Nonstatistical sampling and sample sizes that hold up

• Relate the AU-C 530.A13 factors to a nonstatistical sample size.
• Apply random or haphazard selection without bias.
• Defend a nonstatistical sample size by reference to a comparable statistical sample.

Same factors, judgment instead of formula

AU-C 530.05 classifies any approach without both random selection and statistical evaluation as nonstatistical. AU-C 530.A14 says:

• the choice between statistical and nonstatistical is a matter of judgment, and sample size is not a valid criterion for choosing;
• a nonstatistical sampler exercises judgment to relate the same factors used in statistical sampling to determine size; and
• ordinarily, this results in a sample size comparable to an efficient and effectively designed statistical sample using the same parameters.

The same paragraph says this does not require you to compute a statistical size alongside. But "comparable" is the benchmark a reviewer will apply. A nonstatistical sample of 15 where a statistical design would need 90 is not comparable.

The factors

For tests of details, AU-C 530.A13 lists the desired level of assurance, which depends on the assessed risk of material misstatement and assurance from other substantive procedures on the same assertion; tolerable misstatement; expected misstatement; stratification; and, for some methods, the number of sampling units in each stratum. For tests of controls: tolerable rate, expected rate, desired assurance and very small population sizes.

Higher risk, lower tolerable misstatement, more expected misstatement and less assurance from other procedures all push the size up. Stratification can bring it down.

A practical way to size

Many firms use a methodology table or formula that maps these factors to sizes. If yours does not, a defensible approach:

1. Remove key items and test them 100%.
2. Compute what a statistical MUS sample would need for the remainder, using the MUS calculator.
3. Use that as the anchor. Adjust down only with documented reasons, such as substantial assurance from a substantive analytic on the same assertion.
4. Document the factors and the result.

Selection

AU-C 530.08 requires selection you can reasonably expect to be representative. AU-C 530.A17 says the principal nonstatistical techniques are random selection and haphazard selection.

Haphazard selection means selecting without a conscious bias or predictable pattern. It is not choosing what is easy to find. Risks: favoring large items, skipping items stored offsite, picking from the first pages of a listing or the same month. Spread selections across the whole population and period.

Random selection with a random number generator removes most bias and costs little, so many auditors use it even for nonstatistical samples.

Evaluation

AU-C 530.13 requires you to project results to the population; nonstatistical samples are not exempt. AU-C 530.14 requires you to evaluate results, including sampling risk, and whether sampling provided a reasonable basis for conclusions. Without a statistical measure, compare projected misstatement plus known misstatement with tolerable misstatement. AU-C 530.A27 says that as projected misstatement approaches or exceeds tolerable misstatement, it becomes more likely that actual misstatement exceeds it. When projected misstatement is close to tolerable, the allowance for sampling risk is too thin to accept.

Common findings

• Sample sizes like "25, firm default" with no link to risk or tolerable misstatement.
• "Haphazard" samples concentrated in one month or the largest items.
• No projection, only "exceptions immaterial."
• Remainder population above tolerable misstatement but sample size unchanged from the year when it was below.

Sizing a nonstatistical expense sample