## Statistical Applications in Accounting

This article focuses on how statistical sampling techniques are utilized in the field of accounting. Techniques such as auditing sampling are discussed. The role of the American Institute of Certified Public Accountants in the development of guidelines for this approach is highlighted. In addition, there is a historical overview of how statistical techniques were introduced into the field of accounting.

Keywords American Institute of Certified Public Accountants; Audit Sampling; Dollar Unit Sampling; Simple Random Sampling; Statement on Auditing Standard; Statistical Correlation Technique; Statistical Sampling Technique

### Accounting: Statistical Applications in Accounting

### Overview

Many have argued that statistics is important to the field of accounting. The tools of statistics can assist accountants with more effectively performing their job. In addition, "there is definite evidence in accounting periodicals of an increasing interest in the use of statistics, especially statistical sampling techniques, in accounting" (McGurr, 1960, p. 60). Many scholars have recognized that the two fields can yield creative results when they are combined. As a result, there was considerable interest in relating statistical methods to accounting, auditing, and management control during the post-war years (Trueblood & Cooper, 1955). Fan & Zhang (2012) show that statistical reporting is key to quality accounting practices.

### Methods for Combining Statistics

Trueblood (1953) provided some foundational principles for guiding and organizing research in this area. Based on his report, the principles were:

- Collaboration between the two disciplines is crucial to the success of the partnership between the two fields. The accountant must be willing to work closely with the statistician when stating and defining accounting problems and objectives. The statistician is responsible for understanding the accountant's point of view in order to develop a joint development of technique. Both individuals must gain an understanding of the other's field in order to develop the basis for a common language.
- Statistical techniques that are used in other areas cannot be blindly accepted for accounting. There is a belief that time will be saved when existing statistical methods can be applied directly. However, it should be noted that there may be certain accounting problems that require new statistical techniques to be developed in order to solve them.
- Satisfactorily operating accounting techniques should not be supplanted by statistical procedures for the sake of change only. An increase in the use of accounting, auditing or management control techniques is the criterion for suggesting integration of present or new statistical techniques in the accounting field.

### Further Study on Statistical

According to Trueblood and Cooper (1955), the Pittsburgh group found that many of the published statistical applications did not conform to the above mentioned principles. As a result, this group decided to conduct its own studies to support the principles that were discussed earlier. Some of these studies included:

- Internal accounting procedures and management control problems.
- In a small specialty steel manufacturing corporation, quality control charts were developed as a way to investigate performance variances on a daily basis. This experiment also produced practical procedures involving statistical correlation techniques to evaluate the consistency of cost standards.
- A LIFO price index based on statistical sampling was developed to yield reductions in cost, higher quality results and simplication of administrative problems. It was found that the data could be used for other managerial initiatives such as price index purposes. Some of these correlative initiatives included forecasting, establishing cost of sales determinants, and calculation of interim inventory turnover rates.
- Auditing cases.
- The aging of accounts receivable in department stores. The sampling procedures developed for aging purposes are directed toward both the control and audit processes.
- A statistical application was made to the evaluation of the recorded book value of inventory. The evaluation was completed by statistical analyses of adjustments to records developed from past cycle counts.
- An audit application had been made in relation to physical tests of bulk inventories for internal and external audit purposes. Two significant findings of this experiment were: The external auditor decided that his sample should be increased versus decreased, and; Statistical sampling cannot yield significant protection to the auditor in fraud detection without large samples.

### Audit Sampling Technique

The American Institute of Certified Public Accountants' (AICPA) auditing standards board (ASB) had formed a task force to develop and implement an audit sampling policy for using the sampling techniques as described in Statement on Auditing Standards (SAS) number 39, Audit Sampling (Journal of Accountancy, 1983). The policy became effective for any examination of financial statements for periods ending on or after June 25, 1983. However, when a meeting was held in April, 1983, the ASB recommended that the AICPA provide additional guidance to practitioners for implementing the provisions. The task force's response was to create a question and answer (Q&A) list with the five most frequently asked questions by practitioners.

In 1992, the Audit Sampling and Analytical Techniques Committee of the New York State Society of CPAs conducted a survey of New York accounting firms. According to Hitzig (1995), the purpose of the survey was to obtain information regarding the use of audit sampling based on SAS No. 39, Audit Sampling. The main interest was to determine the level of use of the audit sampling technique by local accounting firms. A survey had been conducted in 1984 by the Audit Testing Techniques Subcommittee of the AICPA. However, it did not address the use of sampling in practice.

### Application

### Statistical Sampling

"To meet their clients' needs in an environment of heightened competition and runaway inflation, many auditors are turning to scientifically supported methods of planning, executing and evaluating audit procedures to obtain evidential matter. Statistical sampling is one such method" (Akresh & Zuber, 1981, p. 50). There are many ways that an accountant can set up a statistical sampling. Hitzig (2004) provided a model that worked on the premise that one could set up a statistical sampling by defining the population, frame and sampling unit.

### The Population

The population is the set of all accounts or transactions that the auditor wishes to use in order to arrive at the conclusion. The first step in the process is to define the test objective. Once the test objective has been determined, the auditor should define the population. The steps are in this order so that the auditor can draw a sample based on the specific test objective.

### The Frame

Once the testing has been completed, the auditor must attribute the results to the items versus the population since auditors do not select a sample directly from the population. This representation is referred to as the frame. The frame provides the auditor with a foundation for identifying items to be included in a sample.

In most cases, the accounting population is presented in the form of a list (i.e. payroll file, accounts receivable detail). This list (or frame) tends to streamline and simplify the sample selection process. However, the population's sampling frame does not have to be a list. Sometimes, the physical locations provided by floor plans or other population identifiers...

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