ACCA Applied Skills · Audit and Assurance

Audit sampling and other means of testing: formula sheet

Full chapter guide

Key formulas

Definition of audit sampling: Procedures on < 100% of items, each sampling unit with a chance of selection; Both parts matter. Selecting only the items you choose by judgement, with no chance for others, is not sampling.
Sampling risk and sample size: Larger sample → lower sampling risk; Non-sampling risk is not reduced by increasing sample size.
Tolerable error and sample size: Lower tolerable error → larger sample; Tolerable misstatement is based on performance materiality.
Expected error and sample size: Higher expected error → larger sample; Expected error must be below tolerable error, or sampling is unlikely to be suitable.
Projected misstatement: Projected error = (Error found ÷ Sample value) × Population value; Used when the sample is by value. Compare the result with tolerable misstatement.
Sampling interval (systematic): Interval = Population size ÷ Sample size; Choose a random start between 1 and the interval, then take every nth item.
Sampling interval (monetary unit sampling): Interval = Total population value ÷ Sample size; With fixed-interval selection, items with a value at or above the interval are certain to be selected.
Probability of selection in MUS: Probability = Item value ÷ Sampling interval, for items below the interval; This is exact with fixed-interval selection from a random start. It explains why larger items are more likely to be picked. Items equal to or above the interval are certain to be selected.
Statistical sampling test: Statistical sample = random selection of items + evaluation of results using probability theory; Systematic selection with a random start and MUS can be used in a statistical sample when results are evaluated using probability theory. Selection alone does not make a sample statistical. Haphazard and block selection are non-statistical.
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.
Three means of selection (ISA 500): Select all items | Select specific items | Audit sampling; Learn the names exactly. Auditors may use any one or a combination, depending on the circumstances.
When 100% examination suits: Few items + high value, OR significant risk, OR cheap automated check; Typical triggers: small population of large items, significant risk where other evidence is not enough, or recalculation by software.
When specific items suit: Key items, high-risk or unusual items, items to gain information, items to test a control; Results apply only to the items tested. You cannot extrapolate to the rest of the population.
When sampling suits: Large population + similar items + conclusion about the whole population needed; Every item must have a chance of selection. Sampling risk exists and results can be projected.
Reliability of evidence (rule of thumb): More reliable: external > internal; direct > indirect; original > copy; written > oral; A general guide, not an absolute rule. Internal evidence from strong controls can be more reliable than external evidence from a weak source.
Recalculation vs reperformance: Recalculation = check the arithmetic; Reperformance = repeat the procedure or control independently; Use the right term in the exam. Redoing a bank reconciliation is reperformance.
Analytical procedure comparison: Expected value vs recorded value → investigate differences above the threshold; Build your expectation first, then compare, then investigate the unexpected differences.

Quick revision

Audit sampling is applying procedures to less than 100% of a population so every item has a chance of selection.
Sampling risk is the risk that the conclusion from the sample differs from testing the whole population.
Non-sampling risk comes from things like using the wrong procedure or misreading evidence. A larger sample does not reduce it.
Tolerable error is the maximum error the auditor will accept in the population.
A higher assessed risk or lower tolerable error means a larger sample.
Random selection gives every item an equal chance. Systematic selection uses a fixed interval from a start point.
Monetary unit sampling gives larger-value items a higher chance of selection.
Haphazard and block selection are not statistically based, so use them with care.
Testing all items, selecting specific items and selecting key items are not audit sampling.
If you find an error, consider whether it is anomalous, then project it across the population.
Procedures: inspection, observation, inquiry, external confirmation, recalculation, reperformance and analytical procedures.
Match the procedure to the assertion: for example, confirmation helps with existence of receivables.

Common mistakes

Saying a larger sample reduces non-sampling risk. Fix: Only sampling risk falls with sample size. Non-sampling risk is managed by quality of procedures, training and review.
Treating tolerable error and expected error as the same thing. Fix: Tolerable is the maximum acceptable. Expected is the amount you predict. Expected should be lower than tolerable.
Calling haphazard selection a statistical or random method. Fix: Random means every item has a known chance, usually through a number generator. Haphazard is judgemental and non-statistical.
Using monetary unit sampling to test understatement or completeness of liabilities. Fix: MUS favours large items and misses small or zero items. Use it for overstatement. For completeness, test from outside the recorded population.
Projecting only the error found, not extrapolating to the population. Fix: Always scale the error to the full population, then compare with tolerable misstatement.
Calling any one-off error an anomaly and ignoring it. Fix: An anomaly must be demonstrably unrepresentative, with extra work proving it. Otherwise, project it.
Treating specific item selection as a type of sampling. Fix: Remember that sampling gives every item a chance of selection. Specific items are chosen by judgement, so you cannot project the results.
Saying 100% examination is always the most reliable and so always best. Fix: Say it is suited to small populations, significant risks or automated checks. For large populations it is usually uneconomic.
Writing vague procedures such as 'check the inventory' or 'review the invoices'. Fix: Use the verb, item, check pattern: 'Inspect a sample of sales invoices and agree the price to the approved price list.'
Confusing recalculation with reperformance. Fix: If you only check the maths, it is recalculation. If you repeat a control or process independently, it is reperformance.

Exam tips

Always state whether a risk is sampling or non-sampling and give the reason, using the scenario fact that caused it.
In sample size questions, give the direction of change for each factor. Examiners mark direction.
Show a projected error calculation clearly, then compare it with tolerable error. Do not stop at the number.
Do not state that sampling gives certainty. Say it gives reasonable, not absolute, assurance.
In objective questions, watch for reversed wording on tolerable error. This is a common trap.
Always state whether the method is statistical or non-statistical. Markers look for this.
For every method, write one advantage and one disadvantage. Link them to the scenario given.
In calculation questions, show the interval formula first, then the working. Method marks are available in Section C.