  In this paper, we consider methods for performing hypothesis tests on data
protected by a statistical disclosure control technology known as differential
privacy. Previous approaches to differentially private hypothesis testing
either perturbed the test statistic with random noise having large variance
(and resulted in a significant loss of power) or added smaller amounts of noise
directly to the data but failed to adjust the test in response to the added
noise (resulting in biased, unreliable $p$-values). In this paper, we develop a
variety of practical hypothesis tests that address these problems. Using a
different asymptotic regime that is more suited to hypothesis testing with
privacy, we show a modified equivalence between chi-squared tests and
likelihood ratio tests. We then develop differentially private likelihood ratio
and chi-squared tests for a variety of applications on tabular data (i.e.,
independence, sample proportions, and goodness-of-fit tests). Experimental
evaluations on small and large datasets using a wide variety of privacy
settings demonstrate the practicality and reliability of our methods.
