Project 05Audit sampling
Monetary Unit
SamplingA dollar-unit sampling calculator for tests of details: sample size, systematic selection and the upper misstatement limit, with every factor derived and every layer of the bound laid out.
Monetary unit sampling is the auditor's workhorse for balances like receivables. Every dollar is a sampling unit, so large balances are more likely to be picked, and the result is a statistical ceiling on overstatement that compares directly with tolerable misstatement. This calculator runs the whole cycle: set risk and materiality, select from a population, enter what the testing found, and read the conclusion, with the Poisson factors computed rather than looked up and each component of the Stringer bound shown.
- Inputs
- A population of balances (sample included; paste or drop a CSV), tolerable and expected misstatement, risk of incorrect acceptance, audited values for the items selected
- Method
- Sample size by the confidence-factor formula; fixed-interval or cell selection with a seeded random start; Stringer upper limit with basic precision and incremental allowance
- Standards
- CAS 530 Audit Sampling; AICPA Audit Guide Audit Sampling, monetary unit sampling chapter
- Outputs
- Plan with worked formula and sensitivity table, selection list, evaluation with layered bound and chart, conclusion, CSV exports
- Sample data
- Thames Valley Office Supply Ltd. (fictional), trade receivables at December 31, 2025: 240 customers
- Privacy
- Static page, no server. Everything is computed in your browser; nothing is sent anywhere.
PopulationStep 01
Thames Valley Office Supply Ltd.
Sample data · all figures inventedTrade accounts receivable at December 31, 2025. The sampling units are the dollars in the balance; the logical units the auditor confirms are the customer accounts they sit in. Nil and credit balances contain no dollars to select and are set aside for separate procedures.
Columns are matched by header: an identifier (ID, Account, Customer no.), a description (Customer, Name, Description) and a book value (Balance, Amount, Book value). Without a header row the last numeric column is taken as the balance. An optional Audited column pre-fills audited values. Nil and credit balances are listed but excluded from the sampling population.
Balances by size
PlanStep 02
Sample size and interval
Three judgements set the sample: how much misstatement the balance can absorb before the financial statements are materially wrong, how much the auditor expects to find, and how much risk of accepting a materially misstated balance the audit can bear. The formula turns them into a number of dollars to select and, more usefully, an interval between selections.
SelectionStep 03
Systematic selection, proportional to size
Line the balances up end to end, pick a random dollar in the first interval, then take every interval-th dollar after it. Whichever account a chosen dollar falls in is selected. Any balance at least as large as the interval is certain to be hit and forms the top stratum, examined in full.
The seed makes the selection reproducible: the same seed, population and interval always give the same sample, which is what a reviewer re-performing the work needs. Change it to draw a different sample.
The population as a line of dollars
EvaluationStep 04
From misstatements found to an upper limit
Enter the audited value for each selected item. A misstated item below the interval is projected through its tainting; a top-stratum item counts at its actual misstatement. The upper limit adds the allowance for sampling risk in two parts and is compared with tolerable misstatement.
Anatomy of the upper limit
The auditingWhy it works this way
Why every dollar is a sampling unit
In classical variables sampling the sampling unit is the customer balance and every balance has the same chance of selection. In monetary unit sampling the unit is the individual dollar. A $60,000 balance contains 60,000 sampling units and a $600 balance contains 600, so the large balance is a hundred times more likely to be picked. For an auditor testing whether receivables are overstated, that is exactly the bias wanted: the risk is concentrated where the dollars are. The account that gets confirmed is still the whole balance the selected dollar sits in, which is why the sample of 58 dollars in the example turns into 54 customer accounts.
Sample size
Sample size is book value times a confidence factor, divided by tolerable misstatement less expected misstatement times an expansion factor. The confidence factor comes from the Poisson distribution: at a 10% risk of incorrect acceptance, the factor for zero misstatements is the mean at which the chance of finding none is exactly 10%, which is −ln(0.10) = 2.30, shown as 2.31 because the published tables round up. Expected misstatement is inflated by the expansion factor because, once the auditor anticipates finding some misstatement, the evaluation will carry an incremental allowance for it, and the sample has to be big enough to leave room for that too. Dividing book value by the sample size gives the sampling interval, and practitioners think in intervals: "one dollar in every $18,107" is a more useful description of the test than "58 items".
Selection and the top stratum
With the balances lined up end to end, a random dollar in the first interval fixes every later selection: add the interval repeatedly and note which account each selected dollar falls in. Any balance at least as large as the interval is certain to be hit, often more than once. Those accounts form the top stratum, are examined in full, and their misstatements are taken at face value rather than projected, because nothing about them was sampled. Nil and credit balances contain no dollars and are never selected, which is a weakness of the method, so they are listed separately for other procedures. Cell selection, offered as an alternative, draws one random dollar within each interval instead of a fixed step; it removes any pattern in the spacing at the cost of making the top stratum slightly less predictable.
Evaluation: the Stringer bound
Each misstated item below the interval is expressed as a tainting, the misstatement as a fraction of the book value. The dollar that was selected stands for every dollar in its interval, so the projected misstatement for that item is the tainting times the interval: a 30% tainting on an $18,107 interval projects $5,432 whatever the size of the account it came from. Summing the projections gives the most likely misstatement in the sampled stratum, to which the top stratum's actual misstatements are added.
The allowance for sampling risk has two parts. Basic precision is the confidence factor for zero misstatements times the interval; it exists even when the sample is clean, and it is what the sample-size formula built in. The incremental allowance rewards the auditor for finding small taintings rather than large ones: the taintings are ranked from largest to smallest, and each is multiplied by the increase in the confidence factor from one more misstatement, less one, since the projection itself already counted once. Upper misstatement limit is top-stratum misstatement plus projected misstatement plus basic precision plus incremental allowance. If it is at or below tolerable misstatement, the sample supports the recorded balance at the chosen risk.
Understatements
The method is built for overstatement. An understated balance has fewer dollars than it should and is less likely to be selected; a balance that should exist and doesn't has no dollars at all. The AICPA guide projects any understatements found the same way but evaluates them separately and does not use them to reduce the overstatement limit. The approach in Arens's text computes an understatement bound as well, then offsets each bound by the other's most likely misstatement. Both are offered above; the separate treatment is the more conservative and is the default.
When the limit exceeds tolerable
A failed evaluation is information, not a verdict. The options are to ask the client to investigate the misstatements found and correct them, which reduces the projection once known misstatements are booked; to expand the sample, since a larger sample shrinks both the interval and every allowance that is a multiple of it; to perform other procedures on the balance; or, if the misstatement is real, to propose an adjustment. What the auditor cannot do is accept the balance and move on, because the whole point of the calculation is that the evidence, at that risk level, does not support it.
What this calculator does not do
It treats a logical unit selected more than once as one sample item, as most audit software does. It caps tainting at 100% when an audited value is negative. It does not stratify beyond the top stratum, does not handle populations in more than one currency, and does not decide materiality: tolerable misstatement is an input, set from performance materiality by the auditor. Sample size formulas and factor tables differ slightly between texts and firm methodologies; this one follows the AICPA guide and the Canadian editions of Arens, which agree with each other.
How it's builtNotes
One self-contained HTML file, no libraries. The confidence factors are not typed in from a table: for each risk level and number of misstatements the page solves the Poisson distribution numerically for the mean at which the cumulative probability equals the risk, then rounds up to two decimals, and the result reproduces the published tables exactly. The random start comes from a small seeded generator so that a selection can be re-performed. The model was written first in Python with assertions against hand-worked textbook examples, and the browser version is tested against its output, including the selection itself.
- Stack
- HTML, CSS, vanilla JavaScript, inline SVG
- Dependencies
- None (fonts from Google Fonts)
- Data handling
- Entirely client-side; nothing leaves the page
- Money
- Integer cents throughout; factors to two decimals, rounded up as the published tables are
- Sample
- Thames Valley Office Supply Ltd., a fictional company. Customer names, balances and misstatements are invented.