Paul R. Yarnold
Optimal Data Analysis, LLC
Chi-square analysis is often used to analyze data in contingency tables created by crossing two categorical variables, with at least one having three or more categories. Researchers report the associated omnibus (overall) p value to indicate the statistical reliability (not the strength) of the association between the variables. A statistically significant omnibus p value indicates two or more categories differ, but the exact structure of the inter-category difference(s) isn’t explicit. Pairwise comparisons are needed to reveal the precise effect, but in practice this may be substituted for a non-statistical “eyeball analysis-based” summary of the data. In contrast, ODA models provide exact p values and an index of effect strength that is normed against chance and can be used to directly compare the classification accuracy achieved by alternative models. Furthermore, ODA models explicitly identify the structure of the omnibus effect, and an efficient optimal pairwise comparison methodology is used to ensure the statistical integrity of the model. These methods are illustrated for a sample of N = 2,420 adults at risk of developing a pressure ulcer.