Random, systematic or monetary unit sampling?
Which audit sampling method suits which test under ISA 530, and when to test specific items or the whole population instead of drawing a sample.
By Achekam · · 5 min read · For Accountants & audit firms in South Africa, Nigeria, Kenya
A senior is told to "sample receivables" and reaches for the method used on the last file, whatever that was. If it was monetary unit sampling, the large balances dominate the selection, which is exactly right for testing that receivables exist and exactly wrong if the worry is that credit notes have been suppressed. If it was random selection, a population with a few very large balances and a great many small ones yields a sample of small balances that tells the auditor little about the figure that matters.
The choice of method is part of designing the procedure, not an administrative step after it. ISA 530 leaves the choice to the auditor's judgement, but the judgement has a logic: what is being tested, in which direction, and how the population is made up.
Statistical and non-statistical sampling
ISA 530 defines statistical sampling as an approach with two features: random selection of the sample items, and the use of probability theory to evaluate the results, including measuring sampling risk. An approach without both is non-statistical.
Both are acceptable. A non-statistical sample still has to be selected so that every sampling unit has a chance of selection and the sample can be expected to be representative. Haphazard selection, choosing items without conscious bias, can serve for non-statistical samples. Block selection, taking a run of consecutive items, rarely gives a representative sample and is seldom appropriate.
The practical difference lies in evaluation. A statistical sample lets the auditor quantify the risk that the conclusion is wrong; a non-statistical sample relies on judgement to evaluate it. Either way, the file must explain how the sample size and the evaluation were reached.
Monetary unit sampling for overstatement
Monetary unit sampling treats each unit of currency in the population as the sampling unit, so an item's chance of selection is proportional to its value. That makes it efficient for testing overstatement: existence of receivables, occurrence of revenue, existence and valuation of assets. Large items, where overstatement matters most, are almost certain to be selected.
Its limits follow from the same feature:
- items recorded at nil cannot be selected, and small items rarely are, so it is poor at finding understatement and omissions;
- negative balances, such as credit balances in receivables, need separate treatment;
- if many misstatements are expected, the sample sizes it requires grow quickly.
Evaluation uses the proportion by which each selected item is misstated, its tainting, projected over the interval it represents.
Random and systematic selection
Random selection gives every item an equal chance. It suits populations of broadly similar items, tests of controls (where the question is how often a control failed, not by how much), and tests for understatement drawn from a population that should contain the omitted items, such as dispatch notes or payments after year end. For skewed populations, combine it with stratification: divide the population by value bands and sample each band.
Systematic selection takes every item at a fixed interval from a random start. It is simple to apply to a listing in date or document-number order. Its risk is a pattern in the population that coincides with the interval, for example a weekly payroll run where the interval lands on the same week's entries each time. Check the population for patterns before using it.
| Test | Usual method | Why |
|---|---|---|
| Existence of receivables or assets | Monetary unit | Overstatement risk concentrated in large items |
| Completeness of payables | Random or systematic from payments after year end | The population must contain the omitted items |
| Operating effectiveness of a control | Random or systematic | Deviation rate, not value, is the question |
| Payroll validity | Random, stratified if pay varies widely | Each employee matters, not only the highest paid |
| Unusual journals | Criteria applied to every entry | Selection by risk features, not chance |
Specific items and testing every item
Two ways of choosing items are not sampling at all under ISA 530, and their results are not projected.
Specific items: the auditor selects items because of their features, such as every balance above a threshold set by reference to performance materiality, every related-party transaction, or every manual entry at year end. The remainder of the population may still need sampling if it is material.
All items: testing the whole population is appropriate when the population is a small number of large items, when a significant risk calls for it and other means do not give sufficient evidence, or when data analytics can apply a test to every item. The ACCA's article on data analytics and the auditor considers how auditors test every item in a population to reduce sampling risk, and the matters to consider when they do.
Journal entry testing is the clearest example. In Achekam, staff load a whole-population journal extract as CSV and map its columns, and Achekam flags entries such as manual, weekend, after-hours and post-close postings for staff to select and test. The CSV is not stored; its hash and row count are. Selection there is by criteria across the whole population, not by sampling.
Recording the choice
In Achekam's Audit Intelligence, the methods available are random, systematic, monetary unit, specific items and all items. Achekam risk-scores a loaded population and proposes a sample, a reviewer who did not prepare the plan approves it before the draw, and every draw can be reproduced from its stored seed. No size is proposed without approved materiality and a confidence level, and materiality is approved by the engagement partner, never the preparer, with Achekam suggesting no percentage. The mechanics of approval and reproduction are covered in audit samples a reviewer approves before drawing.
On the work item, the sampling step is marked done only with a written response and its documents, or set aside with a reason; steps are never deleted. The response should state the objective and the assertion, the population and how its completeness was established, the method chosen and why it fits the direction of the test, the inputs to the sample size, and how results will be evaluated. When errors turn up, the next step is set out in when a sample finds errors.
A question before every sample
Before choosing the method, finish this sentence on the working paper: "This test is looking for items that are ... overstated / omitted / non-compliant." The method usually chooses itself once the sentence is written.
General guidance only, not advice on your own circumstances. Tax and payroll rules change: check the current position with the authority or your adviser.
