Surveys are an important tool for many areas of social science research, but privacy concerns can complicate the collection and analysis of survey data. Differentially private analyses of survey data can address these concerns, but at the cost of accuracy - especially for high-dimensional statistics. We present a novel privacy mechanism, the Tabular DDP Mechanism, designed for high-dimensional statistics with incomplete correlation. The Tabular DDP Mechanism satisfies dependent differential privacy, a variant of Pufferfish privacy; it works by building a causal model of the sensitive data, then calibrating noise to the level of correlation between statistics. An empirical evaluation on survey data shows that the Tabular DDP Mechanism can significantly improve accuracy over the Laplace mechanism.