THE ANALYSIS OF CROSS-CLASSIFIED DATA: INDEPENDENCE, QUASI-INDEPENDENCE, AND INTERACTIONS IN CONTINGENCY TABLES WITH OUR WITHOUT MISSING ENTRIES.

The article discusses the analysis of cross-classified data. There are two different kinds of contingency tables, that is, truncated contingency tables in which the entries in some of the cells of the table are omitted from the analysis and the more usual contingency tables in which none of the cells of the table are omitted. In the usual non-truncated contingency table, one need to calculate statistician Karl Pearson's chi-square statistic for testing the null hypothesis of independence in the table, using the appropriate number of degrees of freedom. The concept of "quasi-independence" is useful in analyzing tables for which some of the cells are truncated and also in analyzing the more usual kinds of cross-classification tables since it leads to methods that focus attention in turn on various subsets of the entire table, making possible a more detailed analysis of the association between the row and column classifications in the table. For the non-truncated cross-classification table, if the rows and columns are not independent, it will often be of interest to estimate what are the kinds of interaction or association present in the table and what are their magnitudes.