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The statistical analysis of discrete multivariate data has received a great deal of attention in the statistics literature over the past two decades. The develop ment ofappropriate models is the common theme of books such as Cox (1970), Haberman (1974, 1978, 1979), Bishop et al. (1975), Gokhale and Kullback (1978), Upton (1978), Fienberg (1980), Plackett (1981), Agresti (1984), Goodman (1984), and Freeman (1987). The objective of our book differs from those listed above. Rather than concentrating on model building, our intention is to describe and assess the goodnessoffit statistics used in the model verification part of the inference process. Those books that emphasize model development tend to assume that the model can be tested with one of the traditional goodnessoffit tests 2 2 (e.g., Pearson's X or the loglikelihood ratio G ) using a chisquared critical value. However, it is well known that this can give a poor approximation in many circumstances. This book provides the reader with a unified analysis of the traditional goodnessoffit tests, describing their behavior and relative merits as well as introducing some new test statistics. The powerdivergence family of statistics (Cressie and Read, 1984) is used to link the traditional test statistics through a single realvalued parameter, and provides a way to consolidate and extend the current fragmented literature. As a byproduct of our analysis, a new 2 2 statistic emerges "between" Pearson's X and the loglikelihood ratio G that has some valuable properties.
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