audit-sampling-memo

Audit Sampling Memo

This skill helps an auditor design a statistically and professionally defensible audit sample and write the supporting memo. It applies public ISA 530 (Audit Sampling) concepts to choose a sampling method, size the sample from the population characteristics and the risk you are willing to accept, document the selection approach, and frame how exceptions will be evaluated and projected. It is for external auditors, internal auditors, and reviewers preparing or critiquing a sampling workpaper.

When to use this

• You are performing a test of detail over an account balance or class of transactions (revenue, AR, additions to PP&E, payroll runs, journal entries) and must decide how many items to test and which.
• You are performing a test of controls and need an attribute sample sized to a tolerable deviation rate.
• You need to justify a sample size to a reviewer, regulator, or quality reviewer and want the rationale documented against the standard.
• You are evaluating results: a misstatement or deviation was found and you must project it and conclude.
• You want a clean, reusable sampling memo template grounded in public methodology.

Inputs

Provide whichever of the following you have. The bundled sample samples/population_extract.csv shows the minimum useful tabular input.

• The population: a CSV with one row per sampling unit. Useful columns: item_id, description, book_value, date, account. The sample file has 20 vendor invoices for a fictional payables population.
• The assertion under test (e.g. existence, completeness, valuation, occurrence).
• The test type: substantive test of detail, or test of controls.
• Planning judgments: materiality / tolerable misstatement (for balances) or tolerable deviation rate (for controls), expected misstatement / expected deviation rate, and desired confidence (the complement of sampling risk, commonly 90-95%).
• Any items you intend to test 100% (key items, individually significant items, related-party or fraud-risk items) so they can be stratified out of the sampling population.

If a planning input is missing, state the assumption explicitly in the memo and flag it for the engagement lead rather than inventing a number.

How to do it

1. Define the population and sampling unit precisely

Confirm the population is complete and appropriate for the assertion (ISA 530.7). For completeness, sample from a source independent of the recorded ledger (e.g. goods-received records, not the AP ledger). State the sampling unit: an invoice, a balance, a line item, or a monetary unit. Reconcile the population total to the general ledger and record the reconciling figure in the memo.

2. Stratify and remove items tested 100%

Separate items that will be examined in full and so are not subject to sampling risk:

• Individually significant items: any item with book value >= tolerable misstatement (or >= the sampling interval, see step 4).
• Key items by risk: related parties, unusual descriptions, period-end cut-off items, manual journals. Subtract their value from the population. The remaining "residual population" is what you sample. Document both totals.

3. Choose the sampling method

• Monetary-unit sampling (MUS / PPS) for substantive tests where you expect few misstatements and want to weight selection toward larger book values. It gives each monetary unit an equal chance, automatically emphasises large balances, and is efficient for overstatement testing (existence, valuation of assets). It is less suited to populations with many expected errors, understatement, or zero/negative balances.
• Classical attribute sampling for tests of controls, where the unit is a control instance and the metric is a deviation rate.
• Haphazard or random selection with a judgmental size when statistical projection is not required (small populations, corroborative procedures). Haphazard must be free of conscious bias; it is not statistical and cannot be projected with a measurable sampling risk.

State the choice and why, tied to the assertion and the expected error profile.

4. Compute the sample size

MUS (substantive):

1. Choose a confidence factor (reliability factor) for zero expected errors from the Poisson distribution:
   • 90% confidence -> 2.31
   • 95% confidence -> 3.00
   • 99% confidence -> 4.61
2. Sample size n = (Population book value x Reliability factor) / Tolerable misstatement. Equivalently, sampling interval J = Tolerable misstatement / Reliability factor, and n = Population book value / J.
3. If you expect some misstatement, reduce tolerable misstatement by an expansion for expected error before dividing (i.e. use Tolerable - (Expected x expansion factor)), which increases n. Keep expected misstatement well below tolerable, or MUS is the wrong tool.

Attribute (controls): size from the tolerable deviation rate, the expected deviation rate, and confidence, using a standard attribute-sampling table. As a rule of thumb at 95% confidence with a 0% expected deviation rate, n is approximately 3 / tolerable deviation rate (e.g. tolerable 10% -> ~30 items; tolerable 5% -> ~60). Round up, never down.

Haphazard / judgmental: there is no formula; document the basis for the chosen count (e.g. minimum coverage of value, prior-year results) and that no statistical projection will be made.

5. Select the sample

• MUS: use systematic monetary selection. Pick a random start between 1 and J, then select every Jth cumulative monetary unit; the physical item containing that unit is selected. Document the random start and seed.
• Attribute/random: use a random-number generator over the row index with a recorded seed so selection is reproducible.
• Haphazard: select without a pattern and without bias; record how items were chosen. Record selected item_ids in the memo or an attached schedule.

6. Plan the evaluation before testing

State in advance how exceptions will be treated:

• MUS projection: for an item tested in full that is misstated, the projected misstatement on items >= J equals the actual misstatement; for items < J, projected = tainting x J, where tainting = misstatement / book value. Sum projected misstatements and add an allowance for sampling risk (basic precision plus incremental allowance) to compare against tolerable misstatement.
• Attribute: compute the upper deviation rate (sample deviation rate plus an allowance for sampling risk) and compare to the tolerable deviation rate.
• Define what a deviation/misstatement is, and what you will do if the projection exceeds tolerable (extend the sample, perform alternative procedures, or conclude the population is misstated).

Output

Produce a Markdown audit sampling memo with these sections:

1. Header - entity, period, account/assertion, preparer, date, reviewer line.
2. Objective - the assertion tested and the test type.
3. Population - description, sampling unit, total book value, count, GL reconciliation.
4. Stratification - items tested 100% (value and count) and the residual sampling population.
5. Method and rationale - method chosen and why, tied to expected error profile.
6. Parameters - tolerable misstatement / deviation rate, expected misstatement / rate, confidence, reliability factor, sampling interval.
7. Sample size calculation - the formula with numbers substituted, and the result.
8. Selection - method, random seed/start, and the list of selected items (or reference to an attached schedule).
9. Evaluation plan - projection method and the decision rule against tolerable.
10. Conclusion / next steps - to be completed after testing.
11. Disclaimer.

If a tabular selection schedule is helpful, also emit a CSV with columns item_id, book_value, cumulative_value, selected (Y/N), tainting, projected_misstatement.

Quality checks

• Population total reconciles to the GL; the reconciling difference is explained.
• Items tested 100% are removed from the sampled population so they are not double-counted or wrongly projected.
• Sample size is rounded UP. Never round down a statistical sample size.
• Reliability factor matches the stated confidence level (2.31 / 3.00 / 4.61 for 90 / 95 / 99%).
• MUS is not used where many errors or understatements are expected, or where the population contains zero/negative balances without separate treatment.
• The random start/seed is recorded so selection is reproducible by a reviewer.
• Expected misstatement is below tolerable; if not, the test design is reconsidered.
• The evaluation rule (project, compare to tolerable, define the response if exceeded) is set before testing, not after results are seen.

Worked example

Using samples/population_extract.csv (20 fictional payables invoices for Aurora Components Ltd, total book value 487,500), testing the existence/valuation of recorded payables at 95% confidence.

1. Population total 487,500 reconciles to the AP ledger (assume nil difference).
2. Tolerable misstatement set at 75,000. One invoice, INV-0007 at 96,000, exceeds tolerable, so it is tested 100% and removed. Residual population = 487,500 - 96,000 = 391,500.
3. Few errors expected, overstatement focus -> choose MUS.
4. Reliability factor at 95% = 3.00. Sampling interval J = 75,000 / 3.00 = 25,000. n = 391,500 / 25,000 = 15.66 -> round up to 16 monetary selections (so up to 16 distinct invoices, fewer where several units fall in one large item).
5. Random start drawn between 1 and 25,000 (say 11,200, seed recorded); select every 25,000th cumulative monetary unit; record the invoices hit.
6. Evaluation: if INV-0014 (book value 18,000) is found overstated by 4,500, tainting = 4,500 / 18,000 = 0.25, projected = 0.25 x 25,000 = 6,250; add basic precision and compare the total projected misstatement against the 75,000 tolerable amount before concluding.

The memo records each of these steps with the numbers substituted, ready for review.

Disclaimer

Disclaimer: This skill is a drafting and analysis aid, not professional advice. It does not provide accounting, audit, tax, investment, or legal advice. All output must be reviewed and approved by a qualified professional before use or reliance.

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