The Methodology Behind Sampling Maestro
Sampling Maestro is not just software. It is the implementation of a documented, peer-reviewed finding: that attribute sampling formulas are routinely misapplied to dollar-value populations in unclaimed property and indirect tax examinations, with consequences that can be off by orders of magnitude.
Every calculation in Sampling Maestro traces directly to published statistical literature. This page explains the foundation.
The Problem: Attribute Sampling Applied to Dollar-Value Populations
Attribute sampling was designed to estimate the proportion of a population with a particular characteristic – for example, what percentage of invoices contain an error. The formulas assume binary outcomes (yes/no, error/no error) and produce sample sizes calibrated to estimate a proportion.
Dollar-value populations – accounts payable, unclaimed property liabilities, indirect tax transactions – are continuous, highly skewed distributions. When you apply an attribute formula to estimate a dollar amount rather than a proportion, the resulting sample size is statistically meaningless for that purpose. Confidence intervals computed from that sample lack their stated coverage probability.
This is not a matter of professional judgment. It is a mathematical mismatch between formula and data type – documented in the academic literature and, as Four Sigmas has found, widespread in practice.
The Solution: Cochran’s Formula for Continuous Data
The correct approach for estimating a population mean or total from a continuous distribution is stratified variable sampling, using Cochran’s formula (1977) for sample size determination. This approach:
- Accounts for the actual variance of dollar amounts within each stratum
- Produces confidence intervals with correct, verifiable coverage probability
- Supports four estimators (MPU, Difference, Ratio, Regression) with formal optimality criteria
- Handles skewed, heavy-tailed distributions through stratification
- Generates documentation that withstands Daubert scrutiny
Sampling Maestro implements this approach in full – including all 11 stratification algorithms, 3 allocation methods, bootstrap confidence intervals, and a complete diagnostic suite.
Published Research
Four Sigmas has documented the misapplication of attribute sampling in unclaimed property and indirect tax examinations in a peer-reviewed article currently under review.
Article Publication Pending
The article quantifies the magnitude of the error, identifies the specific formula configurations most commonly misapplied, and provides practitioners with a framework for evaluating whether an existing sample meets accepted statistical standards.
Notify Me When PublishedMethodology Reference
The following table summarizes the statistical foundations implemented in 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), Efron & Tibshirani (1993) |
| Dollar Sampling (MUS) | Poisson probability model, PPS systematic selection, tainting analysis, Stringer bound | Stringer (1963), AICPA Audit Sampling Guide, ISA 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) |