Complex sample designs typically invalidate the direct application of the familiar Pearson or likelihood-ratio chi-squared statistics for testing the fit of a model to a cross-classified table of counts. This article discusses the adjustment of these statistics through a jackknifing approach. The technique may generally be applied whenever a standard replication method, such as the jackknife, bootstrap, or repeated half-samples, provides a consistent estimate of the covariance matrix of the sample estimates. Properties of the limiting distribution of new test statistics, Xj and GJ, are described. The new statistics may be used to test goodness of fit and to compare nested models.