Statistical Support of Forensic Auditing

During a three year period, $4.38 million of gold was stolen from the vaults of Sammartino's House of Diamonds. A civil suit between the gold's owner and its insurance company centered on when the gold was stolen. The time of the loss was critical to the insurer's contention that it was not liable because the gold was missing prior to the inception date of the policy. The insurer's attorneys retained an accounting firm to conduct a forensic audit (a financial audit to investigate fraud). The key to this investigation was reconstructing a daily gold inventory balance by sampling sales invoices. Since the audit's sampling methodology was open to question, we were retained to use various statistical techniques to verify the process. To test the results of the forensic audit, we constructed two formal hypotheses: The first to test for nonrandomness in the selected sample observations; the second to test if the amount of sales dollars selected in the sample was proportional to the amount of sales dollars in the monthly population. To accomplish this, we utilized a one-sample runs test, time-series charts, regression analysis, and interval estimations. We found that the sampled invoice transactions exhibited no evidence of nonrandomness or bias and appeared to be representative of the population. Hence, these results supported the inventory reconstruction obtained by the accounting firm.