Exact goodness of fit tests with applications in the social sciences

Goodness-of-fit tests are useful as an exploratory tool in identifying parsimonious statistical descriptions of datasets. Ordinary Monte Carlo tests produce exact p-values for any choice of test statistics in any non-parametric formulation from which random samples can be generated; and parametric formulations can often be transformed into non-parametric ones by appropriate conditioning. When direct simulation is not feasible, it can be replaced by Markov chain Monte Carlo and, surprisingly, the exactness of the p-value can be maintained. The talk will describe both types of procedure, illustrated by applications in the social sciences. Examples will include sparse contingency tables in two or more dimensions, for which standard chi-squared theory is no longer appropriate, the Rasch model in educational testing and in the struggle for existence (Darwin's finches), binary Markov chains in analyzing patterns of schizophrenic behavior, and models for social networks.