How to use the monetary unit sampling selector
- Paste the ledger, one item per line: a reference and an amount, separated by a comma or tab. A first line of headings is skipped.
- Choose the sample size, the number of sampling points, and a seed. The seed picks the start inside the first interval and makes the selection repeatable.
- Open the advanced section to fix the start yourself if you are reproducing a published selection.
- Read the interval, the start and the selected items with their hits, then copy the table or download the CSV.
Formula
interval = population value / sample size
sampling points = start + k x interval, for k = 0 to sample size - 1, with 0 <= start < interval
a point selects the item whose cumulative range contains it
items at least as large as the interval always receive a point
The items are laid end to end in the order given, so each item occupies a stretch of the total equal to its amount. Larger items are hit more easily, which is why the method suits finding overstatements.
Ten ledger items and four points
The sample ledger has ten items worth $20,081.50 in total. With 4 sampling points the interval is $5,020.375. The seed 2026 gives a start of $2,286.32, so the points fall at $2,286.32, $7,306.69, $12,327.07 and $17,347.44.
They land on INV-003 ($8,800.00) twice, INV-006 ($5,200.00) once and INV-009 ($2,475.75) once. That is 3 items holding $16,475.75, which is 82.0% of the value. Two items, INV-003 and INV-006, are at least as large as the interval, so they had to be selected whatever the start.
Why it favors large items
Each dollar in the population is a unit, and the sample picks units at a regular spacing. An item with more dollars has more units and so a higher chance of being picked, in proportion to its size. Items larger than the interval cannot be missed and can be hit more than once.
Small items are less likely to be selected, so the method is aimed at finding errors that matter in value, not at estimating how many items have errors. Items with zero or negative amounts have no dollars to sample and are listed apart.
What the page does not decide
The page gives the mechanics of selection. The size of the sample for a given confidence, the treatment of negative items and the evaluation of any errors found are judgments for the person doing the work, following the standards they work under. It is not audit or accounting advice.
Related checks include the Benford’s Law Digit Analyzer for unusual amounts, the Transposition Error Detector for swapped digits, and the Subset Sum Reconciliation Finder for an unexplained difference.
Assumptions and limits
- Items are taken in the order given, and the order affects which items are hit for a given start.
- The start is random between 0 and the interval, from a seeded generator. The same seed and the same list give the same selection.
- The ledger is limited to 5,000 items and the sample to 1,000 points. Amounts are read in cents.
- Items of zero or less are not sampled and appear in a separate table.
- Nothing typed here leaves your browser.
Frequently asked questions
Can one item be selected twice?
Yes. An item larger than the interval can contain two or more sampling points. It appears once in the table, with the number of hits in the Hits column.
What is the seed for?
It makes the start repeatable. The same seed, ledger and sample size give the same selection, so someone else can check your work. Change the seed for a different valid selection.
Why are some items listed as not sampled?
An item with an amount of zero or less holds no dollars, so no sampling point can land in it. Test such items separately if they matter.
What if I need a published start?
Open the advanced section and enter a fixed start between 0 and the interval. The page then uses it and ignores the seed.