Statistics
Statistics
The systematic study of quantitative facts, numerical data, comparative materials, obtained through description and interpretation of group phenomena.
The method of using and interpreting processes of classification, enumeration, measurement and evaluation of group phenomena.
In a restricted sense, the materials, facts or data referring to group phenomena and forming the subject of systematic computation and interpretation.
The Ground of Statistics. Statistics have developed from a specialized application of the inductive principle which concludes from the characteristics of a large number of parts to those of the whole. When we make generalizations from empirical data, we are never certain of having expressed adequately the laws connecting all the relevant and efficient factors in the case under investigation. Not only have we to take into account the personal equation involved and the imperfection of our instru ments of observation and measurement, but also the complex character of physical, biological, psychological and social phenomena which cannot be subjected to an exhaustive analysis. Statistics reveals precisely definite trends and frequencies subject to approximate laws, in these various fields in which phenomena result from many independently varying factors and involve a multitude of numerical units of variable character. Statistics differs fiom probability insofar as it makes a more consistent use of empirical data objectively considered, and of methods directly inspired by the treatment of these data.
The Method of Statistics. The basic principle of statistical method is that of simplification, which makes possible a concise and comprehensive knowledge of a mass of isolated facts by correlating them along definite lines.
The various stages of this method are
precise definition of the problem or field of inquiry;
collection of material required by the problem;
tabulation and measurement of material in a manner satisfying the purpose of the problem;
clear presentation of the significant features of tabulated material (by means of charts, diagrams, symbols, graphs, equations and the like),
selection of mathematical methods for application to the material obtained;
necessary conclusion from the facts and figures obtained;
general interpretation within the limits of the problem and the procedure used.
The special methods of treating statistical data arecollecting, sampling, selecting, tabulating, classifying, totaling or aggregating, measuring, averaging, relating and correlating, presenting symbolically. Each one of these methods uses specialized experimental or mathematical means in its actual application.
The special methods of interpreting statistical data already treated areanalyzing, estimiting, describing, comparing, explaining, applying and predicting.
In order to be conclusive, the various stages and types of the statistical method must avoid
loose definitions,
cross divisions resulting ftom conflicting interpretations of the problem,
data which are not simultaneous or subject to similar conditions,
conclusions from poor oi incomplete data,
prejudices in judging, even when there is no conuption of evidence.
The philosophy of statistics is concerned in general with the discussion and evaluation of the mathematical principles, methods and results of this science; and in particular with a critical analysis of the fitness of biological, psychological, educational, economic and sociological materials, for various types of statistical treatment. The purpose of such an inquiry is to integrate its results into the general problems and schemes of philosophy proper. Cf.. Richard von Mises, Statistics, Probability, and Truth.
— T.G.