Partitioning of Chi-Square, Analysis of Marginal Contingency Tables, and Estimation of Expected Frequencies in Multidimensional Contingency Tables

Abstract

Abstract A step-by-step method is presented herein for partitioning a certain kind of hypothesis H about the m-way contingency table into (a) a series of hypotheses about marginal tables formed from the m-way table by ignoring one or more of table's m dimensions; and (b) a hypothesis about independence, conditional independence, or conditional equiprobability in the m-way table. This step-by-step method facilitates both the testing of H and the calculation of , the estimated expected frequencies in the m-way table under H. The method introduced herein for calculating is easier to apply than the usual iterative-scaling method in many cases.