The Methodology Behind Sampling Maestro
Sampling Maestro is built on a principle that is well established in the statistical literature but routinely missed in practice: attribute sampling formulas do not belong on dollar-value populations. Misapply them in an unclaimed property or indirect tax examination and the result can be off by orders of magnitude. Every calculation in Sampling Maestro traces to published statistical literature, and this page shows the foundation.
The problem: attribute sampling applied to dollar-value populations
Attribute sampling was built to estimate a proportion, the share of a population with a given characteristic, such as the percentage of invoices that contain an error. Its formulas assume a yes-or-no outcome and size the sample to pin down that rate.
Dollar-value populations like accounts payable, accounts receivable, checks, and indirect tax transactions are continuous and highly skewed. Apply an attribute formula to estimate a dollar amount instead of a rate, and the sample size it returns is meaningless for that purpose, and any confidence interval computed from it is wrong.
This is not a matter of professional judgment. It is a mathematical mismatch between the formula and the data, documented in the academic literature and, as Four Sigmas has found, widespread in practice.
The solution: the right formula for the data
The right approach is stratified variable sampling, with the formula chosen to fit the data and the quantity being estimated, not the attribute formula that common tools default to because it is easy to reach and quick to run. Those tools will produce what they call a sample from whatever formula you give them, and they give no warning when the formula is wrong for the job. Calling a selection a sample does not make it the right one for estimating a dollar amount. Done correctly, stratified variable sampling:
- Accounts for the actual variance of dollar amounts within each stratum
- Produces confidence intervals with correct, verifiable coverage
- Supports four estimators, Mean-Per-Unit, Difference, Ratio, and Regression, with formal optimality criteria
- Handles skewed, heavy-tailed distributions through stratification
- Produces documentation that holds up under challenge
Sampling Maestro implements this in full, with four allocation methods, ten stratification algorithms offered as eleven selectable options, bootstrap confidence intervals, and a complete diagnostic suite.
Published research
Four Sigmas has documented this misapplication in unclaimed property and indirect tax examinations in an article now under peer review.
Article publication pending
The article quantifies the size of the error, identifies the formula configurations most often misapplied, and gives practitioners a framework for judging whether an existing sample meets accepted statistical standards.
Methodology reference
This table summarizes the statistical foundation behind each of Sampling Maestro’s three engines.
| Engine | Statistical Foundation | Key References |
|---|---|---|
| Transaction Sampling | Stratified variable sampling, Cochran SRS formula, Neyman optimal allocation, MPU/Difference/Ratio/Regression estimators, Bootstrap BCa CI | Cochran (1977), Neyman (1934), Dalenius & Hodges (1959), Satterthwaite (1946), DiCiccio and Efron (1996) |
| Dollar Sampling (MUS) | Poisson probability model, PPS systematic selection, tainting analysis, Stringer bound | Stringer (1963), AICPA Audit Sampling Guide, AU-C §530, Neter & Loebbecke (1975) |
| Sample Review | Forensic evaluation of stratified samples, allocation forensics, attribute formula detection, precision analysis | Cochran (1977), MTC Sampling Policy Manual §4.07–4.08, Neyman (1934) |