Complex Contingency Tables Treated by the Partition of χ2

Summary The partition of χ2 can be used to investigate the interactions of all orders in the higher contingency tables. The χ2, obtained by partition, in the case of the 2 × 2 × 2 table for the second order interaction is asymptotically equal to that obtained by Bartlett (1935). Difficulties arise when an attempt is made to find an exact solution. The method of obtaining matrices for orthogonal transformations of variables arranged in hierarchical order is explained. The orthogonal transformation in the case of the 2 × 2 × 2 table is given in full.