do so -- you have little basis for choosing the right equation. As a consequence, conventional statistical tests are widely misapplied.
The bootstrap method is just as meaningful mathematically as the classical approach, and the ordinary researcher is more likely to use it appropriately and arrive at a sound conclusion. PhDs in mathematics will undoubtedly continue to prefer deductive formulae for many statistical calculations. But for most of us, the Bootstrap method is easier to understand, less subject to error, and much more pleasant to learn. These advantages have been shown by controlled experiments in both high school and college classes conducted by my former colleagues and myself at the University of Illinois.
To dramatize the advantages of the Bootstrap method, I have offered to wager $5,000 in this contest with any teacher of classical probability and statistics: After six or nine hours of Bootstrap Monte Carlo instruction, my students will answer correctly more numerical problems, both simple and complex, than will students taught conventionally for three times that long.