  Many data producers seek to provide users access to confidential data without
unduly compromising data subjects' privacy and confidentiality. One general
strategy is to require users to do analyses without seeing the confidential
data; for example, analysts only get access to synthetic data or query systems
that provide disclosure-protected outputs of statistical models. With synthetic
data or redacted outputs, the analyst never really knows how much to trust the
resulting findings. In particular, if the user did the same analysis on the
confidential data, would regression coefficients of interest be statistically
significant or not? We present algorithms for assessing this question that
satisfy differential privacy. We describe conditions under which the algorithms
should give accurate answers about statistical significance. We illustrate the
properties of the proposed methods using artificial and genuine data.
