Analysis of One-Way ANOVA Model using Synthetic Data

In this paper we consider the age-old ANOVA problem of testing the equality of means of several univariate normal populations with a common unknown variance, except that the data used for analysis arise from a synthetic version of the original observations. We address two versions of the synthetic data: one obtained under Plug-In sampling(PIS) method and the other under Posterior Predictive Sampling(PPS) method. We study its distributional properties (null and non-null) and provide enough computational details. A comparison of power is also provided. As expected, the power under the PIS method is more than that under the PPS method. A measure of privacy protection is also evaluated and it turns out that the PIS method provides less protection than the PPS method, thus confirming the standard belief that accuracy of inference and privacy protection work in opposite directions. Robustness of the proposed tests under deviations from normality is also studied.