The report summarises exemplar statistical tests of numerical election results, but also shows that such tests must be combined with other types of observations, informed by countryspecific expertise—and are still fallible then. While there is a broad range of statistical tests for election irregularities, the tests cannot be relied upon exclusively: they are subject to unknown rates of false positives and false negatives. The difficulty quantifying error rates is in part because statistical election forensic tests rely on probability models for the results of clean elections, and those models are largely heuristic, because there is no “physics” of political preference and voting behaviour against which to check numerical results.