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Background:  Upon finding a significant association between rows and columns of an r x c contingency table, the next step is to study the nature of the association (i.e., lack of independence) in more detail. This can be particularly difficult for “sparse” tables, where the cell sample sizes are small. Snedecor and Cochran (1989) propose that, in r x c tables, the entries providing the largest percentage contributions to Χ2 are those that will suggest departure from the null hypothesis of independence.  The “scree plot” is often used in principal component analysis (PCA) to visually identify the PCs that contain most of the variance (as expressed through the eigenvalues). In PCA, the eigenvalues are plotted against the corresponding PC to produce a scree plot that illustrates the rate of change in the magnitude of the eigenvalues for the PC. This plot is monotonic non-increasing and the rate of decline tends to be fast first, eventually leveling off. The ‘elbow’, or the point at which the curve bends, is considered to indicate the maximum number of PCs to extract.  We propose an adaptation of the scree plot to visualizing the largest contributions to Χ2 among all of the cells of the r x c table. Graphical visualization should reveal a sequence of non-increasing contributions that will level off in such a way as to indicate which cells are primarily responsible for the departure from the null hypothesis.

An Exploratory Graphical Method for Identifying Associations in r x c Contingency Tables