Probability Theory
Sociologists, as much as researchers in any field perhaps, use a variety of approaches in the investigation of their subject matter. Quite successful and important are the historical and exegetical approaches and those in the traditions of anthropology and philosophy. Also of great importance are the systematic approaches that use mathematical models. Here the social investigator proposes a model, a mathematical depiction of social phenomena. A successful mathematical model can be very powerful, providing not only confidence in the theory from which the model was derived, giving us an explanation of the phenomena, but producing as well a method for predicting, giving us a practical means for controlling or affecting the social phenomena.
The social mathematical model is first of all a description of the relationship of the properties of social objects—groups, states, institutions, organizations, even people. If the model is derived from a theory, or if it contains features implied by a theory, and if the model fits data (i.e., has been found to satisfy some criterion of performance), the model can in addition be regarded as evidence to support that theory. In this case we can think of a true, underlying model that generated the observations we are studying and a proposed model that will be tested against data.
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