Audit and Assurance · Audit sampling and other means of testing

Designing Audit Samples and Evaluating Results (ISA 530)

Updated 11 October 2026 · Fact-checked

Audit sampling means testing less than 100% of a population so you can conclude on the whole. You define the population, set a sample size using risk and tolerable misstatement, test each item, project errors to the population, and compare the result with tolerable misstatement to conclude.

Understand Designing Samples and Evaluating Results

Auditors rarely test every item. Sampling lets you apply procedures to fewer than 100% of items in a population so that every item has a chance of selection. You then draw a conclusion about the whole population. ISA 530 governs this.

Start by defining the population and the test objective. The population must be complete and relevant to the objective. To test for overstated receivables, the population is the receivables ledger, not the sales ledger. To test for unrecorded liabilities, sampling from the payables ledger is wrong, because the missing items are not in it.

Sample size depends on how much risk you will accept and how much error you can tolerate. A bigger sample gives more assurance. Higher assessed risk of material misstatement, a lower tolerable misstatement, a higher expected misstatement and a larger population (only slightly) all push sample size up. Reliance on other substantive procedures for the same assertion lets you reduce it. Stratifying the population can reduce the sample size needed, because variability within each stratum is lower.

Next you perform the procedure on each item. If you cannot test an item, try an alternative procedure. If that fails, treat the item as a misstatement. Investigate every deviation or misstatement for its nature and cause. An anomaly is a misstatement that is demonstrably not representative of the population, for example a one-off error from a known system breakdown. You may exclude it from projection only if you are highly certain it is isolated, and you must do extra work to prove that. The anomaly is excluded from projection but is still treated as a known misstatement and included in the total.

Finally, evaluate. Project the misstatements found to the whole population. Add any anomalous misstatement, and add known errors in items not sampled where relevant. Compare this total (projected misstatement + anomalous misstatement + other known misstatements) with tolerable misstatement. If the total is close to or above tolerable misstatement, sampling risk may be unacceptable, and you extend testing or ask management to adjust. Also consider non-sampling risk, such as using the wrong procedure or misreading evidence.

Key rules to remember

Projected misstatement (ratio method): Projected misstatement = (Error found in sample ÷ Value of sample) × Population value; Use when errors scale with item value. Exclude any proven anomaly first.
Projected misstatement (average error method): Projected misstatement = (Error found ÷ Number of items in sample) × Number of items in population; Use when errors relate to count of items, not value.
Tolerable rate of deviation test: Deviation rate in sample = Deviations ÷ Items tested; Used for tests of controls. Compare with the tolerable rate of deviation.
Evaluation rule: Total = projected misstatement + anomalous misstatement (+ other known misstatements). Compare the total with tolerable misstatement.; If the total is close to or above tolerable misstatement, sampling risk may be unacceptable, so extend testing or request adjustment.
Sample size factors: Larger sample if: higher assessed risk, lower tolerable misstatement, higher expected misstatement, less reliance on other procedures; Population size has little effect unless the population is small.

How to solve Designing Samples and Evaluating Results questions

Use this order for any sampling question, whether it asks about design or evaluation.

1State the test objective and the assertion being tested (for example, overstatement of receivables).
2Define the population so it matches the objective and is complete, and state any stratification.
3Identify the factors that raise or lower sample size, and say the direction of each in the scenario.
4Choose the selection method (random, systematic, monetary unit, haphazard) and justify it briefly.
5Perform the procedure on each item, use alternative procedures for untested items, and investigate causes of every error.
6Decide whether any error is a true anomaly. Exclude it only with high certainty and extra evidence.
7Project errors to the population using the ratio or average method and add other known errors.
8Compare with tolerable misstatement, conclude, and state the action: accept, extend testing, or request adjustment.

Quickest way: Five-line projection and conclusion

When to use it: Numerical OT questions and Section C parts asking you to project errors and conclude.

Write the error found, sample value and population value.
Divide error by sample value, multiply by population value.
Remove an anomaly only if the question says it is isolated and proven.
Compare with tolerable misstatement given.
Write one sentence: below, close to, or above, and what you do next.

Common mistakes in Designing Samples and Evaluating Results

Projecting only the error found, not extrapolating to the population.
Students treat the sample as the whole test.
Fix: Always scale the error to the full population, then compare with tolerable misstatement.
Calling any one-off error an anomaly and ignoring it.
It seems convenient and the result then looks acceptable.
Fix: An anomaly must be demonstrably unrepresentative, with extra work proving it. Otherwise, project it.
Choosing the wrong population, such as sampling the payables ledger for unrecorded liabilities.
Students sample what is easy to access, not what fits the assertion.
Fix: Choose a population that could contain the misstatement, such as post year-end payments or goods received notes.
Saying a larger population always means a much larger sample.
It sounds logical.
Fix: Population size has little effect unless the population is very small. Risk and tolerable misstatement matter more.
Getting the direction of a factor wrong, such as a higher tolerable misstatement needing a larger sample.
Students learn the list but not the reasoning.
Fix: Ask: does this make me need more assurance? A higher tolerable misstatement means you accept more error, so the sample can be smaller.
Stopping when an item cannot be tested, such as a missing invoice.
Students assume the item is skipped.
Fix: Perform alternative procedures. If none work, treat the item as an error.

Worked examples

Example 1

An auditor tests a trade receivables population of $2,400,000 using a sample of items worth $300,000. Errors of $9,000 (overstatement) are found. Tolerable misstatement is $60,000. No anomaly is identified. Project the misstatement and conclude.

Show the solution

Use the ratio method: error ÷ sample value = 9,000 ÷ 300,000 = 3%.
Multiply by population: 3% × 2,400,000 = $72,000.
Compare with tolerable misstatement of $60,000: $72,000 is higher.
Projected misstatement exceeds tolerable misstatement, so the population cannot be accepted as it stands.

Answer: Projected misstatement is $72,000, above tolerable misstatement of $60,000. Ask management to adjust the receivables or extend testing before concluding.

Example 2

Using the same facts, the $9,000 error includes $4,000 from one invoice posted twice because of a one-off system crash on a single day, which management has fixed and the auditor has confirmed affected no other items. Assume there are no other known misstatements. The question gives no value for the duplicated invoice, so assume the sample value stays at $300,000 and treat the result as an approximation. Evaluate.

Show the solution

The crash error is demonstrably isolated, and extra work has confirmed it, so it qualifies as an anomaly.
Exclude it from projection: remaining error in the sample = 9,000 − 4,000 = $5,000.
Strictly, the anomalous item's value should also come out of the sample value base. The question gives no value for it, so we assume the base stays at $300,000. This makes the result an approximation: removing the item's value would raise the rate and the projection slightly.
Ratio: 5,000 ÷ 300,000 = 1.667%. Projection: 5,000 ÷ 300,000 × 2,400,000 = $40,000. This projected figure already covers the $5,000 actually found in the sample.
The anomaly is not projected but is still a known misstatement. Add the $4,000: 40,000 + 4,000 = $44,000.
Compare with tolerable misstatement of $60,000: $44,000 is below, but not by a wide margin.

Answer: Total misstatement is approximately $44,000 (projected $40,000 plus the $4,000 anomaly as a known misstatement), under the assumption that the sample value base stays at $300,000 and there are no other known misstatements. Adjusting the base for the anomalous item would make the projection slightly higher. The total is below tolerable misstatement of $60,000. The population may be accepted, but the auditor should consider sampling risk and whether the unadjusted error is acceptable alongside other misstatements.

Exam tips

In OT questions, check the direction of each sample size factor before you choose an option. Wrong direction is the classic trap.
In numbers questions, show the ratio, the projection and the comparison with tolerable misstatement. Method marks are available in Section C.
Only call an item an anomaly when the scenario says the cause is isolated and the auditor has verified it.
Match the population to the assertion. Completeness tests need a population from outside the ledger.
End every evaluation with an action: accept, extend sample or request adjustment.

Designing Samples and Evaluating Results in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

CMA IntermediateSample Design, Size and Evaluation of Results

Designing Samples and Evaluating Results: frequently asked questions

What factors affect sample size in audit sampling?

Sample size rises with higher assessed risk of material misstatement and higher expected misstatement. It rises when tolerable misstatement is lower or when you rely less on other procedures. Population size matters little unless it is small.

How do you project errors from an audit sample?

Find the error rate in the sample, then apply it to the population. With the ratio method, divide error by sample value and multiply by population value. With the average method, divide error by items tested and multiply by number of items in the population.

What is an anomaly in audit sampling?

An anomaly is a misstatement or deviation that is demonstrably not representative of the population. You must be highly certain of this and gather extra evidence. If you cannot, project it like any other error.

What if the projected misstatement is close to tolerable misstatement?

Sampling risk is then unacceptably high. Extend the sample, perform other procedures, or ask management to correct the error. Do not conclude the population is acceptable without further evidence.