Optimal Bounds Used in Dollar-Unit Sampling: A Comparison of Reliability and Efficiency
Bibliographic record
Abstract
Auditors typically employ one-sided confidence bounds to estimate the total error in an audit population. This estimate provides an auditor with a given level of assurance that the total error does not exceed the upper confidence bound. This paper summarizes the results of an extensive simulation study using both real and simulated data comparing 14 bounds. No one method was found to be superior in terms of reliability and efficiency. A 95% upper bound is reliable if, when used repeatedly, the bound exceeds the true audit error 95% of the time. Efficiency measures the size of the bound; the smaller the bound is, the more efficient it is said to be. The multinomial-Dirichlet method [Tsui, K. W., Matsamura, E. M., Tsui, K. L. (1985). Multinomial-Dirichlet bounds for dollar-unit sampling in auditing. Acc. Rev. 60(1):76–96] demonstrated the best reliability for a variety of populations. The Bayesian normal bound [Menzefricke, U., Smieliauskas, W. (1984). A simulation study of the performance of parametric dollar unit sampling statistical procedures. J. Acc. Res. 22(2):588–604] and the Cox and Snell bound [Cox, D. R., Snell, E. J. (1979). On sampling and the estimation of rare errors. Biometrika 66(1):125–132] are reliable and more efficient than the multinomial-Dirichlet bound for particular populations. The Augmented Variance Estimator bound [Rohrbach, K. J. (1993). Variance augmentation to achieve nominal coverage probability in sampling from audit populations. Auditing J. Practice Theory 12(2):79–97] is reliable and efficient for populations with error rates of less than 10%. The extended multinominal-Dirichlet bound [Matsumura, E., Tsui, K., Wong, W.K. (1990). An extended multinomial-Dirichlet model for error bounds for dollar-unit sampling. Contemporary Acc. Res. 6:485–500] is reliable and efficient for most of the real populations studied.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.130 | 0.399 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.006 | 0.004 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".