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Learn how to select and evaluate samples in connection with performing auditing procedures. This course uses case studies to give you experience performing and evaluating samples using several important statistical and non-statistical (or quasistatistical) techniques such as proportion estimation, mean estimation, PPS sampling and rules of thumb to approximate PPS sampling. You will learn to use statistics to evaluate sampling risk, even if you do not understand all the underlying probability theory. You will learn how to perform (using a calculator or PDA that has a square root function) and document samples in conformity with generally accepted auditing standards.
Objectives:Prerequisite: None
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Chapter 1
Introduction to Audit Sampling Risk Assessment
Learning Objectives
Chapter Overview
The use of sampling to estimate a proportion is covered first in this course because it is the simplest sampling technique to learn and is great for learning what statistical sampling does in general. It provides a convenient way to become comfortable with using statistics to evaluate sampling risk. It also provides a standard that is useful for understanding the value of the other techniques in audits of financial statements and in other attestation services.
In an audit engagement this technique can be useful when an auditor needs an independent estimate of a percentage that is reported in notes to financial statements or needs an independent estimate of a percentage that is relevant to an accounting estimate. For example, this technique could be used to independently estimate the percentage of customers in a geographic or industry concentration disclosed in notes to financial statements. The auditor would select customers, examine evidence pertaining to the location of the customers, and use statistics to calculate a range in which the percentage probably falls. Or, for example, this technique could be used to independently estimate the percentage of inventory items that have shown no sales activity since a certain date for the sake of evaluating reserves for obsolescence. In an attestation engagement, it could be used to estimate any percentage to which an auditor is attesting. For example, in an attestation engagement in which it is important to estimate the percentage of patients of an HMO that qualify for medicare, this sampling technique can be used to estimate the percentage. The method of assessing sampling risk for this technique is the same for all audit and attestation applications in which it is used.
In addition to explaining this particular sampling technique, the goal of this chapter is to illustrate how sampling risk can be assessed by using a statistical formula. This sampling technique involves calculating a confidence interval than an auditor can use to estimate sampling risk or to assess the likelihood that a reported proportion is reliable. For example, if an auditor
has used this technique to estimate the percentage of customers in a geographic concentration, statistics will tell the auditor the likely range in which the true percentage falls. It will tell the auditor, for example, that based on the sample results the auditor has 95% confidence that the percentage of customers that are located in the United States is between 10% and 15%. In other words, it tells the auditor that the chance that the percentage of customers falls outside of the 1015% range is 5% (100% - 95% = 5%.) The auditor can then assess whether this range estimate is precise enough considering the auditor's assessment of materiality. The auditor can also then assess whether or not 5% sampling risk allows the auditor to conclude that the evidence is sufficient. That assessment involves evaluating whether or not 5% would be considered an acceptably low level of risk under auditing standards in the circumstances. Most auditing approaches available to an auditor (e.g., analytical procedures) do not provide such precise assessments of risk. Sampling is unique in this respect among all the other approaches available to an auditor.
This chapter contains two cases. Each case is followed by an analysis of the case and related sampling topics. The two cases are
The analysis of Case 1-A includes practice problems that illustrate how sample size, proportion size and population size can affect estimates. A discussion of sampling risk in an audit follows the analysis of Case 1-A. Review questions and a summary of the most important points are presented at the end of the chapter.
Case 1-A – Using Sampling to Estimate a Proportion
Introduction and Overview
A sample can be used to estimate the proportion of a population that has a particular characteristic. For example, political pollsters use such samples to estimate election results. An auditor could use such a sample to estimate the percentage of customers located in a particular geographic region or to estimate the error or deviation rate in accounting transactions or balances.
The tasks involved in using sampling are generally easier to perform than they are to understand. In addition, it is easier to understand the significance of sampling tasks after the tasks themselves have been mastered. With those realities in mind, this course uses cases that provide an opportunity to learn and practice using sampling tasks before the significance of the tasks is explained and analyzed.
Estimating a proportion using sampling involves performing four tasks:
This case involves performing those tasks. You will prepare a population to sample by tearing sheets of paper into small pieces, shuffling them, and placing them in a pile. Then you will select a sample by blindly drawing pieces of paper from the pile, calculate the proportion, and then calculate the confidence interval. After you have performed these tasks you will be ready to examine their significance.
Step 1: Prepare the Population to Sample for this Case
Remove the 10 pages of Appendix A from the course manual.
Tear or cut each page into sixteen pieces using the lines as guides. Notice that each page shows the page number in the four corner boxes. These numbers will be important in the case.
When you are finished tearing or cutting, you will have 160 pieces of paper and one-fourth of the pages will have numbers on them.
Shuffle the pile.
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