Sample statistics as convincing evidence: a tax fraud case†

Abstract

Abstract This work deals with the analysis of data used by tax officials to support their claim of tax fraud at a pizzeria. The possibilities of embezzlement under study are overreporting of takeaway sales and underreporting of cash payments. Standard methods based on normal assumptions and models based on Gamma assumptions are contrasted. Criteria for the choice of method in practice are discussed, among them, how easy the method is to understand, justify and communicate to the parties. Some dilemmas present itself: the choice of statistical method, its role in building the evidence, the choice of risk factor, the application of legal principles like ‘clear and convincing evidence’ and ‘beyond reasonable doubt’. The insights gained may be useful for both tax officials and expert witnesses, as well as defenders of the taxpayer. A detailed exposition is given, both from the frequentist and Bayesian position, in order to prepare for the various statistical arguments that may be used by the parties. The presented Gamma approach may be applied to any business dealing with ratios of aggregated sales.