Audit Sampling

Question 1

What is Audit Sampling?

Answer 1

Refers to the **examination of less than 100% of a population and using the results as a basis for drawing a general conclusion on the entire population **

Question 2

What are the characteristics of Statistical Sampling?

Answer 2

• Statistical Sampling refers to the use of **quantitative measures of the risks the auditor is taking in the use of sampling. **
• Based on formulas
• Statistical sampling helps the auditor to: (1) design an efficient sample, (2) measure the sufficiency of the audit evidence obtained, and (3) evaluate the sample results.
• Helps the auditor to design an efficient sample, measure the sufficiency of the audit evidence obtained, and evaluate sample result → An advantage of statistical sampling over nonstatistical sampling

Question 3

What are the characteristics of Non-Statistical Sampling?

Answer 3

• Based on human decision - lack mathematical certainty - judgmental sampling
• Equally acceptable as Statistical Sampling
• Still be **effective but not efficient **

Question 4

When Audit sampling is used during the Audit

Answer 4

• **During Internal Control phase **of the audit - auditor will perform test of controls on a sample to determine the operating effectiveness of controls they plan to rely on - Attribute sampling
• During the substantive testing phase **of the audit, the auditor will perform test of details of transactions, accounts and disclosures on a sample basis to obtain sufficient appropriate audit evidence to support management assertions - **Variables sampling **
• **Both Attribute sampling and Variable sampling may be either statistical or nonstatistical **
• Dual-purpose tests are those in which a single sample is used to test a control and to serve as a substantive test
  of a recorded balance or class of transactions. When a dual-purpose test is used, auditors select the sample size
  as the higher of that required for the two purposes. For example, if the test of control test required thirty-five
  items, and the substantive test required forty, both tests would be performed using the forty items.

Question 5

Types of Statistical Sampling Plans

Answer 5

a. ** Attributes sampling** (used in tests of controls) reaches a conclusion in terms of a rate of
occurrence—
b. Variables sampling (used in substantive testing) reaches a conclusion in dollar amounts (or
possibly in units).

    (1) **Probability-proportional-to-size** (PPS) **sampling**
     (2) **Classical variables sampling techniques**

Question 6

What are the characteristics of Variables sampling?

Answer 6

• Generally used for substantive testimate
• Estimate value of population based on value of items in sample
• Determine whether or not estimated value is close enough management’s assertion as to valuation
• Testing for a dollar amount

Question 7

Attribute Sampling

Answer 7

• Attribute sampling is ** used for test of controls**
• Used to reach a conclusion about a population in term of rate of occurence
• **Determine whether or not estimate error rate indicates control is working effectively **
• _Deals with deviation rate _ - Errors are stated in terms of %- not dollar amounts
• Attributes sampling is generally used when there is a trail of documentary evidence
• Attribute sampling is based on the binomial distribution which describes yes/no decisions, and error/nonerror situations.

Question 8

How does Sampling Risk compare to Non-Sampling Risk?

Answer 8

• Nonsampling risk includes all aspects of audit risk that are not due to sampling. It is controlled by adequate planning and supervision of audit work and proper adherence to quality control standards. **risk of “human” type errors **(e.g., failure to detect a misstatement).
  Types The followingare examples of nonsampling risk: (a) The failure to select appropriate audit procedures (b) The failure to recognize misstatements in documents examined (c) Misinterpreting the results of audit tests
• Sampling risk is the risk that the auditor’s conclusion, based on a sample, might be different from the conclusion that would be reached if the test were applied in the same way to the entire population (AU-C 530).

Question 9

Sample risk and test of control

What is the risk of assessing Control Risk too high?

Answer 9

• Type I
• Population is okay but the Sample is bad
• Under-rely on Internal Control
• Assess RRM ↑
• More substantive tests expanded beyond the necessary level- Sample overstates Control Risk-
• Leads to an - overall audit inefficiency
• Audit ends up being effective (correct result) - but you do more work

Question 10

Sample risk and test of control

What is the risk of assessing Control Risk too low?

Answer 10

• Type II Error
• Population is bad but the Sample is OK
• Over-rely on Internal Control
• Assess RRM ↓
• Less substantive tests -
• Leads to an - less effective
• Audit ends up being ineffective incorrect result – greater concern

Question 11

Sample risk and substantive test

What is the risk of Incorrect Acceptance?

Answer 11

A risk of Substantive Testing - Auditor accepts a balance as fairly stated- when in fact it is not fairly stated - Hurts audit effectiveness

• Wrong conclusion reached
• related to audit effectiveness
• Type II Error / Beta

Question 12

Sample risk and substantive test

What is the risk of Incorrect Rejection?

Answer 12

A risk of Substantive Testing - Auditor rejects balance as fairly stated when in fact it is fairly stated - Hurts audit efficiency

• Wrong recommendations given
• audit efficiency
• Type I Error

Question 13

Planning Attribute sampling

— Determine the sample size —

Answer 13

In planning for attribute sampling, the auditor should

1) Determine Allowable risk of overreliance or sampling risk (assessing control risk too low)
2) Establish Tolerable deviation rate
3) Determine the Expected population deviation rate
4) Calculate the Sample Size

Question 14

How do you determine if Control Procedures are operating properly or not operating properly?

Answer 14

Control Procedures are either operating properly or they are not operating properly - based on Error Rate and the tolerance you have for errors

Question 15

What is the Tolerable Rate (tolerable deviation rate)?

Answer 15

• Error rate in population **that you are willing to accept/tolerate without modifying the planned level of control risk (RMM) **
• The auditor’s determination of the tolerable deviation rate is a function of
  a] The planned assessed level of control risk.
  b] The degree of assurance desired by the sample.
• Inverse relationship to Sample Size
• Higher Tolerable Rate = Smaller Sample size
• Lower Tolerable Rate = Larger Sample size
• If you’re willing to accept a higher probability that errors exist- there is less pressure on the sample

Question 16

What is the Expected Population Deviation Rate?

Answer 16

• Refers to the % of time the auditor expects the control to have been violated - Judgment call- based on exp__erience
• Direct relationship to Sample Size
• More errors = Larger Sample
• Less errors = Smaller Sample
• Must be lower than the tolerate rate in order for the auditor to rely on a control

Question 17

What is the Allowable Risk of Over-reliance?

Answer 17

• Risk of Assessing Controle Risk too low
• Has an inverse effect on sample size
• Gives you the Sampling Risk

Question 18

Attributes Sampling relationship to sample size

Answer 18

• **_ Inverse_ **relationship to sample size
  
  • ↑ Risk of assessing control risk too low ⇒↓ Sample size
  • ↑ Tolerate rate ⇒ ↓ Sample size
• Direct relationship to sample size
  
  • ↑ Expected population deviation rate ⇒ ↑ Sample size
  • ↑ Population ⇒ ↑ Sample Size (have a very small effect)

Question 19

What is Systematic Sampling?

Answer 19

• Method of selecting the sample - attribute sampling
• Every nth (poplulation/sample size) item is selected after a random start
• Provides every sampling unit in the population an equal change of being selected
• Primary advantage is that population doesn’t require pre-numbering
• One problem is that population may be systematically ordered

Question 20

How does Block Sampling compare to other sampling methods?

Answer 20

Easy to implement- but is the worst method of sampling

Question 21

Random number sampling

Answer 21

• Numbered documents or transaction are selected through the use of random number tables or computer software
• Every sampling unit has the same probability of being selected

Question 22

What is Sequential Sampling / Stop or Go Sampling?

Answer 22

• Also called Stop or Go sampling
• Appropriate when expected population deviation rate is low
• Each audit step determines the next step
• Form of attributes sampling
• No fixed sample size may result in lower sample if few or no error detected

Question 23

What is Discovery Sampling?

Answer 23

• Audit is testing an area that is so crucial that zero population errors can be tolerated - Any phony employees on payroll?
• Discovery samplet sizes is constructed to measure the probability of at least one error occuring in a sample, if the error rate in the population exceeds the tolerable rate
• any error in the sample results in rejection
• sample large enough to detec at least 1 error if it exist

Question 24

Calculation of sample deviation rate

Answer 24

Deviation sample rate = nb of observed deviation / sample size

Question 25

Planning Variable sampling - Determine the sample size -

Answer 25

In planning for Variable sampling, the auditor should 1) considered the **Variation within the population**—Increases in variation (standard deviation in classical sampling) re­sult in increases in sample size. 2) dertermine the **Acceptable level of risk/ Allowable risk of incorrect acceptance** 3) establish **Tolerable misstatement —** As tolerable misstatement increases, sample size decreases. 4) determine the** Expected amount of misstatement or expected variation **— As expected misstatement increases, a larger sample size is required. 5) determine **Population Size** 6) Calculate the **Sample Size**

Question 26

Variable Sampling relationship to sample size

Answer 26

INVERSE * ↑ Risk – **Incorrect Acceptance** ⇒↓ Sample size (**inverse**) * ↑ Risk – **Incorrect Rejection** ⇒↓ Sample size (**inverse**) * ↑ **Tolerate Misstatement** (error) ⇒ ↓ Sample size (**inverse**) DIRECT * ↑ **Expected Misstatement** (error) ⇒ ↑Sample size (**direct**) * ↑ **Population** ⇒ ↑ Sample Size (**direct**) * ↑ **Variation** (standard deviation) ⇒ ↑ Sample Size (**direct**)

Question 27

What are the characteristics of Probability Proportionate to Size (PPS) sampling?

Answer 27

* **A form of dollar unit /variable Sampling** * **Advantages over classical variable sampling ** ## Footnote - Standard deviation not needed - Items with larger dollar amount have a greater probability of being selected * **Disadvantages of PPS** - Understated items have a lower probability of being selected - Items with zero or negative balances are not generally included in the sample * **PPS is most effective when** - Few or no errors are expected - The auditor is concerned about overstatement of the account **NOTE**: The risk of incorrect rejection is not typically controlled when using PPS sampling, but is controlled when using classical methods.

Question 28

Calculation Projected Misstatement PPS

Answer 28

* **Misstatement =** Book amount **-** Audited amount * **Tainting Factor** **=** Misstatement/Book amount * **Projected misstatement** * if SI\> Book amount * PM=TF x SI * if SI \< or = Book amount * PM = Misstament

Question 29

What is Classic Variable Sampling?

Answer 29

Classical variable sampling models **use normal distribution theory to evaluate selected characteristic of a population on the basis of a sample of the items constituting the population** **Variations of classical variables sampling** * Mean per estimation * Difference estimation * Ratio estimation - can not be used when there is no book value to make a comparaison, appropriate when testing a population for which a large number of errors of this nature is expected * Regression estimation * Difference and ration estimation - used as an alternative to mean per unit estimation

Question 30

**Comparison of PPS Sampling to Classical Variables Sampling **

Answer 30

**a. Advantages of _PPS_ sampling** (1) Generally easier to use. (2) Size of sample not based on variation of audited amounts. (3) Automatically results in a stratified sample. (4) Individually significant items are automatically identified. (5) Usually results in a smaller sample size if no misstatements are expected. (6) Can be easily designed and sample selection can begin before the complete population is available. **b. Advantages of classical variables sampling** (1) May result in a smaller sample size if there are many differences between audited and book values. (2) Easier to expand sample size if that becomes necessary. (3) Selection of zero and negative balances does not require special sample design considerations.

Question 31

Calculation of Sampling Interval and Sample Size - PPS

Answer 31

* **Sampling Interval =** Tolerable misstatement **/ ** Reliabity factor from table (or population amount / sample size) * **Sample size =** Population amount **/** Sampling Interval

Question 32

Ratio estimation

Answer 32

**Ratio estimation **is a classical variables sampling technique that uses the ratio of audited amounts to recorded amounts in the sample to estimate the total dollar amount of the population and an allowance for sampling risk. e ratio estimation sampling technique is based upon comparing the ratio of the book value to the audited value of the sampled items Ratio estimation **= (Sample AV/Sample BV) × Population BV**

Question 33

Difference estimation and ratio estimation ## Footnote more efficient because the differences between audit and book values are expected to vary less than the actual items in the population.

Answer 33

* Difference estimations and ratio estimations **are classical variables sampling techniques** * Difference estimations and ratio estimation are u**sed as alternatives to mean-per-unit estimation.** The auditor should use these approaches when applicable because **they require a smaller sample size** (i.e., they are more efficient than mean-per-unit estimation). ## Footnote (a) One factor in the calculation of sample size for classical variables sampling models is the estimated standard deviation. **If the standard deviation of differences or ratios is smaller than the standard deviation of audit values, these two methods will produce a smaller sample size.** * *1] Difference estimation** will be used if the differences between sample audit values and book values are a relatively constant dollar amount, regardless of account size. * *2] Ratio estimation** will be used if the differences are a constant percentage of book values. (b) In order to use either difference or ratio estimation, **the following constraints must be met**: 1] The individual book values must be known and must sum to the total book value. 2] There must be more than a few differences (20 is often suggested as a minimum) between audit and book values. (c) **These two methods will usually be more efficient than mean-per-unit estimation when stratification of the population is not possible**. **The regression approach is similar to the difference and ratio approaches**. This approach has the effect of using both the average ratio and the average difference in calculating an estimate of the total amount for the population.