The Information in Contingency Tables

Abstract : Data which result from experiments in the physical sciences and engineering are usually outcomes of controlled experiments, and expressible in quantitative terms. In many other fields however, the data are seldom results of controlled experiments. In addition, the observations usually can be expressed only in qualitative or categorical terms. If observations are taken over a sample of many such individuals, the result will be a multidimensional contingency table with as many dimensions as there are classifications. Contingency tables are cross-classifications of vectors of discrete random variables showing the number of subjects belonging to distinct categories of each of several qualitative or categorical classifications.