contingency table

Contingency tables, often referred to as cross-classifications or cross-tabulations, are tables of counts which describe and analyse the relationship between two or more variables in a data-set. They contain row variables across the horizontal axis and column variables down the vertical. Cell entries give the number of cases (persons, households, or other unit of analysis) that occur in each cell. The cells themselves are formed by combining one category from each of the row and column variables. Marginal totals (or marginals) give the total number of cases found in each category of the variables-in other words they are the row and column totals. Normally, cell entries are expressed as either row or column percentages (depending on the point the analyst wishes to make), with the total numbers of cases shown in the marginals. These elements are shown in tabular form below.

COLUMN VARIABLE

The above is a template for a typical 2 × 2 cross-tabulation. However, contingency tables can take more complex forms, with three or more variables and several categories of each. In such complex presentations, it is often difficult both to determine the nature of the causal relationships to be found among the variables, and then to demonstrate these to the reader. For example, it may be hard to eliminate spurious correlations , or to establish three-way interaction effects, that is, those cases where two variables are associated, but the strength or direction of the association varies across different categories of the variables. For these reasons the analysis of complex contingency tables is nowadays normally undertaken using the mathematical techniques of loglinear analysis . See also multivariate analysis ; tabular presentation.