Chapter 9 Audit Sampling

What effects will an auditor's belief that the population's actual deviation rate exceeds the tolerable deviation rate have on the test of controls sample size?

When an auditor believes that the expected rate exceeds the tolerable deviation rate, no test of controls will generally be performed. This is because control risk will normally be assessed at the maximum level since the control is believed to be ineffective since the expected deviation rate exceeds the deviation rate exceeding the tolerable deviation rate.

The auditors have sampled 50 accounts from a population of 1,000 accounts receivable. The sample items have a mean book value of $200 and a mean audited value of $203. The book value in the population is $198,000. What is the estimated total audited value of the population using the difference method?

When calculating the estimated audited value of the population using the difference method the average misstatement is first calculated as $203 - $200 = $3. The projected misstatement is then calculated by multiplying the average misstatement times the number of accounts in the population, or $3 x 1000 = $3000. Because the average misstatement is an understatement, the projected misstatement of $3000 is added to the population book value of $198,000 to calculate the estimated audited value of $201,000.

When is difference estimation more appropriate to use?

When the size of misstatements does not vary significantly in comparison to book value. This might be the case when errors are occurring randomly, independently of account size.

When is ratio estimation more appropriate to use?

When the size of misstatements is nearly proportional to the book values of the items. That is, it is appropriate when larger accounts have large misstatements and smaller accounts have small misstatements. (i.e. for receivables)

What are the different types of statistical sampling plans?

1. Attributes sampling (test of controls) 2. discovery sampling 3. classical variables sampling: mean-per-unit, ratio estimation, difference estimation 4. Probability-proportional-to-size sampling

To calculate projected misstatement, what are the 7 columns, left to right?

1. Book Value 2. Audited Value 3. Misstatement 4. Tainting Percentage (misstatement / book value) 5. Sampling interval 6. projected misstatement (tainting percentage x sampling interval) 7. upper limit on misstatements

What are the first 5 steps of the attributes sampling for tests of controls?

1. Determine the objective of the test. 2. Define the attributes and deviation conditions. 3. Define the population to be sampled. 4. Choose an audit sampling technique and specify the risk of assessing control risk too low and the tolerable deviation rate. 5. Estimate the expected population deviation rate.

What are the first four steps of audit sampling for substantive testing?

1. Determine the objective of the test. 2. Define the population and sampling unit. 3. Choose an audit sampling technique, specify the risk of incorrect acceptance and the tolerable misstatement. 4. Determine the sample size.

Once you have the sample size and sampling interval, what is the calculation for PPS Evaluation of Results?

1. Projected misstatement 2. + basic precision (reliability factor x sampling interval) 3. + incremental allowance = Upper Limit on Misstatement

What are the advantages of statistical sampling?

1. design efficient samples 2. measure sufficiency of evidence 3. objectively evaluate sample results, i.e. mathematically measuring risk

To calculate the incremental allowance, what are the 5 columns, left to right?

1. reliability factor (from chart) 2. increment 3. increment - 1 4. projected misstatement 5. incremental allowance (projected misstatement x (increment - 1))

What are the last four steps of audit sampling for substantive testing?

5. Select the sample. 6. Test the sample items. 7. Evaluate the sample results. 8. Document the sampling procedure.

What are the last 5 steps of the attributes sampling for tests of controls?

6. Determine the sample size. 7. Select the sample. 8. Test the sample items. 9. Evaluate the sample results. 10. Document the sampling procedure.

Results: Our sample size of 150 had 8 deviations. We determined that the upper deviation limit is 9.5%. What are the next steps?

8/150 = 5.3% 5.3% is lower than the tolerable deviation rate of 6%, however, this does not account for sampling error. The 9.5% accounts for sampling error, and that is above 6%.

What is the upper deviation limit?

9.5 %

What is nonstatistical sampling?

A sample is said to be nonstatistical when the auditors estimate sampling risk by using professional judgment rather than statistical techniques. Though it is not carelessly selected sampling, nonstatistical sampling provides no means of quantifying sampling risk.

What is the formula for audit risk?

AR = IR x CR x DR Inherent risk x control risk x detection risk

How can non-sampling risk be reduced?

Adequate planning audit samples and supervisions of audit engagements.

In selecting items for examination, an auditor considered three alternatives: (1) random number table selection, (2) systematic selection, and (3) random number generator selection. Which, if any, of these methods would lead to a random sample if properly applied? What if the population is not in random order?

All three of the methods of selecting items for examination (random number table selection, systematic selection, random number generator selection) will produce a random sample if properly applied. However, when using systematic sampling on a population that is not in random order it may be necessary to stratify the population into segments, or to use a relatively large number of starting points to produce a random sample.

What is projected misstatement?

An estimate of the most likely amount of monetary misstatement in a population.

What is audit sampling?

Applying a procedure (test) to less than 100% of a population.

What is block selection?

Block sample consists of all items in a selected time period, numerical sequence or alphabetical sequence. (least desirable)

Which of the following statistical sampling techniques is least desirable for us by the auditors?

Block selection.

What is a disadvantage of a systematic selection?

Disadvantage in that population may occur in a pattern (i.e. same technician, same vendor, etc.), which would destroy the sample randomness.

What is discovery sampling?

Discovery sampling, a form of attributes sampling, is designed to locate at least one deviation (exception) in the population. Discovery sampling often is used in situations in which the auditors expect a very low rate of occurrence of some critical deviation. As an example, the auditors might use discovery sampling to attempt to locate a fraudulent cash disbursement.

What are examples of nonsampling errors?

Examples of nonsampling errors include: the auditors may fail to apply appropriate audit procedures, or they may fail to recognize errors in the documents or transactions that are examined.

PPS Sampling Example/Given: Population book value: $6,250,000 Tolerable misstatement: $364,000 Sampling risk--incorrect acceptance: 5% Expected misstatement: $50,000 Determined sample size is 66. How do you find the sampling interval?

Find the sampling interval: book value of the population/sample size 6,250,000 / 66 = $95,000 approx.

What is an example of the physical representation of the population?

For example, a sample of accounts payable may be selected from a computer listing (the physical representation) of recorded accounts payable.

What is tainting?

In PPS sampling, the percentage of misstatement of an item (misstatement amount divided by book value).

What is basic precision?

In PPS sampling, the reliability factor (for zero misstatements at the planned risk of incorrect acceptance) times the sampling interval.

In PPS, what is incremental allowance?

In PPS, an amount determined by ranking the misstatements for logical units that are less than the sampling interval and considering incremental changes in reliability factors.

What is sampling without replacement?

In using a random number table, it is possible that the auditors will draw the same number more than once. If they ignore the number the second time it is selected and go on to the next number, they are sampling without replacement.

How is sampling risk reduced?

Increasing the size of the sample.

In mean-per-unit estimation, what is the estimated total audited value?

Mean audited value x number of accounts

An auditor needs to estimate the average highway weight of tractor-trailer trucks using a state's highway system. Which estimation method is most appropriate? Why?

Mean-per-unit estimation is best because no "book value" is available for the trucks. The difference, ratio, and probability-proportional-to-size methods all require the comparison of a book value to an audited value.

When performing tests of controls, how are measurements expressed?

Percentages, not dollar values.

What is the tolerable deviation rate?

Rate the auditor will tolerate without modifying the planned assessment of control risk.

What are some risks associated with nonstatistical sampling?

Sample may be larger than necessary or auditors may unknowingly accept a higher than acceptable degree of sampling risk.

What is always present and must be accounted for in calculations?

Sampling risk

What is sampling risk?

Sampling risk is the risk that the auditors' conclusion based on a sample might be different from the conclusion they would reach if they examined every single item in the entire population.

What is sampling with replacement?

Sampling with replacements means once a number is selected in a random number table, it is immediately replaced into the population of eligible items and may be selected a second time. The procedure is to include the number in the analysis as frequently as it occurs in the sample.

Which is more common in practice, nonstatistical or statistical sampling?

Statistical sampling can be more time consuming, requires training and can be more costly, so nonstatistical sampling is widely used by auditors.

PPS Sampling Example/Given: Population book value: $6,250,000 Tolerable misstatement: $364,000 Sampling risk--incorrect acceptance: 5% Expected misstatement: $50,000 Reliability factor: 3.0 Expansion factor: 1.6 Calculate the sample size.

Step 4: determine the sample size. recorded amount of population * reliability factor/ tolerable misstatement - (expected misstatement*expansion factor) 6,250,000*3.0/364,000-(50,000*1.6) = 18,750,000/284,000 = 66 The sample size is 66.

What is stratification?

Technique of dividing population into relatively homogeneous subgroups.

What is a tolerable misstatement?

The auditor's estimate of the maximum amount of dollar misstatement that may exist in an account balance without causing the financial statements to be materially misstated.

Explain how the auditors may obtain an estimate of a population's standard deviation to determine an appropriate sample size.

The auditors may obtain an estimate of the dollar amount of the standard deviation by procedures such as by (1) using the results obtained in previous years, (2) calculating the standard deviation of the population's book values, or (3) taking a small pilot sample.

How do auditors use difference estimation?

The auditors use a sample to estimate the average difference between the audited value and the book value of items in a population.

How do auditors use ratio estimation?

The auditors use a sample to estimate the ratio of the misstatement in a sample to its book value and project it to the entire population.

In attributes sampling, what is the confidence level?

The confidence level is the complement of the risk of assessing control risk too low. (Accordingly, if the risk of assessing control risk too low is .05, then the confidence level is .95).

Known: Deviations from sample 8/150 = 5.3% Tolerable deviation rate = 6% Upper deviation rate = 9.5% What can be concluded?

The control risk is high, more substantive testing needs to be done. The CR is going up, so DR needs to go down by doing more substantive testing.

The auditors have sampled 50 accounts from a population of 1,000 accounts receivable. The sample items have a mean book value of $200 and a mean audited value of $203. The book value in the population is $198,000. What is the estimated audited value of the population using the mean-per-unit method?

The estimated total audited value of the population using the mean-per-unit method is calculated as $203 (mean audited value in sample) x 1000 accounts = $203,000.

In which of the following circumstances is least likely that tests of controls will be performed?

The expected deviation rate exceeds the tolerable deviation rate.

In performing a substantive test of the book value of a population, auditors must be concerned with two aspects of sampling risk. What are the two aspects of the sampling risk, and which aspect is of greater importance to auditors? Explain.

The first is the risk of incorrect rejection (alpha risk) of an account. This is the possibility that sample results will indicate that an account balance is materially misstated when, in fact, it is not misstated. The second is the risk of incorrect acceptance (beta risk) of an account. This is the possibility that sample results will indicate that an account balance is not materially misstated when, in fact, it is materially misstated. The risk of incorrect acceptance of an account is of greater importance to the auditors because the effectiveness of the audit is compromised.

What is the risk of assessing the control risk too high?

The risk is the possibility that the sample results will cause the auditors to assess the control risk at a higher level than is warranted based on the actual operating effectiveness of the control. (relates to efficiency)

What is inherent risk?

The risk of a material misstatement in an assertion, assuming there were no related controls.

What are the three major factors that determine the sample size for an attributes sampling plan?

The risk of assessing control risk too low, the tolerable deviation rate, and the expected population deviation rate. In addition, the size of the population has a small effect on the sample size.

What is nonsampling risk?

The risk pertaining to nonsampling errors is referred to as nonsampling risk.

What is control risk?

The risk that a material misstatement that could occur in an assertion will not be prevented or detected on a timely basis by internal control.

What is detection risk?

The risk that the auditors' procedures will fail to detect a material misstatement if it exists.

What is systematic selection?

The technique of selecting a sample by drawing every nth item in the population, following one or more random starting points.

What is statistical sampling?

The use of statistical sampling does not eliminate professional judgment from the sampling process. It does, however, allow the auditors to measure and control sampling risk. Statistical sampling may assist auditors in (1) designing efficient samples, (2) measuring the sufficiency of the evidence obtained, and (3) objectively evaluating sample results.

What do you need to remember when listing the items for incremental allowance?

They are listed, ranked by highest projected misstatement (expect the top part to be mixed up).

Step 5, "estimate the expected population deviation rate," explain.

This is an estimate and need NOT be known to evaluate results of an attributes sample.

What is the risk of assessing the control risk too low?

This more important risk is the possibility that the sample results will cause the auditors to assess control risk at a lower level than is warranted based on the actual operating effectiveness of the control. (relates to effectiveness)

Results: Our sample size of 150 had 8 deviations. What do you do next?

You have to find the upper deviation limit. You do that by looking at the chart: "Statistical sampling results evaluation table for tests of controls: Achieved Upper Deviation Rate at 5 Percent Risk of Assessing Control Risk Too Low."

Assumptions/Given: Risk of assessing control risk too low is 5 % Tolerable deviation rate is 6 % Expected Population Deviation Rate is 2.5 % How do we determine sample size? What is the answer?

You look at the chart to determine sample size. The chart is "statistical sample sizes for tests of controls at 5 percent risk of assessing control risk too low." 150

The auditors' primary objective in selecting a sample of items from an audit population is to obtain...

a representative sample.

Which of the following is accurate regarding tolerable misstatement? a. tolerable misstatement is directly related to materiality. b. tolerable misstatement cannot be determined until the sample results are evaluated. c. tolerable misstatement does not affect sample size. d. tolerable misstatement is a measure of reliability of the sample.

a. Tolerable misstatement is directly related to materiality.

Which of the following is an example of sampling risk? a. choosing an audit procedure that is inconsistent with the audit objective. b. concluding that no material misstatement exists in a materially misstated population based on taking a sample that includes no misstatement. c. failing to detect an error on a document that has been inspected by an auditor. d. failing to perform audit procedures that are required by the sampling plan.

b. Concluding that no material misstatement exists in a materially misstated population based on taking a sample that includes no misstatement.

Discovery sampling is particularly effective when a. There are a large number of errors in the population. b. The auditors are looking for critical deviations that are not expected to be frequent in number. c. The auditors know where deviations are likely to occur. d. The population is large in size.

b. The auditors are looking for critical deviations that are not expected to be frequent in number.

Which of the following sampling techniques is typically used for tests of controls? a. mean-per-unit sampling. b. difference sampling. c. attribute sampling. d. probability-proportional-to-size sampling.

c. Attribute sampling.

The auditors are using unstratified mean-per-unit sampling to audit A/R as they did in the prior year. Which of the following changes in characteristics or specifications would result in a larger required sample size this year than that required in the prior year? a. larger variance in the dollar value of accounts. b. smaller population size. c. larger tolerable misstatement. d. higher risk of incorrect acceptance.

c. Larger variance in the dollar value of accounts.

An increased Tolerable Misstatement will ...

decrease the sample size.

When performing substantive testing, we express measurements of misstatement as...

dollar values.

In assessing sampling risk, the risk of incorrect rejection and the risk of assessing control risk too high relate to the...

efficiency of the audit.

In mean-per-unit estimation, what is the acceptance interval?

estimated total audited value plus & minus allowance for sampling risk

Population size has little effect on determining sample size except for...

very small populations.

Remember, if the expected population deviation rate is higher than the tolerable deviation rate then...

you would not sample.