Statistical sampling is a method of examining part of a population instead of all of it, in which the items are selected at random so that every item has a known, non-zero chance of being chosen, and the result found in the sample is projected to the whole population with a sampling risk that can be measured. That measurement is the point. It lets whoever relies on the sample state how much uncertainty the projection carries.
The Two Features That Make Sampling Statistical
The AICPA’s auditing standards, which govern audits of nonissuers, meaning any entity not subject to the oversight authority of the PCAOB (AICPA, AU-C Sections, glossary), draw the line precisely. Statistical sampling is an approach to sampling with two characteristics, random selection of the sample items and the use of an appropriate statistical technique to evaluate sample results, including measurement of sampling risk (AICPA, AU-C 530, Audit Sampling, .05). An approach missing either characteristic is nonstatistical sampling. A random pull evaluated by judgment fails that test, and so does a judgmental pull run through a formula.
Statistical samples are selected using random selection techniques, while the principal techniques for selecting a nonstatistical sample are random selection and haphazard selection, a term the section names without defining (AU-C 530, .A17).
Sample size is not the divider. The choice between the two approaches is a matter for professional judgment, sample size is not a valid criterion for making it, and a nonstatistical approach that relates the same factors ordinarily produces a comparable sample size on the same sampling parameters (AU-C 530, .A14).
Sampling Risk Versus Nonsampling Risk
Sampling risk is the risk that a conclusion drawn from the sample differs from the conclusion the same procedure applied to the entire population would have given. Nonsampling risk is the risk of reaching an erroneous conclusion for any reason not related to sampling risk (AU-C 530, .05), such as using an inappropriate audit procedure, misinterpreting the evidence, or failing to recognize a misstatement or deviation (.A4). Only the first is measurable. Nonsampling risk is reduced to an acceptable level through such factors as adequate planning and proper conduct of a firm’s audit practice, not by a larger sample (.A4).
Where a CPA Firm Meets It
AU-C 530 applies once the auditor has decided to use audit sampling, and it defines audit sampling as the selection and evaluation of less than 100 percent of the population of audit relevance, where the selected items are expected to be representative of it (AU-C 530, .01 and .05).
Sampling is the step that decides which items the rest of the work lands on. It picks the instances of a control that a test of controls inspects, and the recorded items that a test of details then vouches back to their documentation. The auditor determines a sample size sufficient to reduce sampling risk to an acceptably low level, and selects items so the auditor can reasonably expect the sample to be representative of the relevant population (AU-C 530, .07 and .08). Both of those decisions stay with the auditor even when someone else performs the fieldwork, a line drawn in outsourced audit support.
What the projected result is measured against depends on the test. For a test of details it is tolerable misstatement, a monetary amount the auditor sets and seeks assurance the actual misstatement in the population will not exceed, and the projected misstatement is the auditor’s best estimate of that population misstatement (AU-C 530, .05 and .A27). For a test of controls the benchmark is a separate one, the tolerable rate of deviation, a rate of deviation the auditor sets on the same footing (.05). Tolerable misstatement is covered in materiality in auditing.
Statistical Sampling on a Tax Return
The method carries a second rulebook on the tax side. When permitted by the Service, taxpayers may use statistical sampling procedures to support items on their income tax returns, and samples that fail the stated criteria are rejected (IRS, Rev. Proc. 2011-42, sections 3 and 4).
The estimate has to rest on a probability sample in which each sampling unit has a known, non-zero chance of selection, drawn by either a simple random or a stratified random sampling method, and it has to be computed at the least advantageous 95 percent one-sided confidence limit, whichever of the upper or lower limit gives the taxpayer the least benefit (IRS, Rev. Proc. 2011-42, section 4.02(2)(b) and (c)).
That last requirement relaxes as precision improves. Where the relative precision for the sampling plan does not exceed 10 percent, the point estimate may be used in place of the least advantageous confidence limit, and where relative precision is greater than 10 percent and less than 15 percent, the estimate is computed at a stated point between the two (IRS, Rev. Proc. 2011-42, section 4.02(2)(c)). A written sampling plan has to exist before the sample is executed (Appendix A).
Common Questions
It is audit sampling performed with random selection and evaluated with a statistical technique, and the objective is to give the auditor a reasonable basis for conclusions about the population the sample came from (AU-C 530, .04). The result is projected to that population, and on a test of controls the sample deviation rate is also the projected deviation rate (.13 and .A25).
Neither auditing standard fixes a canonical four, and both write their lists as open. AU-C 530 names simple random, systematic random, and probability weighted including monetary unit as random selection techniques (AU-C 530, .A16). The PCAOB standard for audits of issuers gives, as examples of random-based selection, random sampling, stratified random sampling, sampling with probability proportional to size, and systematic sampling with one or more random starts (PCAOB, AS 2315, footnote 4).
Accountably places trained offshore accountants and tax preparers inside US CPA and EA firms on accounting and tax work rather than audit fieldwork, and a firm can grade that work on its own files through a trial task.
