Audits Act III. Sampling

1. Audits Act III. Sampling DR. WILL YANCEY, CPA CATHLEEN BUCHOLTZ, CPA TRUE PARTNERS CONSULTING 2009 Annual Conference

2. Parable of the Footballs and the Fish • You are asked to determine the weight of 1,000 footballs. You know they are identical in weight. You can weigh only one ball at a time. How many must you weigh? • You are asked to determine the weight of 1,000 different fish taken from a lake. They are highly variable in weight. You can weigh only one fish at a time. How many must you weigh? • Suppose we can group and count the fish before we weigh them. What can we do so that we do not need to weigh so many?

3. Sampling Uncashed Checks Suppose the UP auditor sees thousands of uncashed checks for the past five years, wants to sample them, and project the UP-to-Revenue ratio onto an earlier period with unavailable records. Should sampling be allowed? Possible ways to group by attribute or stratify • By account type: Payroll, A/P, rebates, etc. • By status type: outstanding, void, stop, cancelled, etc. • By days outstanding • By dollar amount

4. What is the best sample size? • Larger samples take more time. • Approximately 1 hour of staff time per sample item. • Smaller samples may be less accurate. • By random chance a small sample may produce an estimate that is significantly overstated or understated. • Small samples are more sensitive to outliers (such as unusually large items distorting the results). • Start with a smaller sample, and expand later? • Yes, that is reasonable. • But some auditors disagree with that.

5. Accuracy and Precision • Accuracy is how close the estimates are to the true value. • But in large populations, we never know the true value unless we examine every single item. • Precision is how close the results are to each other. High accuracy Low accuracy Low precision High precision

6. Validity Do the results measure what they intend to measure? • Sampling risk (“random draw”): • Random chance that randomly selected sample has much higher or lower percentage of UP than population. • Increasing sample size reduces sampling risk. • Measurement error (“garbage in, garbage out”): • Auditor conclusion contradicts evidence presented by holder. • Non-response (“unavailable documents”): • Are available records representative of unavailable records? • Coverage (“right population”): • Journal entries that are not transactions with payees.

7. Validity and Precision Assume true value is $50. Both of these statements are valid: • A. Estimate is between $0 and $100 ($50 ± 100%). • B. Estimate is between $45 and $55 ($50 ± 5%). B has much better precision.

8. Assessment and Precision Assume you do not know the true value. Statistical analysis of the sample reports 90% confidence that this interval contains the true value: $108 K to $132 K [also known as $120 K ± $12 K or $120K ± 10% [ Where should the assessment be made? $108K or $120K or $132K

9. QUESTIONS

10. Contact Information DR. WILL YANCEY, CPA WILL@WILLYANCEY.COM (972) 387-8558 CATHLEEN BUCHOLTZ, CPA TRUE PARTNERS CONSULTING CATHLEEN.BUCHOLTZ@TPCTAX.COM (213) 417-2501

11. DR. WILL YANCEY, CPA WILL@WILLYANCEY.COM CATHLEEN BUCHOLTZ, CPA TRUE PARTNERS CONSULTING CATHLEEN.BUCHOLTZ@TPCTAX.COM Audits Act III. Sampling