And even computer sampling might be much less accurate than analysis without an inordinate amount of computer time devoted to the problem. There is an excellent chance that anyone except a very skilled probabilist will use the wrong calculating formula, and the erroneous answer might well be worse than no answer at all, and worse than computer sampling or perhaps even sampling by hand. This realistic possibility of conceptual analytic error cannot be ignored in any practical situation. It is as much a source of possible error as the sampling procedure, physical characteristics of the cards, and unsound computer programming if a computer is used. Just as with the calculation of the possibility of a disaster at a nuclear reactor, each possible source of trouble must be gauged and allowed for in proportion to its likely importance.
Small Samples Imagine a sample of the heights of four persons.
You wish to estimate a confidence interval for the population mean or median. It is rather obvious that the interval should go beyond the range of the four observations, but a resampling procedure will never give that result. Implicit in the conventional method is an assumption about the shape of the distribution. Making this assumption is in no way different in principle from a Bayesian prior. And the nature of the assumption is crucial.