Partial statistical independence in contingency matrix

This paper focuses on how statistical independence can be observed in a contingency table when the table is viewed as a matrix. Statistical independence in a contingency table is represented as a special form of linear dependence, where all the rows or columns are described by one row or column, respectively. This also means that the rank of the matrix is equal to 1.0. When the rank is equal to 1, we also have some interesting properties corresponding to collinearity in project geometry. Then, we consider the cases where the rank of a given matrix is not full. In these cases, partial statistical independence is observed, where at least one row (column) can be represented by linear combinations of other rows (columns).