Statistical activity can be divided for descriptive and analytical purposes into (a) discovery/imposition of structure, (b) assessment of variation conditional on structure and (c) execution of techniques. Each of these three areas of activity has an associated type of uncertainty, respectively, structural uncertainty, risk and technical uncertainty. In any statistical analysis, an analyst has limited supplies of time, money, know how and computational power and must use these resources to diminish and to characterize better the three main types of uncertainty and the many subtypes that comprise them. No existing school of statistical thinking provides a comprehensive framework for considering the various types of uncertainty and the tradeoffs among them that analysts must make. One result of this is the absence of a system that properly accounts for all of the types of uncertainty. This paper describes the types of uncertainty, catalogues and evaluates current methods as tools for characterizing and diminishing them, considers the types of tradeoffs that analysts must make in applying statistical methods in problems and examines the bias introduced into deliberations by the absence of a proper system of accounting for uncertainty. This paper is an attempt to begin the construction of such a proper system and thus to reduce or eliminate that bias.