As an auditor, you often hear about Monetary Unit Sampling or even using it on assignments. It’s a simple tool and provides a statistical result in dollars or other currency, thus making the sampling technique popular among auditors. This post will elaborate on the definition, a brief history, and some synonyms for the method. Let’s dive in.
What is Monetary Unit Sampling?
Monetary unit sampling (MUS) is the most used statistical sampling method for substantive testing in audits. MUS is based upon attribute sampling, a sampling to infer qualitative characteristics of the population. But instead of measuring the number of characteristic occurrences like other attribute sampling results, MUS is expressed in dollar amount.
With the MUS method, a population is the total recorded dollar in an account balance. On the other hand, each dollar acts as a sampling unit. The setup makes transactions with a higher value more likely to be chosen for examination.
MUS techniques have been applied in auditing since the early 1960s due to their ability to address certain drawbacks of traditional variable sampling methods. These drawbacks include dealing with low misstatement rates in many accounting populations. Additionally, MUS has gained popularity because of its straightforward approach when contrasted with the complexities of designing traditional statistical techniques.
A Brief History of Monetary Unit Sampling
The MUS appearance has been a while. Here are several publications on the early days of MUS’s life.
| Year | Author(s) | Title | Source |
| 1960 | Deming, W. E. | Sample Design in Business Research | As mentioned by Horgan (1994) |
| 1961 | Van Heerden, A. | Statistical Sampling as a Means of Auditing | As mentioned by Horgan (1994) |
| 1972 | Meikle, G. R. | Statistical Sampling in an Audit Context: An Audit Technique Study | As mentioned by Horgan (1994) |
| 1973 | Anderson, R. J. and A. D. Teitlebaum | Dollar-Unit Sampling. A solution to the audit sampling dilemma | As mentioned by Kaplan (1975), Knight (1979), and Horgan (1994) |
| 1973 | Anderson, R. J. | Audit Uses of Statistical Sampling | As mentioned by Horgan (1994) |
| 1975 | Leslie, D. A. | Monetary-Unit Sampling in Auditing | As mentioned by Horgan (1994) |
| 1975 | Robert S. Kaplan | Sample Size Computations for Dollar-Unit Sampling | https://www.jstor.org/stable/2490487 |
| 1978 | John Neter, Robert A. Leitch and Stephen E. Fienberg | Dollar Unit Sampling: Multinomial Bounds for Total Overstatement and Understatement Errors | https://www.jstor.org/stable/245727 |
| 1979 | P. Knight | Statistical Sampling in Auditing: An Auditor’s Viewpoint | https://www.jstor.org/stable/2988206 |
| 1984 | James Godfrey and John Neter | Bayesian Bounds for Monetary Unit Sampling in Accounting and Auditing | https://www.jstor.org/stable/2490661 |
| 1986 | Lowell Dworin and Richard A. Grimlund | Dollar-Unit Sampling: A Comparison of the Quasi-Bayesian and Moment Bounds | https://www.jstor.org/stable/247521 |
| 1986 | Janet L. Leichti | An Introduction to Dollar Unit Sampling | https://egrove.olemiss.edu/cgi/viewcontent.cgi?article=3149&context=wcpa |
| 1994 | Jane M. Horgan | Monetary-unit sampling: An investigation | https://openaccess.city.ac.uk/id/eprint/29945/ |
Horgan (1994) gave a decent amount of information about the history of Monetary Unit Sampling.
He mentions Deming, who was the pioneer in introducing the concept of monetary unit sampling. Deming proposed that a single dollar investment could serve as the sampling unit, but he didn’t provide additional details or insights into MUS.
The initial documented research into the application of MUS to accounting populations was conducted by Van Heerden in 1961. His study defined the sampling unit as a guilder, a specific monetary unit.
He proposed that an account balance could be envisioned as a compilation of monetary units, some of which were entirely accurate, while others were utterly erroneous, following an all-or-nothing approach for assigning error amounts to these monetary units.
Van Heerden recommended adopting a straightforward random sampling approach for selecting monetary units from the overall balance.
In 1968, the Canadian Institute of Chartered Accountants (CICA) initiated a research project to explore the application of statistical sampling in auditing to enhance auditors’ comprehension of this statistical technique. The study was published in 1972 by Meikle and included an exposition of a MUS method called Cumulative-Monetary-Amounts sampling.
In 1973, Anderson and Teitlebaum devised a MUS method called Unrestricted Dollar-Unit sampling. It’s the same as what Meikle explained in 1972 as Cumulative-Monetary-Amounts sampling. Simply put, you can think of Unrestricted Dollar-Unit sampling as randomly picking some monetary units from the population.
Their study also talked about systematic sampling, where you divide the total book value amount into equal sections and then systematically pick some units after starting randomly in the first section.
Around the same time, Anderson (1973) talked about using statistical sampling in auditing and gave a quick glimpse of MUS.
Leslie (1975) explained MUS in a way that’s easy to understand, especially for government auditors.
I tried to find older research than Leslie’s in 1975, which used Monetary Unit Sampling terminology, but I still had no luck. Thus, at the moment, I think the research was the first to coin MUS terminology formally. But you should take it with a grain of salt or use your skepticism, as the auditor always says.
As you might see in the table, up until Leslie’s publication in 1975, the researchers used Dollar Unit sampling as the main terminology. Even some of the later publications still used the dollar-unit sampling term. Is there another terminology synonym for MUS? Yes, there are.
What is the other term for monetary unit sampling?
- Combined attributes/variables sampling
- Cumulative Monetary Amount sampling
- Dollar-Unit Sampling (DUS)
- Probability Proportional to Size (PPS) sampling
Although Probability Proportional to Size (PPS) often appears in the MUS discussion, those two terminologies aren’t interchangeable.
PPS is an unequal probability sampling technique where the likelihood of picking each item from the population is determined based on its proportion to a related auxiliary variable. PPS involves choosing individual dollars from a population through random or systematic selection methods.
MUS employs PPS as its method for selecting samples.
In their Audit Sampling guide, AICPA (American Institute of Certified Public Accountants) used PPS to describe a sample selection method, while MUS was used to describe the sample size and evaluation methods.
I hope the previous section gives you a clear definition of MUS, an informative brief history of the method, and a helpful synonym list. But you shouldn’t stop here. Below is the reading list about Monetary Unit Sampling, or audit sampling in general.
MUS-Related Reading List
- Audit Guide: Audit Sampling. AICPA
- Auditing: The Art and Science of Assurance Engagements. Alvin A. Arens et. al.
- Monetary-unit sampling: An investigation. Horgan, J. M. (1994)
- Statistical Auditing. Donald M. Roberts
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