Most accounting studies use only public enforcement actions (SEC cases) to measure accounting fraud. However, private cases (securities class actions) also play an important enforcement role. We discuss the legal standards and processes for both public and private enforcement regimes, emphasize the importance of screening cases for credible fraud allegations, and show both yield credible fraud measures. We'll also demonstrate these research design choices affect inferences from prior research and a hypothetical research setting. Finally, we show common measures of accounting irregularities using Audit Analytics to proxy for fraud result in significant false positives and negatives and develop a fraud prediction model for use in future research. We recommend using both public and private enforcement with appropriate screening when examining accounting fraud to reduce Type I and II errors, or reporting the sensitivity of findings across regimes. This is particularly important given the reduction in accounting-related enforcement after 2005.