Constructing Some Categorical Anomalies

Three situations in which the interpretation of categorical data can appear anomalous are considered: (a) Berkson's fallacy, (b) an example involving retrospective and prospective epidemiological studies from Neyman, and (c) Simpson's paradox.The odds ratio is used as the statistic of interest.Methods are presented to determine whether an anomaly could exist for a given parameterization and to construct an anomaly where feasible.The methods may require at most the preparation of a simple graph and some simple hand calculator computations.