Contingency table analysis: Proportions and flow graphs

Summary

Two tabular analyses, 30 years apart, illustrate changes in contingency table research. The originalAmerican Soldier discussion of a cross-tabulation of race, home region, region of military station and preference for military station is unsystematic, though subtle and insightful. In print, at least, it appears to consist of selectively citing percentages (proportions) and percentage differences that seem to support the analysts' argument. The approaches of 20-plus years later are, by contrast, relentlessly systematic, more concerned with sampling error, and harder to explain (which is why I was asked to write this essay).

The new approaches — both those illustrated here and alternatives now available in the published literature — draw heavily on two major traditions for analyzing interval level data. From regression and Lazarsfeld's pioneering work on tables, we draw a concern with decomposing zero-order associations into causally meaningful paths as the paradigmatic exercise for the social science data analyst. From experimental design and the analysis of variance we draw the logic for assessing interaction effects. In both cases, however, the techniques for statistical inference and the interpretation of the data have been modified to be germane to tabular data.

Some people (I for one) love tabular data since they enable us to study interesting variables that are difficult to handle as interval level scales (religion, political party, family type, ethnic group, geographical region, industrial sector, disease category, reading matter, etc. etc., etc.). Others are antagonistic toward the crudity of such measurement. I suspect these are matters of personal taste, not scientific merit. However, I think it fair to say that if the contemporary research worker opts for tables, there is no longer any dearth of sophisticated and systematic statistical tools for examining and interpreting the information.