Audit Sampling

Sampling is where audit files are most often indefensible, and almost never because the sample was too small. It is because the basis was never written down. A reviewer three years later cannot tell why 40 items were chosen, how they were chosen, whether the population was complete, or what the result implies about the balance as a whole.

This skill produces a selection that can be re-performed exactly and a worksheet that states its own basis. Everything else is secondary.

The gate

No selection is produced unless:

1. The population ties to a stated control total. You supply the general ledger or trial balance figure the population should equal. If the population does not agree to it, sampling stops — a sample drawn from an incomplete population supports nothing, and the projection will understate misstatement by exactly the amount that was missing.
2. A random seed is recorded. Every selection is reproducible from the seed, the method, and the parameters. This is what makes the workpaper defensible.
3. Sample size is derived, not chosen. It follows from tolerable misstatement, expected misstatement, and risk of incorrect acceptance — all of which are recorded on the workpaper.
4. Negative and zero balances are handled explicitly, not silently dropped. See below.

Standing rule on parameters

Sample sizes depend on firm methodology. This skill computes what can be computed and requires you to supply what is a matter of methodology.

• The reliability factor for zero expected misstatements is computed exactly as -ln(risk of incorrect acceptance) — mathematics, not a remembered table.
• The expansion factor used when misstatement is expected varies by methodology. Supply your firm's factor with --expansion-factor. The script will not invent one, and says so on the workpaper if none was given.
• Tolerable misstatement and risk of incorrect acceptance come from your planning. The script records them; it does not suggest them.

If your firm has sampling tables, use them and enter the resulting size with --sample-size — the script will still perform the selection, the reproducibility, and the projection, and will document that the size came from firm tables.

Choosing a method

MUS examines every item at or above the sampling interval with certainty. That property is why it is preferred for substantive testing: the largest items are not left to chance, and the sample naturally concentrates where the money is.

Step 1 — Prove the population

python3 scripts/select_sample.py --population pop.csv \
  --control-total 4128455.19 --validate-only

Reports population count, total, negative and zero items, the largest items, and whether the total agrees to the control total. Resolve any difference before selecting.

Negative balances in a MUS population are a genuine professional problem, not a data issue. Credit balances in receivables, credit memos in disbursements, and contra items cannot be sampled proportionally to size. Handle them one of three ways, and record which:

• Test them 100% separately as their own population — usually correct when few
• Exclude and disclose, testing them by another means
• Sample them separately with their own parameters

The script requires an explicit --negatives choice and refuses to guess.

Step 2 — Select

python3 scripts/select_sample.py \
  --population pop.csv \
  --control-total 4128455.19 \
  --method mus \
  --tolerable-misstatement 125000 \
  --expected-misstatement 25000 \
  --expansion-factor 1.6 \
  --risk 0.05 \
  --negatives separate \
  --seed 20260729 \
  --client "Harbour Freight Systems Inc" \
  --assertion "Existence of trade receivables at 12/31/2025" \
  --out "Harbour Freight - AR Existence Sample.xlsx"

The seed is yours to choose and must be recorded before selection — not after. Choosing a seed after seeing results is not random selection. Use the engagement date or any documented value.

Step 3 — Test, then project

Fill in the worksheet: for each selected item record the evidence examined, the audited amount, and the difference. Then:

python3 scripts/select_sample.py --project results.csv \
  --population pop.csv --control-total 4128455.19 \
  --method mus --tolerable-misstatement 125000 --risk 0.05 \
  --seed 20260729 \
  --out "Harbour Freight - AR Existence Conclusion.xlsx"

For MUS the projection uses tainting: an item examined in full (at or above the interval) projects its actual difference; an item below the interval projects (difference ÷ book value) × sampling interval. The script reports projected misstatement and compares it to tolerable misstatement.

The comparison is the conclusion, and it is not a formality. Projected misstatement below tolerable supports the balance. Projected misstatement approaching tolerable means the balance may be materially misstated even though every individual difference looked small — that is precisely the situation sampling exists to reveal, and the one most often waved away.

Basic precision and an allowance for sampling risk depend on methodology; supply your firm's factors or compute the upper limit under your own approach. The script reports the components so either can be applied, and states which were supplied.

Step 4 — Deliver

Workbook tabs:

1. Sampling Plan — assertion tested, population and how it was obtained, control total and the tie-out, method, every parameter, computed sample size and the arithmetic behind it, seed, negative-balance treatment, and the sign-off block. This is the tab that has to answer a reviewer's questions without anyone present to explain.
2. Selection — every selected item with its row in the population, book value, selection basis (top stratum / interval hit / random), and blank columns for evidence examined, audited amount, difference, and disposition.
3. Population Summary — count, total, distribution by size band, coverage achieved in items and in dollars, and the top-stratum items examined in full.
4. Not Selected — the population that was not selected, so the untested remainder is visible and quantified rather than implicit.
5. Projection — once results are entered: differences found, tainting per item, projected misstatement, comparison to tolerable, and the conclusion.
6. Reproducibility — the exact command, seed, parameters, and a hash of the population file so a reviewer can confirm the same population produces the same sample.

Things that quietly invalidate a sample

Worth checking before you rely on the result:

• The population was filtered before you received it. Ask what the export excluded. Date ranges, posted-only flags, and excluded accounts are the usual culprits.
• The control total is the wrong total — a subtotal, a net figure, or a balance after reclassification.
• Items were added after selection. The selection binds to the population as it stood; re-perform if it changed.
• A selected item was swapped because it was inconvenient to test. Replacing an item without documenting why destroys the statistical basis. If an item cannot be tested, that is a scope limitation, not a substitution.
• The sample tests a different assertion than the one planned. A sample selected proportional to recorded value tests overstatement of what is recorded — it says very little about completeness, because unrecorded items are not in the population at all.
• Deviations treated as isolated. A deviation is isolated only with evidence that it is; otherwise it projects.

Security posture

Fully local: standard library plus openpyxl. No network calls, no uploads, no telemetry. The population file is read-only and hashed for reproducibility, never transmitted. Output filenames carry client name and assertion only.

Dependencies

pip install openpyxl

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