Statistical independence as linear dependence in a contingency table

A contingency table summarizes the conditional frequencies of two attributes and shows how these two attributes are dependent on each other. Thus, this table is a fundamental tool for pattern discovery with conditional probabilities, such as rule discovery. In this paper, a, contingency table is interpreted from the view-point of granular computing. The first; important observation is that; a contingency table compares two attributes with respect to the number of equivalence Classes. The second important; observation is that; matrix algebra, is a key point of analysis of this table. Especially, the degree of independence, rank plays a, very important role in extracting a probabilistic model from a given contingency table.