Advanced Audit Sampling: Variables, PPS & Smart Projections
Overview: Sampling in substantive testing helps auditors estimate numerical balances like AR. This guide covers variables sampling, PPS sampling, how to project errors, stratify populations, and apply sampling plans like mean-per-unit, ratio, and difference estimation.
✅ Variables Sampling in Substantive Tests
- Purpose: Estimate the true monetary amount of a population.
- Define objective → Identify population → Define sampling unit → Determine sample size → Select sample → Evaluate results → Form conclusions → Document.
- Tolerable Misstatement: Max misstatement allowed before FS are materially misstated. May be equal to or smaller than performance materiality.
- Use stratification for highly variable populations — separates items into similar groups to reduce sample size.
✅ Projected vs. Tolerable Misstatement
- Project sample results to the whole population.
- If projected misstatement is much lower than tolerable misstatement, sampling risk is low.
- If projected is close to tolerable, risk increases — use judgment and possible further procedures.
✅ Classical Variables Sampling Methods
- Mean-per-Unit (MPU): Estimate = Average sample value × Number in population.
- Ratio Estimation: Uses ratio of audited to book values to project true value.
- Difference Estimation: Uses average difference between audited and book values to adjust total population.
- MPU is sensitive to variability; stratify when using MPU to reduce sample size.
✅ Example of Point Estimate
For AR:
- MPU: $875 avg × 5,000 accounts = $4,375,000
- Ratio: (Audited $175,000 / Book $184,200) × $4,500,000 = $4,275,244
- Difference: ($184,200 – $175,000) / 200 × 5,000 = $230,000 → $4,500,000 – $230,000 = $4,270,000
✅ PPS Sampling (Probability-Proportional-to-Size)
- Sampling unit: individual dollar; larger items more likely to be selected.
- Great when no errors are expected; smaller sample size than variables sampling.
- Zero or negative balances require special care.
✅ PPS Sample Size Example
- Tolerable misstatement ÷ Reliability factor = Sampling interval.
- Population ÷ Interval = Sample size.
- Example: Tolerable $15,000, risk 5% → Factor 3 → $15,000/3 = $5,000 interval; $500,000/$5,000 = 100 items.
✅ Dual-Purpose Samples
- Use same sample for tests of controls and tests of details.
- Sample must be large enough for both purposes.
- Evaluate deviations and monetary misstatements separately.
✅ Qualitative Considerations
- Analyze nature and cause of deviations (error vs. fraud).
- Consider how issues link to other audit areas.
🔗 Helpful References
👉 Master advanced sampling — estimate, project, and conclude with confidence!
