Department of Statistics, UCLA

Karl Pearson's seminal article on the criterion is reviewed, formalized in modern notation and its method is extended beyond the normal distributions using the Mahalanobis distance as a vehicle. The extension yields a simple method, firmly rooted in history, for computing exact p-values and acceptance regions for hypotheses under a large class of probability distributions and of arbitrary dimension. As a by-product it is for example shown that the so-called method of acceptance intervals by percentiles is a univariate special case of Pearson's method. The article's content is discussed in context of other sources, in particular Pearson's The Grammar of Science, yielding a holistic approach to verification/falisfication of hypotheses through empirical observation.