The purpose of sampling is to help an auditor obtain reasonable assurance that the financial statements are free of material misstatements. Although sampling allows the auditor to do less extensive work, the work done is more efficient and effective when it comes to finding out any incorrect account balances on the financial statements.
Non-Statistical sampling is when the auditors uses professional judgment rather than statistical techniques. This provides no means of quantifying sampling risk, therefore an auditor may be taking on a higher degree of risk if non-statistical methods are implemented.
Statistical sampling still requires professional judgment in that it allows the auditor to measure and control sampling risk.
Statistical sampling helps auditors:
- design efficient samples
- measure the sufficiency of the evidence obtained
- objectively evaluate sample results
Obtaining a random sample can be done with or without replacement:
- Sampling with replacement is when an item is selected; it is immediately replaced with another eligible items in the population.
- Sampling without replacement is when an item is selected; it is immediately taken out of the sample.
These are three primary methods of obtaining samples.
- Systematic selection is when every nth term is selected, starting with a random point.
- Example: An auditor wants to test the accounts receivable account so they test every 10th account, starting from the 5th account (5th, 15th, 25th, 35th, etc.)
2. Stratification is when the population is divided into groups with similar traits referred to as strata. These strata can be sampled together or separately.
Ex: Selection of Accounts Receivable in a population of diverse accounts.
3. Block Selection consists of taking a sample that can be comprised of a time period or a numerical sequence. Most of the time, block selection does not efficiently produce a representative sample hence sampling risk.
- Example: An auditor wants to test the internal controls over cash receipts from September to December. So here the sampling unit is the number of months, not the cash receipts.
In reference to auditing fieldwork standard three: an auditor must obtain sufficient appropriate audit evidence by performing audit procedures to afford a reasonable basis for an opinion regarding the financial statements under audit. An auditor cannot test every detail of the financial statements; therefore an auditor uses audit sampling to test controls and perform substantive tests. Audit sampling is referred to on an auditors report in the scope paragraph where it states "An audit includes examining, on a test basis, evidence supporting the amounts and disclosures in the financial statements".
To test controls, an auditor can implement attribute sampling. Attribute sampling helps an auditor detect an occurrence or an “attribute” of the internal control system. Here an "attribute" refers to a deviation therefore attribute sampling focuses on discovering if any deviations have occurred. Discovery sampling is a special type of attribute sampling, in that it specifically is designed to test for a critical deviation. It is used when an auditor believes a population deviation rate is zero or close to zero therefore the auditor is investigating to find a critical mistake in an entity's internal control.
- There are some terms that are used specifically in attribute sampling:
1- Deviation Rate: is the auditor’s best guess of how much a sample can differ from the average. There is an upper deviation rate and a lower deviation rate.
2- Tolerable Deviation Rate: is the maximum amount of incorrect procedures an auditor can tolerate before reassessing the control risk.
3- Allowance for sampling risk: is a limit or a range developed to indicate where the true value may lie. This is developed to make sure there is some precision in what the auditor finds.
This equation is very important when it comes to assessing and analyzing the control risk. The allowance for sampling risk plus a sample deviation rate must always be less than the tolerable deviation rate. If it is higher, the auditor must modify the assessed control risk.
- An example of Attribute Sampling:
During the audit of a non-issuer, Adequate Disclosure’s staff auditor plans to assess the control risk by reviewing the internal control function of the shipping department. The auditor examines the file of bill of lading documents and determines the tolerable rate of the population to be 4% and the allowance for sampling risk to be 1%. The population consists of 300 documents; however the auditor takes a sample size of 60 and realizes that there were 20 deviations.
- What is the total upper deviation rate?
- Allowance for Sampling Risk: 1%
- Sample Deviation Rate: 20/60 = 3.3%
- 1% +3.3% = 4.3%
Yes, the auditor should modify the assessed the level of control risk since the Allowance for Sampling Risk plus the Sample Deviation Rate is greater than the Tolerable Deviation Rate.
Alongside sampling risk, there are two other risks associated with the assessment of control risk.
These are some factors affecting the Sample Size during Attribute Sampling.
Variable Sampling helps an auditor perform substantive procedures. Variable Sampling helps auditors determine the “numerical quantity” of an account. There are some specific terms that are used when implementing variable sampling.
- Tolerable Misstatement: this is the maximum monetary mistake the auditor is willing to accept before determining an account balance to materially misstated.
- Projected Misstatement: this is similar to deviation rate in attribute sampling, where the auditor estimates how much of a misstatement can be expected in a sample.
There are three types of variable sampling techniques an auditor can implement.
- Mean Per Unit Estimation (MPU):
MPU uses the average value of items in a sample to estimate an accurate value in the population.
Formula:
- Average Value x Population =Point Estimate
- Point Estimate +/- Allowance for Sampling Risk
Example:
- $96.67 x 2,600 = $251,333
- $251,333 – 2,300 = $249,033 & $251,333+2,300 = $253,633
- Range ($249,033-$253,633)
- Ratio Estimation:
Ratio estimation uses audited values of accounts to their book values to determine an accurate value in the population.
Formula:
- Audited Value/Book Value x Total Book Value = Point Estimate
- Point Estimate +/- Allowance for Sampling Risk
Example:
- $29,000/33,000 x $75,000 = $65,909
- $65,909 – 2,300 = $63,609 & $65,909 + 2,300 = $68,209
- Range ($63,909 - $68,209)
- Difference Estimation:
Difference estimation uses the average difference between the book value and the true value to estimate an accurate value in the population.
Formula:
- Book Value-True Value/Sample x Population = Projected Error
- Total Value – Projected Error = Point Estimate
- Point Estimate +/- Allowance for Sampling Risk
Example:
- $33,000 - $29,000 / 300 x 2,600 = $2,959
- $75,000 - $ 2,959 = $72,041 (Point Estimate)
- $72,041 – 2,300 = $69,741 & $72,041 + 2,300 = $74,341
- Range ($69,741 - $74,341)
Alongside sampling risk, variable sampling has two distinct risks associated with it.
(Click on the above chart for enlargement)
These are some factors affecting the Sample Size during Variable Sampling.
Attribute Sampling and Variable Sampling can be mixed together to develop a hybrid form of sampling called: Probability-Proportional-To-Size (PPS) also known as Monetary-Unit Sampling. This method is considered to be a hybrid since it takes attribute sampling to estimate a numerical quantity. This method is very complicated compared to the other methods.
- Determine the Sampling Interval:
- Tolerable Misstatement/Reliability Factor (Taken from the AICPA Audit Guide)
- Determine the Sample Size:
- Population / Sampling Interval
Example:
Auditors of Adequate Disclosure during the audit of a public company, assess the tolerable misstatement of the accounts receivable balance to be $600 and the risk of incorrect acceptance at 7%. The recorded amount of accounts receivable is $90,000.
- $600/5 = $120
- $90,000/$120 = $750