Design the sample around the assertion
SA 530 applies when an auditor decides to use sampling. Sampling tests fewer than all items and gives every sampling unit in the defined population a chance of selection. Examining all items or selecting particular high-risk items under SA 500 can be appropriate; neither provides a representative sample of the remainder. Start with the objective, assertion and complete relevant population, then reconcile the extract to its source and test coverage. A recorded ledger alone is often an inadequate population for completeness testing.
| Decision | What to document |
|---|---|
| Sampling unit and population | Transactions, balances, physical items or monetary units; dates, strata and exclusions. |
| Statistical design | Random selection and use of probability theory to evaluate results, including sampling risk. Sample size alone does not determine whether a design is statistical. |
| Non-statistical design | How size and selection reduce sampling risk and avoid bias. Haphazard selection can be non-statistical, but selecting convenient or suspicious items alone is specific-item testing. |
| Tolerable misstatement | Amount set for a tests-of-details population. It is an application of performance materiality and may be the same as or lower than it. The standards do not prescribe fixed percentages. |
| Tolerable deviation | Rate for the particular control test. Compare the observed results and sampling risk with the planned reliance. |
Determine a sample size sufficient to reduce sampling risk to an acceptably low level. Consider expected error, risk assessment, tolerable misstatement or deviation and the evidence from other procedures. SA 530 does not prescribe a general risk multiplier or a mandatory percentage increase where controls fail. Consider whether a larger sample, different procedures or a different population is more effective.
Project and evaluate results
Investigate the nature and cause of deviations and misstatements. In tests of details, project sample misstatements to the population or relevant stratum. Use a method consistent with selection: a ratio estimate can suit errors related to book value, while a mean difference estimate can suit a representative equal-probability item sample. If ₹3 lakh of overstatement is found in a ₹30 lakh representative sample from a ₹3 crore stratum, a suitable ratio estimator gives ₹30 lakh. The estimate includes the sampled error; do not add it again. A monetary-unit design generally requires a matching evaluation method, including sampling risk, rather than automatically applying that ratio formula.
For a genuinely anomalous misstatement, obtain a high degree of certainty through additional procedures that it is not representative before excluding it from projection; consider its effect separately if uncorrected. A projection near or above tolerable misstatement calls for further evaluation and may require management investigation or further audit procedures. The audit opinion depends on the sufficient appropriate evidence and the materiality and pervasiveness of remaining issues, not on a sampling result alone.
Seven worked cases
1. Receivables: stratification and monetary units
The receivables ledger has 450 accounts totalling ₹42 crore. Assume overall materiality ₹80 lakh, performance materiality ₹52 lakh and clearly trivial threshold ₹4 lakh as engagement judgements. Use ₹52 lakh as the illustrative tolerable misstatement for the sampled stratum only if supported by the overall plan. A clearly trivial threshold for accumulating misstatements is not an automatic exemption from testing low-value items in aggregate.
| Stratum | Accounts | Book value | Planned work |
|---|---|---|---|
| Individually significant | 18 | ₹19.50 crore (46.43%) | Test all 18 using the appropriate assertion-specific procedures. |
| Middle layer | 212 | ₹20.80 crore (49.52%) | Illustrative monetary unit sample. |
| Low-value layer | 220 | ₹1.70 crore (4.05%) | Separately design procedures for this aggregate; tracing cash receipts is a test of details, not an analytical procedure. |
For a zero-expected-error planning illustration, use a rounded-up 2.31 Poisson factor for approximately 90% one-sided assurance. The interval is ₹52 lakh ÷ 2.31 ≈ ₹22.51 lakh; population value divided by interval gives 92.4, rounded up to 93 monetary hits for planning. Use a documented random start and method, and recalculate the implementation interval if necessary. Hits can map to fewer accounts. If the actual selection yielded 54 unique accounts and tested amounts in the first two strata totalled ₹32.85 crore, that is 72 accounts and 78.21% of book value; neither figure proves sufficiency. Assess credit, nil and unrecorded balances separately where relevant.
2. Inventory: project damage within the correct stratum
Of 4,200 SKUs worth ₹18 crore, test 15 worth ₹6 crore separately; assume no misstatements there. The remaining 4,185 total ₹12 crore. A suitable representative sample of 60 has ₹1.50 crore book value. Four damaged SKUs are carried at ₹8.50 lakh but have an assessed net realisable value of ₹2.50 lakh; the overstatement is ₹6 lakh. The sample ratio is 4%, giving a ₹48 lakh point estimate for this stratum, above ₹30 lakh tolerable misstatement before considering sampling risk.
If management examines the full stratum and identifies an actual ₹52.40 lakh write-down, verify the extent and reliability of its work and the posting. Do not automatically add the original sample projection to the verified full-population adjustment. A clean opinion is not an automatic outcome of booking the adjustment.
3. Cut-off: test the period when the service occurred
Repair and maintenance records contain 8,500 vouchers worth ₹9.20 crore. The auditor examines all 420 vouchers from the 15 days before and after year-end. This is full examination of a defined cut-off window, not sampling that represents the entire year. Eighteen April postings total ₹14.50 lakh. If supporting evidence shows that the services were received and the obligation existed before year-end, propose the corresponding accrual. Invoice date alone does not establish cut-off. Consider a separate search for unrecorded items outside the extract.
4. Control deviations: authorisation of purchase orders
Start with eligible POs over ₹50,000 drawn from the company’s 12,000 annual POs. With zero expected deviations, 5% tolerable deviation and 10% acceptable overreliance, a simplified large-population binomial zero-deviation design needs 45 items: 0.95 to the power 45 is about 9.94%. Three deviations in 45 give 6.67%, already above tolerance. Investigate them, reassess planned reliance and revise substantive procedures. A universal 200% increase or a specific amount of subsequently detected misstatement is not implied by the calculation.
5. Asset additions: report value coverage accurately
Twelve high-value additions total ₹12.80 crore out of ₹14.50 crore, or 88.28%. The remaining 128 total ₹1.70 crore. A random sample of 20 items totals ₹42 lakh. If all selected items were tested, total tested book value is ₹13.22 crore, or 91.17%, across 32 of 140 additions. Check capitalisation, delivery, installation and the applicable date; no errors found does not prove the untested items are correct.
6. Payables: search subsequent disbursements
There are 350 subsequent payments totalling ₹6.50 crore. The 40 selected payments over ₹5 lakh total ₹3.80 crore, or 58.46% by value. This is specific-item testing unless there is a separate representative design. Eight payments totalling ₹85 lakh relate to pre-year-end construction obligations omitted from the balance sheet, on the assumed evidence. Verify the proposed accrual and consider the remaining 310 disbursements, unpaid invoices and other sources for completeness. Do not project the observed percentage to the whole population using this selection.
7. An isolated pricing error still needs evidence
A ₹15 lakh error is found in a sales invoice in a ₹40 crore population. Management calls it a typo. Inspect the cause, test the relevant clerk and terminal records and assess whether the two sets of 30 additional invoices overlap or cover the entire potentially affected set. No further errors in those checks do not by themselves prove an anomaly. Exclude it from the projection only after obtaining the required high degree of certainty; otherwise project according to the design. Track the correction and any uncorrected effect separately.
Document the decision and the evidence
Record the source and completeness of the population, assertion, tolerances, rationale for the sample size, method and random start where applicable, selected units, audit work, exceptions and evaluation. If a procedure is not applicable to a selected item, apply it to a replacement under paragraph 10. If the designed or a suitable alternative procedure cannot be applied to a selected item, paragraph 11 requires treating it as a deviation in a control test or as a misstatement in a test of details. Document and evaluate the effect rather than assuming every unavailable item always implies a full book-value error.
Sampling risk is the possibility of a different conclusion from testing the whole population. Non-sampling risk includes applying the wrong procedure or misinterpreting evidence and is managed through planning, training, supervision and review. Retain the workpapers so an experienced auditor can understand what was done and why.
Sources
- ICAI: SA 530, Audit Sampling, paragraphs 5–15 and application material
- ICAI: Implementation Guide to SA 530, including monetary unit sampling
- ICAI: SA 320, Materiality in Planning and Performing an Audit
- ICAI: SA 450, Evaluation of Misstatements Identified during the Audit
- ICAI standards directory, including SA 230, SA 330, SA 500 and SA 505