# Is there a standard, easy to understand example of application of statistics in the accounting profession?

A course that is offered in most business undergraduate programs is an introductory statistics course that is often titled 'Business Statistics'. The examples used in these courses to motivate the application of statistics in business often come from either marketing (e.g., surveys), finance (e.g., stock market returns) or operations (e.g., quality control).

Is there an example that is accessible at the undergraduate level that can be used to explain the application and relevance of statistics in the context of accounting?

• Perhaps the question would be better directed if you asked for a good reference book rather than an individual example – Hugh Mar 25 '16 at 19:45
• I personally don't know of one (I don't work in that area). We could probably make one up for you. What statistical concept do you want an example of? What kinds of empirical studies / statistical analyses do accountants actually do? – gung - Reinstate Monica Mar 25 '16 at 19:46
• You might be interested in e.g. the Wikipedia article Data analysis techniques for fraud detection – Silverfish Mar 25 '16 at 20:39
• I don't see how there could be a "standard example". There are many fundamentally different applications of statistics in accounting. There will of course be some simple examples, but I doubt any could be called "standard". My guess is you'd be best served by looking for some of the fairly large number of basic statistics books with "Accounting" in the title. With a quick search I turned up several, including "Statistics for Economics, Accounting, and Business Studies" (Barrow). I expect books like these have quite a few accounting-related examples in them. – Glen_b -Reinstate Monica Mar 26 '16 at 0:41

The possibilities are literally endless.

Among other things, I study survey sampling. Sampling is used a lot in business accounting for estimating various amounts, when it's too time-consuming or costly to obtain exact figures.

For example, say you worked for a large company with hundreds of thousands of invoices. You might be interested in determining how many of the invoices are accurately billed. One way of doing this is to randomly sample invoices, obtain the mean $\bar{y}$ difference between the invoice amount and what the invoice should have been (perhaps using some methodology or system of record) and the total number of invoices $N$. If you then multiply the mean and total number of invoices, $\bar{y}N$, you can obtain an estimate of the total amount of all invoices without having to add up every single invoice, which could take a small army of workers to do and be very expensive. You could use additional methods from statistics to form 95% confidence intervals around your estimate as well, so you could have some idea of how reliable your estimate is. In this example the variance, used in calculating the 95% confidence interval would be:

$V(\bar{y}N)=N^2V(\bar{y})=N^2{(1-f)\over{n}}S^2$,

where $N$ is the total number of invoices, $n$ is the number sampled, $f={n\over{N}}$ and $S={1\over{n-1}}\sum_{i=1}^n(y_i-\bar{y})$.

The large-sample $100(1−\alpha)\%$ confidence interval for the total invoice discrepancies would then be give by:

$[\bar{y}N-Z_{\alpha/2}V(\bar{y}N), \bar{y}N+Z_{\alpha/2}V(\bar{y}N)]$

What's more interesting, is that if you study sampling and statistics a bit more, you will understand that it's usually better to stratify the invoices into, say, large, medium, and small billing amounts. Then, you could carry out disproportionate sampling so that you sample more invoices with larger dollar amounts than smaller amounts, since the larger invoices are more likely to have large billing errors (making up most of the difference). Using business and survey sampling statistics allows you to disproportionately allocate your sample among large, medium, and small billing amounts on invoices and still obtain an unbiased answer of how large the companies invoices are off.

You can find a similar example like this in Sharon Lohr's sampling book.