By Lothar Sachs (auth.)

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In the presentation and summary of observations (descriptive statistics). In the estimation of parameters (estimation theory). In the formulation and verification of the hypotheses (test theory). g. when we estimate election results from known particular results for a selected constituency)--general statements which are valid beyond the observed aggregate. In all empirical sciences, it makes possible the assessing of empirical data and the verification of scientific theories through confrontation of results derived from probability theoretical models-idealizations of special experimental situations-with empirical data; the probabilistic statements, which are of course the only kind here possible, then offer the practitioner indispensable information on which to base his decisions.

40 14 + 6 20 ' 40% ± o· 3. Multiplication: The actual product lies somewhere between the limits 27 . 19 = 513 and 33 ·21 = 693. 5%, 693 - 30 . 20 = 693 - 600 = 93 = 0 1 5 30 . 20 600 600 . 5%. n 4. 737 (division "crossover"). 500· = + 1580/ . /0· Of all the basic arithmetic operations on inaccurate numbers subtraction is particularly risky, the final error being substantially higher than for the other arithmetic operations. 1 STATISTICAL DECISION TECHNIQUES The beginner should on first reading confine himself to sections indicated by an arrow ~, paying particular attention to the examples, disregarding for the time being whatever he finds difficult to grasp, the remarks, the fine print, and the bibliography.

Four levels can be distinguished: 1. Description of the problem and definitions. Observations are made. 2. Analysis: essential elements are abstracted to form the basis of a hypothesis or theory. 3. Solution I of problem: The hypothesis or theory is developed to where new conclusions can be stated and/or results predicted. Formulation of new (partial) problems. 4. New data are gathered to verify the predictions arrived at from the theory: observations II. The whole sequence of steps then starts all over again.

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