Sampling techniques Flashcards
(17 cards)
What is the primary objective of using stratification as a sampling method in auditing?
A. To increase the confidence level at which a decision will be reached from the results of the sample selected.
B. To determine the occurrence rate for a given characteristic in the population being studied.
C. To decrease the effect of variance in the total population.
D. To determine the precision range of the sample selected.
C. To decrease the effect of variance in the total population.
(Choice A) Increasing the confidence level is not the primary objective of using stratification as a sampling method.
(Choice B) Determining the occurrence rate is not the primary objective of using stratification as a sampling method.
(Choice C) Stratified sampling is a technique of breaking the population down into subpopulations and applying different sample selection methods to the subpopulations. Stratified sampling is used to minimize the variance within the overall population.
(Choice D) Determining the precision range is not the primary objective of using stratification as a sampling method.
Which of the following statements is correct about the sample size in statistical sampling when testing controls?
A. The tolerable detection risk level has an inverse relationship to sample size.
B. The expected error rate does not impact the sample size.
C. The sample size determines the assessed risk of material misstatement.
D. The sample size must be unique for each control being tested.
A. The tolerable detection risk level has an inverse relationship to sample size.
The tolerable detection risk level is based on the assessed risk of material misstatement (RMM). The higher the RMM, the lower the tolerable detection risk level.
When the tolerable detection risk level is low, an auditor will seek more audit evidence and perform additional procedures (eg, with a larger sample size) to determine whether controls detect and correct or prevent material errors in the financial statements. Therefore, the tolerable detection risk level has an inverse relationship to the control test sample size (eg, tolerable detection risk level is low, so sample size is large).
(Choice B) The expected rate of error has a direct relationship to both the assessed RMM and the control test sample size. The higher the expected error rate, the larger the sample size needed to gain sufficient evidence about the effectiveness of controls.
(Choice C) An auditor must first assess the RMM. The auditor can then determine the appropriate sample size for obtaining evidence that controls effectively prevent or detect and correct material errors.
(Choice D) Multiple controls can be tested without selecting unique samples for each control. This results in a more efficient audit. For example, testing a single sample of A/P transactions might provide evidence of effective approval, receipt, and payment controls.
Things to remember:
To determine an appropriate control test sample size, an auditor must first assess the risk of material misstatement (RMM). A higher RMM results in a lower tolerable detection risk level and, inversely, a larger control test sample size.
Which of the following would be a consideration in planning an auditor’s sample for a test of controls?
A. Preliminary judgments about materiality levels.
B. The auditor’s allowable risk of assessing control risk too high.
C. The level of detection risk for the account.
D. The auditor’s allowable risk of assessing control risk too low.
D. The auditor’s allowable risk of assessing control risk too low.
Sampling techniques can be used during tests of controls to assess control risk. When planning samples, auditors consider sampling risk—forming an incorrect conclusion because procedures were performed on less than 100% of a population. A sampling risk may be classified as one of two types based on its consequence to an audit:
Type I (Efficiency): risk of assessing control risk too high
Type II (Effectiveness): risk of assessing control risk too low
The allowable risk of assessing control risk too low is the greatest concern with sampling tests of controls. In this Type II risk, the sample results lead an auditor to conclude that internal controls operate effectively when they don’t. The consequence is overreliance on the client’s internal controls and reduced audit procedures, resulting in undetected misstatements and an ineffective audit.
(Choice A) Materiality levels are considered when planning risk assessment procedures or substantive tests. Materiality concerns the size of a misstatement.
(Choice B) The allowable risk of assessing control risk too high (Type I sampling risk) is less concerning than too low. The audit will be effective but inefficient because the auditor will perform more testing than necessary.
(Choice C) Detection risk is the chance that substantive tests will lead the auditor to conclude that misstatements don’t exist when they do.
Things to remember:
In planning a sample for tests of controls, auditors should consider sampling risk. If the sample causes the auditors to assess control risk too low (ie, overreliance on internal controls), the audit will be ineffective (Type II risk).
Which of the following is the primary objective of probability proportional to sample size?
A. To identify overstatement errors.
B. To increase the proportion of smaller-value items in the sample.
C. To identify items where controls were not properly applied.
D. To identify zero and negative balances.
A. To identify overstatement errors.
Overstating assets or understating liabilities is generally done to improve an entity’s financial position. Overstatements tend to be performed in large amounts and understatements in smaller amounts. For example, overstating a $2,000 asset transaction may be recorded as $20,000, whereas an understated liability for the same amount could be recorded as $20.
Probability proportional to size (PPS) is a sample selection method in which items are chosen based on their dollar value; therefore, larger (not smaller) values have a greater chance of selection (Choice B). An advantage of this method is that it helps to identify overstatement errors.
(Choice C) PPS sampling is a variables sampling method used to reach conclusions about reasonableness of dollar amounts. In contrast, control testing is normally performed using attribute sampling, which is used to reach conclusions about the rate of occurrence for a specific qualitative characteristic (eg, properly signing checks).
(Choice D) Classical variables sampling treats individual items as a sampling unit, regardless of dollar amount. Because dollar amount is not factored into the method, it can be easily applied to identify zero and negative balances, which is useful to test for understatements.
Things to remember:
Probability proportional to size (PPS) is a sample selection method in which items are chosen based on their dollar value. Because larger values have a greater chance of selection, PPS is used to test for overstatements. In contrast, classical variables sampling treats individual items as a sampling unit, regardless of dollar amount, which is useful to test for understatements.
If the objective of an auditor’s test of details is to detect the overstatement of sales, the auditor should trace transactions from the
A. Sales journal to the shipping documents.
B. Shipping documents to the cash receipts journal.
C. Cash receipts journal to the customer’s purchase orders.
D. Customer’s purchase orders to the sales journal.
A. Sales journal to the shipping documents.
Revenues must be earned before they are recognized. A company that sells goods generally recognizes revenue after goods are shipped or delivered. Overstatements can be substantiated by testing for existence. Auditors testing for existence will verify that items in the financial statements (F/S) can be supported by corroborating evidence.
Although existence may be tested with a variety of methods in practice, the key for the exam is to understand that the starting point must be the F/S and the ending point is the supporting evidence. In this case, sales are earned when items ship. The auditor will trace items from the sales journal (F/S) to the shipping documents (ie, the supporting evidence) to verify the sale.
NOTE: The exam may use the terms ‘tracing’ and ‘vouching’ interchangeably. Therefore, focus on the purpose of the test rather than whether the test indicates tracing or vouching.
(Choice B) Tracing shipping documents to the cash receipts journal starts at the supporting evidence, not the F/S.
(Choice C) Tracing to customer purchase orders (POs) does not provide evidence that sales were earned, only that customers made the order. Sales of goods are generally earned when shipped or delivered.
(Choice D) Assuming POs could substantiate recognizing a sale, the direction of the testing is still incorrect because it starts at the supporting evidence.
Things to remember:
To detect an overstatement of sales, auditors can test for existence. To perform this test, auditors start at the financial statements (eg, sales journal) and trace/vouch information to the supporting evidence (eg, shipping documents). Items with no corroborating evidence will be investigated further.
An auditor is using probability-proportional-to-size sampling with an interval of $3,000 to select from invoices arranged by invoice number. A random starting point of $1,000 is determined using a random number generator. Which of the following invoices would be selected for testing?
Invoice number Invoice amount
1 $ 3,500
2 975
3 2,500
4 3,750
A. Invoices 1, 2, 3, and 4.
B. Invoices 1, 2, and 4 only.
C. Invoices 2 and 3 only.
D. Invoices 2, 3, and 4 only.
B. Invoices 1, 2, and 4 only.
It goes by intervals.
First is $1,000 so invoice 1 is over that.
Next interval is 4000 )3000+1000) so invoice 1 plus 2 is over that
Next interval is 7000 (4000+3000) so invoice 3 is not over that (4475+2500)
invoice 4 is over interval 3 (6975+3750) so you use invoice 4 too.
For which of the following audit tests would an auditor most likely use attribute sampling?
A. Inspecting purchase orders for proper approval by supervisors.
B. Making an independent estimate of recorded payroll expense.
C. Determining that all payables are recorded at year end.
D. Selecting accounts receivable for confirmation of account balances.
A. Inspecting purchase orders for proper approval by supervisors.
Attribute sampling applies to tests of controls. Tests of controls are performed to determine if the client deviates from an internal control more often than the auditor considers tolerable. If controls are operating effectively, control risk is reduced and the auditor can decrease substantive testing.
For example, auditors might use attribute sampling to inspect a sample of purchase orders for proper approval by supervisors. Approval (ie, authorization) internal controls are the attribute or characteristic being tested. Authorization is a segregation of dutiescontrol activity designed to prevent, detect, and correct errors or fraud.
In contrast, variables sampling pertains to tests of details. Tests of details verify if transactions and account balances are materially correct. Variables sampling is associated with dollar amounts. Examples include:
Estimating the amount of recorded payroll expense to compare with recorded amounts (Choice B)
Determining that all payables are recorded at year end to ensure liabilities are reflected in the correct accounting period (Choice C)
Confirming accounts receivable balances with third parties to verify the amount and existence of assets (Choice D)
Things to remember:
Attribute sampling applies to tests of controls, which are performed to assess the effectiveness of internal controls. Variables sampling is used with tests of details to form a conclusion about dollar amounts
When using classical variables sampling for estimation, an auditor normally evaluates the sampling results by calculating the possible error in either direction.
This statistical concept is known as
A. Precision.
B. Reliability.
C. Projected error.
D. Standard deviation.
A. Precision.
(Choice A) Classical sampling methods are based on the normal curve distribution. They calculate a “best estimate” of a population value and then provide confidence intervals around that estimate. The width of the confidence interval is the precision of the estimate, or the possible error in either direction.
(Choice B) Reliability pertains to the confidence level achieved in the statistical sampling application.
(Choice C) Projected error (or projected misstatement) is the estimate of the total amount of over- or understatement in a population, usually an account balance. It is determined by projecting the sample results to the population as a whole.
(Choice D) Standard deviation measures the amount of variability in the population.
Which of the following characteristics most likely would be an advantage of using probability-proportional-to-size (PPS) sampling rather than classical variables sampling?
A. The selection of negative balances requires no special design considerations.
B. The sampling process can begin before the complete population is available.
C. The sampling method is particularly effective for detecting understatements.
D. The sample size can generally be lower even if many errors are expected.
B. The sampling process can begin before the complete population is available.
There are two statistical approaches primarily used for substantive testing. These are classical variables sampling (CVS) and probability-proportional-to-size (PPS). CVS applies a normal distribution that requires the standard deviation (SD) be calculated for the entire population. Therefore, it cannot be applied until the complete population is available.
In contrast, PPS stratifies the population; items are selected proportional to dollar values (ie, larger values have greater chance of selection). An advantage is that sampling can begin before the complete population is available because each piece of the population can be stratified and sampled separately. A disadvantage of the method is that zero and negative balances require special design consideration (eg, sampled separately) (Choice A).
(Choice C) CVS is more effective than PPS at detecting understatements because they are generally smaller in nature. For example, understating a $2,000 transaction yields an amount less than $2,000 (eg, $20). Using PPS, the $20 understatement has a higher chance of being overlooked.
(Choice D) When using either PPS or CVS, there is generally a direct relationship between expected errors and sample size. When many errors are expected, a larger sample size is needed. This is not an advantage.
Things to remember:
Probability-proportional-to-size stratifies the population based on dollar value, giving larger values a higher chance of selection. An advantage is that sampling can begin before the complete population is available. In contrast, classical variables sampling requires that the standard deviation for the complete population be calculated before sampling can begin.
A CPA has decided to use probability-proportional-to-size (PPS) sampling, sometimes called dollar-unit sampling, in the audit of a client’s accounts receivable balances. The most likely reason this sampling method was chosen is that
A. PPS is designed to test accounts receivable controls.
B. PPS treats each accounts receivable dollar as a sampling unit.
C. PPS is less complex than other sampling methods.
D. PPS allows for the population to be grouped by qualitative factors.
B. PPS treats each accounts receivable dollar as a sampling unit.
Audit sampling involves examining less than 100% of a population and using the results to draw a conclusion about the entire population. Although audit data analytics can test entire populations of data, there are still instances in which sampling is essential.
Probability-proportional-to-size (PPS) sampling considers each dollar in a population a sampling unit. A starting point (eg, $1,000) establishes the first sampling interval. A set interval (eg, $3,000) is used to establish subsequent sampling intervals (eg, $4,000, $7,000, $10,000). The auditor arranges Items in the population in order (eg, by invoice number) and a cumulative dollar amount is calculated for each item. The auditor then samples the first items with cumulative dollar amounts that meet or exceed a sampling interval.
(Choice A) Attribute sampling is used for control testing, and PPS is a form of variable sampling. Controls are associated with policies or procedures, and PPS is designed to select sampled items based on dollars.
(Choice C) PPS is just as complex as other sampling methods because of the need for sampling intervals and cumulative dollar amounts to select sample items.
(Choice D) Variable sampling, not PPS, allows for items to be stratified by qualitative factors (eg, expensive items versus inexpensive items). This is because PPS considers each dollar a sampling unit, whereas variable sampling considers each item (eg, a transaction) a unit to be selected.
Things to remember:
In probability-proportional-to-size (PPS) sampling, each dollar in the sampled population is considered a sampling unit. PPS is a complex variable sampling technique that does not allow for population stratification or for testing attributes (eg, compliance with established controls).
In a probability-proportional-to-size sample with a sampling interval of $5,000, an auditor discovered that a selected account receivable with a recorded amount of $3,000 had an audit amount of $2,700. If this were the only error discovered by the auditor, the projected error of this sample would be
A. $300
B. $500
C. $800
D. $2,300
B. $500
3000-2700 = 300
is recorded amount < sampling interval - yes (3000<5000) (if no to this question then it is a misstatement
300/3000 = .10
.10 * 5000 = 500
Which of the following factors would the auditor not explicitly consider when determining sample size in an attribute sample for a test of controls?
A. An acceptable level of the risk of overreliance.
B. The tolerable deviation rate.
C. The expected population deviation rate.
D. The tolerable misstatement.
D. The tolerable misstatement.
The auditor starts an audit by documenting an understanding of the client’s internal control structure and determining the reliability of the controls using attribute testing. This allows the auditor to determine the level of substantive testing needed to obtain audit evidence to support management representations and the audit opinion.
In general, attribute sampling is used to test internal controls. The auditor examines control activities to ensure that the client does not deviate from the control more often than the auditor considers tolerable. To determine the appropriate attribute sample size, the auditor considers three key factors (ie, TEA):
Tolerable deviation rate: percentage of time for which a control can be violated and still lead the auditor to believe it is operating effectively (Choice B)
Expected population deviation rate: percentage of time for which the auditor expects the control was violated (Choice C)
Acceptable level of risk of overreliance: risk that the sample will cause the auditor to incorrectly rely on the control (Choice A)
Note: For the auditor to rely on a control, the sample deviation rate must be lower than the tolerable deviation rate.
Tolerable misstatements affect the sample size in variable sampling, not attribute sampling.
Things to remember:
In general, attribute sampling is used to test internal controls. The appropriate sample size is based on the tolerable and expected deviation rates and the acceptable levels of risk of overreliance on the sample results. Tolerable misstatements affect the sample size in variable sampling, not attribute sampling.
Which of the following types of sampling allows an auditor to quantify sampling risk?
A. Stratified nonstatistical.
B. Haphazard.
C. Attribute.
D. Block.
C. Attribute.
Auditors select items from a population using either statistical or nonstatistical sampling. Statistical sampling uses the law of probability when selecting a sample size and allows auditors to quantitatively evaluate sample results and measure sampling risk. Attributesampling is used to estimate how much of the population possesses a specific characteristic. It is a type of statistical sampling commonly used in control testing.
In contrast, any sampling method that does not allow the auditor to make a statistical evaluation of the sampling results (eg, haphazard sampling) is considered a nonstatistical sampling method. The sampling risk is unmeasurable because the results of the sample cannot be quantitatively evaluated.
(Choice A) When stratifiednonstatistical sampling is used, the population is stratified (grouped) based on similar characteristics and selections are made using a nonstatistical approach (eg, auditor judgment).
(Choice B) Haphazard sampling is a nonstatistical, nonsystematic method of selecting items. An example is standing in the corner of a room and randomly selecting items by pointing.
(Choice D) Block sampling is a nonstatistical method that involves selecting a sequential series from a population. An example is selecting invoices numbers 51–60 (block 1) and 71–80 (block 2) when selecting a sample of 20 invoices.
Things to remember:
Statistical sampling uses the law of probability when selecting a sample size, which allows auditors to quantitatively evaluate sample results and measure sampling risk. In contrast, any sampling method that does not allow the auditor to make a statistical evaluation of the sampling results is considered a nonstatistical sampling method.
Which of the following statements is correct concerning probability-proportional-to-size (PPS) sampling, also known as dollar unit sampling?
A. The sampling distribution should approximate the normal distribution.
B. Overstated units have a lower probability of sample selection than units that areunderstated.
C. The auditor controls the risk of incorrect acceptance by specifying this risk level for the sampling plan.
D. The sampling interval is calculated by dividing the number of physical units in thepopulation by the sample size.
C. The auditor controls the risk of incorrect acceptance by specifying this risk level for the sampling plan.
PPS sampling (or dollar-unit sampling) defines a sampling unit as an individual dollar associated with a F/S element. For example, in an accounts receivable balance of $3,000,000 that consists of 7,500 accounts, the PPS population is 3,000,000 individual items (eg, dollars) rather than 7,500 items (eg, accounts). When an individual dollar is chosen to be sampled, the entire account balance is examined.
Both PPS and variable sampling methods rationally select transactions upon which tests of details are performed. Since only a sample of transactions is tested, there is the risk that the auditor will incorrectly accept sample results and miss exiting errors. The auditor controls this risk of incorrect acceptance by specifying an acceptable risk level for the sampling plan, based on the overall assessed risk of material misstatement.
(Choice A) In a normal distribution, each item (eg, customer account) has an equal chance of selection. In PPS, each dollar has an equal chance of selection.
(Choice B) An overstated unit (eg, customer account) would have a larger dollar amount (ie, size), producing a greater probability of sample inclusion using PPS.
(Choice D) In PPS, a sampling interval is determined first. Because an entire unit (eg, account) is sampled when its dollar amount falls within the sampling interval, the number of units to be sampled cannot be determined until the sample is selected.
Things to remember:
In PPS sampling (or dollar-unit sampling), the auditor controls the risk of incorrectly accepting sample results by specifying the risk level for the sampling plan.
Which of the following statements is correct concerning statistical sampling in tests of controls?
A. As the population size increases, the sample size should increase proportionately.
B. Deviations from specific internal control procedures at a given rate ordinarily result in misstatements at a lower rate.
C. There is an inverse relationship between the expected population deviation rate and the sample size.
D. In determining tolerable rate, an auditor considers detection risk and the sample size.
B. Deviations from specific internal control procedures at a given rate ordinarily result in misstatements at a lower rate.
The requirement is to identify the correct statement concerning statistical sampling in tests of controls. Answer (b) is correct because while deviations from pertinent control procedures increase the risk of material misstatements, any specific deviation need not necessarily result in a misstatement. For example, a recorded disbursement that does not show evidence of required approval might nevertheless be a transaction that is properly authorized and recorded (AICPA Audit Sampling Guide). Answer (a) is incorrect because increases in population size result in small increases in sample size. Answer (c) is incorrect because a direct relationship, not an inverse relationship, exists between the expected population deviation rate and the sample size—that is, increases in the expected population deviation rate result in an increase in the required sample size. Answer (d) is incorrect because when determining the tolerable rate, the auditor does not yet have the required sample size.
When evaluating results of testing a sample using attribute sampling, the auditor considers the sample’s final error rate to be equal to
A. Errors in the sample / total elements in the sample.
B. (Errors in the sample + missing elements in the sample) / total elements in the sample.
C. (Errors in the sample + missing elements in the sample) / total elements in the sample + allowance for sampling risk
D. ((Errors in the sample + missing elements in the sample) / total elements in the sample + allowance for sampling risk) x proportion of sample to population
C. (Errors in the sample + missing elements in the sample) / total elements in the sample + allowance for sampling risk
Choice C (Correct): To determine the error rate for a sample using attribute sampling, the number of deviations detected is combined with the number of items from the sample that the client was unable to produce (missing elements), which are considered equivalent to deviations. This is divided by the number of items in the sample to give the preliminary sample rate. This amount is adjusted by adding sampling risk, the result of which is the auditor’s estimate of the range of errors in the population. This estimate is also referred to as the Upper Precision Limit. Since the error rate is evaluated to determine if it is not greater than the tolerable rate, the auditor is concerned about the upper limit, not the lower limit.
Choices A, B, D (Incorrect): To determine the error rate for a sample using attribute sampling, the number of deviations detected is combined with the number of items from the sample that the client was unable to produce (missing elements), which are considered equivalent to deviations. This is divided by the number of items in the sample to give the preliminary sample rate. This amount is adjusted by adding and subtracting sampling risk, the result of which is the auditor’s estimate of the range of errors in the population. Since the error rate is evaluated to determine if it is not greater than the tolerable rate, the auditor is concerned about the upper limit, not the lower limit.
If an auditor of a nonissuer is unable to apply a designed audit procedure to an item selected as part of a sample for a test of controls and no alternative procedures are possible, then the auditor should
A. Treat the item as a deviation from the prescribed control.
B. Treat the item as a misstatement.
C. Perform the designed procedure on a replacement item.
D. Revise the sample selection method to a more random selection method.
A. Treat the item as a deviation from the prescribed control.
An auditor of a nonissuer employs attribute sampling to evaluate the effectiveness of internal controls (I/C) by examining a sample of transactions or documents and determining whether they adhere to established procedures.
On occasion, the auditor cannot perform the designed audit procedure on the sample. In such cases, the auditor should first try to perform alternative procedures on the item. For example, if the client cannot find a hard copy of a signed approval, the auditor may perform alternative procedures and assess whether an electronic approval was granted in a timely manner. If alternative procedures cannot be performed and the client cannot provide the document the auditor wishes to examine, the control is not operating as intended and the item should therefore be treated as a deviation from the prescribed control. This practice prevents management from hiding sampled audit evidence and hoping for a better selection.
(Choice B) When a sampled item cannot be tested, it doesn’t necessarily mean that there is a misstatement in the F/S. For example, the failure to properly authorize a purchase does not necessarily mean that the purchase wasn’t correctly accounted for in the financial records.
(Choices C and D) Replacing a sampled item or revising the sample selection may lead to wrong conclusions about the population being tested.
Things to remember:
When a designed test of controls audit procedure cannot be applied to a sampled item and using alternative procedures is not possible, the item should be treated as a deviation from the prescribed control.
