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Why this topic matters
Audit sampling — covered by the clarified auditing standards (AU-C) in AU-C 530 — means applying a procedure to less than 100% of a population so that every sampling unit has a chance of selection, and projecting the results. Auditing and Attestation (AUD) tests the sampling risks, the factors that change sample size, attribute sampling for controls, and monetary-unit sampling for balances — including calculations.
Sampling and non-sampling risk
| Test | Risk that affects effectiveness (worse — wrong opinion) | Risk that affects efficiency (extra work) |
|---|---|---|
| Tests of controls | Overreliance — concluding controls are more effective than they are | Underreliance — concluding controls are less effective than they are |
| Substantive tests | Incorrect acceptance — concluding a balance is not materially misstated when it is | Incorrect rejection — concluding a balance is misstated when it is not |
Non-sampling risk arises from anything other than sampling: using an inappropriate procedure, misinterpreting evidence, or failing to recognize a deviation. It is reduced through planning, supervision, and quality management — not by larger samples.
Statistical versus nonstatistical sampling
- Both are acceptable under generally accepted auditing standards (GAAS).
- Statistical sampling uses random selection and probability theory to measure and control sampling risk quantitatively.
- Nonstatistical sampling relies on judgment; sample sizes should be comparable to a statistical sample giving the same assurance.
- Selection methods: random (every item equal chance), systematic (every nth item after a random start), haphazard (no conscious bias — nonstatistical only), and block selection (generally inappropriate).
Items that are individually significant or high-risk are usually examined 100% and excluded from the sampled population (stratification).
Attribute sampling — tests of controls
| Factor | Effect on sample size |
|---|---|
| Acceptable risk of overreliance ↓ | Increase |
| Tolerable deviation rate ↓ | Increase |
| Expected population deviation rate ↑ | Increase |
| Population size (large populations) | Little or no effect |
Evaluating results
- Sample deviation rate = deviations ÷ sample size.
- Upper deviation rate (from tables) = sample rate + allowance for sampling risk.
- If the upper deviation rate ≤ tolerable rate, the control can be relied on as planned. If it exceeds the tolerable rate, reduce reliance (raise assessed control risk) and expand substantive procedures.
EXAMPLE: Tolerable deviation rate 5%. A sample of 100 invoices finds 2 deviations (sample rate 2%); the table gives an upper deviation rate of 6.2%. Because 6.2% > 5%, the auditor cannot rely on the control as planned.
Also consider the qualitative nature of deviations: an intentional deviation may indicate fraud, which matters more than the rate.
Variables sampling — substantive tests
| Factor | Effect on sample size |
|---|---|
| Acceptable risk of incorrect acceptance ↓ (higher assessed risk of material misstatement) | Increase |
| Tolerable misstatement ↓ | Increase |
| Expected misstatement ↑ | Increase |
| Population variability (standard deviation) ↑ — classical methods | Increase |
| Stratification of the population | Decrease |
Classical variables methods
- Mean-per-unit: average audited value × number of items.
- Ratio estimation: (audited value ÷ book value of sample) × population book value — best when misstatements are proportional to book values.
- Difference estimation: average difference × number of items — best when misstatements are similar in size.
Ratio and difference methods need a reasonable number of misstatements in the sample to work.
Monetary-unit sampling (probability-proportional-to-size)
Monetary-unit sampling, also called probability-proportional-to-size (PPS) sampling, treats each dollar as a sampling unit, so larger items are more likely to be selected. It is designed to detect overstatement, works well when few misstatements are expected, and does not require a standard deviation.
- Sampling interval = population book value ÷ sample size (or tolerable misstatement ÷ reliability factor).
- Any item with a book value ≥ the interval is always selected.
- Zero or negative balances need separate testing; understatements are hard to detect.
Projecting misstatement with PPS
| Item | Projected misstatement |
|---|---|
| Book value ≥ interval | Actual misstatement (no projection) |
| Book value < interval | Tainting % × interval, where tainting % = (book − audited) ÷ book |
Upper misstatement limit = projected misstatement + basic precision (reliability factor × interval) + incremental allowance. If the upper limit ≤ tolerable misstatement, accept the balance.
EXAMPLE: Population $600,000, sample size 60 → interval $10,000. An item recorded at $8,000 has an audited value of $6,000: tainting = 2,000 ÷ 8,000 = 25%; projected misstatement = 25% × 10,000 = $2,500. An item recorded at $15,000 with an audited value of $14,000 contributes its actual $1,000.
Evaluating misstatements
- Project sample misstatements to the population and compare to tolerable misstatement, considering an allowance for sampling risk.
- Investigate the nature and cause of each misstatement — fraud, a systematic error, or an anomaly (an anomaly may be excluded only if the auditor is highly certain it is not representative).
- If projected misstatement is close to or exceeds tolerable misstatement, ask management to investigate and correct, extend testing, or modify the opinion.
How it is tested
- Match sampling risks to effectiveness or efficiency.
- Predict the direction of sample size changes.
- Evaluate attribute sampling results against the tolerable rate.
- Compute the PPS interval and projected misstatement.
EXAM TIP: The two dangerous risks are overreliance (controls) and incorrect acceptance (substantive) — both lead to an audit failure. The other two only waste time.