Statistical Evidence in Two-Way Contingency Tables

Statistical evidence is represented and interpreted via likelihood functions, and its strength is measured by the likelihood ratio. The key quantities for evaluating the performance of this measure are the probability of observing strong misleading evidence along with that of observing weak evidence. It has been proved that when the corresponding likelihood function is expressed in terms of a parametric statistical model that fails, the likelihood ratio retains its evidential value if the likelihood function is robust. This theory is extented to the case when the assumed working model is a characteristic model for two-way contingency tables, which corresponds to a multidimensional parameter space while the cases considered so far in the literature deal with unidimensional parameter spaces. Standard models (independence, association and correlation models) are consider and it is observed that association and correlation models are not equivalent in terms of statistical evidence. The association models are bounded by the bump function while the correlation models are not. Key Words: Independence, association models, correlation models, the law of likelihood, misleading evidence, robust likelihood function, adjusted likelihood