Statistical methodology has great potential for useful application in business, but that potential is seldom realized. However, companies are increasingly exploiting simple statistical tools in quality and productivity improvement and developing "company cultures" congenial to effective use of statistics. Statistical and probabilistic thinking is essential for sound decision-making. Only with understanding of statistical variability can managers distinguish special from common causes of variation, intelligently direct efforts to improve processes, and avoid the tampering that can make processes worse. Statistics can be used most effectively in business when many employees--"parastatisticians"--have some grasp of statistical tools and thinking. Fortunately, there is evidence that very elementary tools suffice to make rough-and-ready studies that can illuminate most business problems and facilitate most decisions.

The Chen-Stein method of Poisson approximation is a powerful tool for computing an error bound when approximating probabilities using the Poisson distribution. In many cases, this bound may be given in terms of first and second moments alone. We present a background of the method and state some fundamental Poisson approximation theorems. The body of this paper is an illustration, through varied examples, of the wide applicability and utility of the Chen-Stein method. These examples include birthday coincidences, head runs in coin tosses, random graphs, maxima of normal variates and random permutations and mappings. We conclude with an application to molecular biology. The variety of examples presented here does not exhaust the range of possible applications of the Chen-Stein method.

In the portion of the paper translated here, Neyman introduces a model for the analysis of field experiments conducted for the purpose of comparing a number of crop varieties, which makes use of a double-indexed array of unknown potential yields, one index corresponding to varieties and the other to plots. The yield corresponding to only one variety will be observed on any given plot, but through an urn model embodying sampling without replacement from this doubly indexed array, Neyman obtains a formula for the variance of the difference between the averages of the observed yields of two varieties. This variance involves the variance over all plots of the potential yields and the correlation coefficient $r$ between the potential yields of the two varieties on the same plot. Since it is impossible to estimate $r$ directly, Neyman advises taking $r = 1$, observing that in practice this may lead to using too large an estimated standard deviation, when comparing two variety means.