Distinguish between:
a) Attribute sampling and variable sampling
b) Sampling risk and non sampling risk
c) Alpha risk and beta risk.

Attribute sampling and variable sampling

Attribute refers to presence or absence of any character. For example, test of control, matching of delivery note with sales invoice is an attribute. The attribute sampling refers to statistics relating to test controls and measures presence of controls or deviations from prescribed procedures. The attribute sampling may be used for example to discover rate of deviations in payroll processing or cash disbursements.

Variable sampling is applied to account balance verification and measures the accuracy of amounts in account balances. For example, an auditor may use variable sampling for accounts receivable, inventories and fixed assets balances.

Sampling risk and non sampling risk

Sampling risk refers to the fact that sample selected by the auditor may not be representative of population. As a result the rate of deviation or monetary error may not be proportionate to these found in the population. The risk can be reduced by increasing sample size. There an inverse relationship between sample size and sampling risk. That is, the greater the sampling size the lower will be the sampling risk. Accordingly, if all items in a population are checked, the sampling risk ill be zero.

Non sampling risks refer to all aspects of audit risks not due to sampling. For example use of an inappropriate audit procedures, or misinterpreting the errors, or reliance on erroneous information received from another party.

Alpha risk and beta risk

The risk of incorrect rejection is called alpha risk. The consequence of the risk is that the auditor may assume on the basis of sample results that a population is materially misstated when, in fact, it is not.

The risk of incorrect acceptance is called beta risk. The consequence the risk is that the auditor may assume on the basis of sample results that the population is free of material misstatement when in fact material errors exist in the population.

List the matters that the auditor should document in relation to sampling?

Following matters should be documented when sampling is used.
a) Objective of test
b) Population
c) Sample units
d) What constitutes an error?
e) Sample size
f) Basis of selection
g) Errors found
h) Evaluation and conclusion

When is it appropriate to examine the entire population of items that make up an account balance or class of transactions during the course of substantive audit procedures?

It will be appropriate to examine the entire population of items that make up an account balance or class of transactions when the population constitutes a small number of large value items; when both inherent and control risks are high and other means do not provide sufficient appropriate audit evidences or when the repetitive nature of a calculation or other process performed by a computer information system makes a 100% examination effective.

Define anomalous error. How should it be treated at the time of
projecting sample errors to population?

Anomalous error means an error that arises from an isolated event that has not recurred other that on specifically identifiable occasion and is therefore not representative of errors in the population.

In projecting the error, anomalous error is first excluded to estimate total projected error. Thereafter such error will be added to projection of non anomalous errors.

Find out the amount of projected misstatement from the
following information? 


Total population 3,453,000
Total population includes items over Rs. 100,000       600,000
These were 100% selected

The errors found in account balances over
.100,000 amounted to                                                   6,060

pie value of accounts up to Rs. 100,000                      410,000
Errors found in account balances up to Rs. 100,000    7,052

Sample value of accounts up to Rs. 100,000                 410,000
Errors found in account balances up to Rs. 100,000      7,052
Error as percentage of total sample 1.72%

Total population                                                              3,453,000

Last Items over Rs. 100,000.                                           600,000



Add errors found in accounts over Rs. 100,000        1.72%


Projected misstatement                                            55,132

Enumerate imitations of sampling

Certain limitations of sampling are:

1. Sample may not be representative of population
2. Auditor’s judgment is required in selecting sample size
3. Judgments are also required in drawing conclusions from sample results.
4. The auditor may use inappropriate population or the population may not be complete.

Explain difference between statistical and non statistical sampling

Statistical sampling is any approach to sampling that uses:
a) random sample selection; and
b) probability theory to:
(i) evaluate sample results quantitatively; and
(ii) measures sampling risk

Non statistical sampling is any approach which does not fulfill all the
characteristics necessary for statistical sampling. Non statistical sampling is also called judgmental sampling.

ISA 530 states that a clear understanding of what constitutes a misstatement is important to ensure that all, and only, those conditions that are relevant to the objectives of the audit procedures are included in the projection of errors. For example, in test of details relating to existence of accounts receivable, such as confirmation, payment made by the customer before the confirmation date but received shortly after that date by the client are not considered as error. Also a posting between customer accounts does not affect the total accounts receivable. Therefore it is not appropriate to consider this an error in evaluating the sample results of this particular audit procedure.

In order to send confirmation letters to customers, the auditor has stratified the receivables as follows:

Less than Rs. 1,000                            400 120,000
Rs. 1,000 to Rs. 10,000                      300 2,100,000
Over Rs. 10,000                                  50 800,000


                                                            750 3,020,000


The auditor did not select any account from first stratum on the grounds  of materiality. From stratum three 100% items were selected and with a nominal exception, all were confirmed. From stratum 2, 30 items were selected on the basis of every 10th item. Value of such 10th items was Rs. 235,000.

Confirmation statistics of the 30 items selected reveals

Confirmed                      160,000
Disagreed                       65,000
No response                   10,000

Those who have not confirmed were satisfactory verified by subsequent collections.

Details of those who have disagreed and the amounts of disagreement refelect. 


Project the misstatement

If the in transit items have been subsequently cleared, these are not
considered as error. Similarly mis posting is not an error in the context of total trade receivables.

Total errors (Rs. 15,000+4-,000)

Projection error

Samplesize                                            235,000
Errors found (Rs. 15,000+4,000)           19,000
Percentage of sample                             8.1%
Population                                              2,100,000

Projected error
8.1% o Rs. 2,100,000                             170,100

You are the audit manager on a client where an annual sale is Rs. 640 million. During the course of annual audit the following table was developed by an audit team member, to categorize the annual sales:

Category A 50 sales transactions to different customers  300m
Category B 100 transactions to different customers         200m
Category B 100 transactions to different customers         200m

Total                                                                                 640m 

Sohail, a team member, is of the view that if verification of the transactions in category A is carried out, there is no need perform further procedures. However, other team member not agree and consider that proper sampling should be earn out from the total population and categorization should ignored.

As an audit manager of the job, you are required to:

(i) Explain how audit efficiency could be improved by using the above table.
(ii) List other ways in which the sales population may be categorized and what precaution should be taken while carrying out such categorization.
iii) Give your opinion on the views expressed by: 

        – Sohail Other audit team members.
        – Other audit team members.

b) Describe the circumstances in which an auditor may decide to examine entire population of items that make up an account balance.

a) (i) Audit efficiency may be improved as the auditor has stratified a
population by dividing it into discrete sub-populations which have an identifying characteristic. The stratification reduces the variability of items within each stratum and therefore allow sample size to be reduced without a proportional increase in sampling risk.

ii) Other ways by which sales population may be stratified are as under:

– Byproduct
– By customers or category of customers
– Geographically
– Terms of sales such as credit and cash.

sub-categorizationlsub-populations need to be carefully defined such that any sampling unit can only belong to one stratum.

iii) Views expressed by Sohail:

His view that if verification of total transaction of category A is carried out than there is no need to perform further procedures is not correct due to the following reasons:

– The results of audit procedures applied to all the items within category A can only provide evidence about the items that make up that category (stratum).

– The, auditor should obtain sufficient appropriate audit evidence regarding items in Categories B & C as these are also material.

Views expressed by other audit team members:

Their view that proper sampling should be carried out from the total population of 640 million and categorization should be ignored altogether is not correct because stratification helps in improving the efficiency of the audit.

(b) Circumstances in which an auditor may decide to examine entire
population of items that make up an account balance.

The auditor may decide to examine the entire population in the following circumstances:

-When the population constitutes a small number of large value items.

– When there is a significant risk and other means do not provide sufficient appropriate audit evidence; or

– When the repetitive nature of a calculation or other process performed automatically by an information system makes a 100% examination cost effective.

You have recently joined a medium size charted accountants firm as their audit manager. While reviewing the firm’s audit methodology you have observed that the firm follows a standard set of audit work programs. These work programs have been used by the firm for the last many years and rely extensively on traditional judgment sampling. You are of the opinion that by following the statistical sampling techniques, you would be able to carry out a more effective and efficient audit.

Briefly narrate the advantages and disadvantages of judgmental and statistical sampling.


1. The approach is well understood
2. Users are aware of its limitations
3. Auditor’s judgment is promoted
4. Time saving
5. More useful to detect overstatement of assets and revenues.

1. Difficult to prove that the sample size selected is adequate
2. Sampling risk cannot be quantified
3. The sample selection may be biased.


1. Sampling risk can be quantified
2. The basis of sample size can be justified
3. Bias is avoided
4. Efficient and effective audit
5. Standardized approach

1. Statistical techniques are not a substitute of human judgment
2. Generally not well stood
3. Not efficient to detect overstatement.

(a) You are the audit manager in a firm of Chartered Accountants. The audit seniors on various jobs have sought your advice in respect of the following independent situations:

(i) The expected rate of deviation based on the auditor’s understanding of controls has increased to an extent which is unacceptably high.

(ii) Number of debtors has increased from 4,500 to 5,000 and the amount of debtors as a percentage of total assets has also increased.

(iii) The expected amount of mis-statement has decreased from Rs. 300,000 to Rs. 200,000f whereas the monetary amount in respect of which an appropriate level of assurance is required has increased by Rs. 50,000.

State with reasons, the effect of each of the above issues on the sample size of:

(i) Tests of controls and
(ii) Substantive procedures

(b) While determining the sample size for tests of controls, the auditor takes into account the expected rate of deviation. State the factors that are relevant to the auditor’s consideration of the expected rate of deviation.

(c) Differentiate between the tolerable mis-statement and performance materiality.

(a)(i) The expected rate of deviation based on auditor’s understanding of control has increased to an extent which is unacceptably high:

(1) Effect on sample size of test of control:

No test of control will be performed because controls cannot be relied on to reduce risk to acceptable level.

2) Effect on sample size of substantive procedures:

No effect as “rate of deviation” relates to tests of control and no to substantive procedures.

(ii) Number of debtors has increased from 4,500 to 5,000 and the amount of debtors as a percentage of total assets have also increased.

(1) Effect on sample size of test of controls:

Negligible effect. For large population, say above 2,000 items, the size of population has little effect on sample size.

(2) Effect of sample size of substantive procedures:

Negligible effect. For large population, say above 2,000 items, the size of population has little effect on sample size.

(iii) The expected amount of misstatement has decreased from Rs. 300,000 to Rs. 200,000 whereas the monetary amount in respect of which an appropriate level of assurance is required has increased by Rs. 50,000.

(1) Effect on sample size of test of controls:

No effect, as the factor relates to substantive procedures.

(2) Effect on sample size of substantive procedures:

Both the factors result in reducing sample size.

(d) Following factors are relevant to the auditor’s consideration
of the expected rate of deviation:

(i) Auditor’s understanding of the business, in particular, risk assessment procedures undertaken to obtain an understanding of internal control.

(ii) Changes in personnel or in internal controls.

(iii) The results of audit procedures applied in prior periods and

(iv) The results of other audit procedures.

(e) Tolerable misstatement and performance materiality:

Tolerable misstatement is a monetary amount set by the auditor in respect of which the auditor seeks to obtain an appropriate level of assurance that the monetary amount set by the auditor is not exceeded by the actual misstatement in the population.

Performance materiality means the amount or amounts set by the auditor at less than materiality for the financial statements as a whole to reduce to an appropriately low level the probability that the aggregate of uncorrected and undetected misstatements exceeds materiality for the financial statements as a whole. Performance materiality also refers to the amount or amounts set by the auditor at less than the materiality level or levels for particular classes of transactions, account balances or disclosures.

(a) Differentiate between the following:
(i) Statistical and non-statistical sampling
(ii) Sampling and non-sampling risk

b) You are the audit manager on Apple Distribution Limited
(ADL). While reviewing the audit planning documentation, you
found that the audit team has selected 100 out of a total of 2,550 debtors for balance confirmation. The details are as follows:

– 50 largest debtors constitute approximately 40% of total debtors. Out of these, 10 have been selected.

– 90 other debtors were selected through haphazard sampling.

– All debtors below Rs. 5,000 were ignored as immaterial.

– Balance due from government and some of the related parties were ignored as prior years working papers showed that they never responded to requests for confirmation.

(i) Comment on the sampling approach adopted by the audit team.
(ii) Suggest alternative means of selecting the sample in which the material balances have a greater probability of selection.

(a) (i) Statistical and non-statistical sampling

An approach to sampling that has the following characteristics called statistical sampling:
– Random selection of the sample items; and

– The use of probability theory to evaluate sample results, including measurement of sampling risk.

A sampling approach that does not have above characteristics is considered non-statistical sampling.

(ii) Sampling and non-sampling risk

Sampling risk is the risk that the auditor’s conclusion based on a sample may be different from the conclusion if the entire population were subjected to the same audit procedure.

Non sampling risk is the risk that the auditor may reach an erroneous conclusion for any reason not related to sampling risk.

(b)(i) The following shortcomings have been observed in the approach adopted by the Audit Team:

– By ignoring less than Rs. 5,000 debtors, the government debtors and some of the related parties, for the purpose of sampling, the following important principles have not been complied with.

– That the auditor should consider the risk of material misstatement on the entire population.

– That the auditor should attempt to ensure that all items in the population have a chance of selection.

– In stratification, the audit efforts are directed towards larger value items. However, the audit planning documentation should explain why the only 10 debtors out of 50 largest debtors were selected.

(ii) Alternative means of sampling material balances are as follows:


This would involve dividing the sample into discrete sub populations
(stratum) which have an identifying characteristics. In Our Case our case, the population may be stratified by monetary value. For example, following strata may be created:

– Above Rs. 1,000,000
– Between Rs. 500,000 and Rs. 1,000,000
– Below Rs. 500,000.

The sample may be made from each strata allowing effort to be directed to the larger value items.

 Value weighted selection (Monetary unit sampling)

When performing test of details, it may be efficient to identify sampling as the individual monetary units that make to the population. In this method, each monetary unit in a population has an equal chance of being selected for testing. Audit effort is directed to the larger value items because they have a greater chance of selection, and can result in smaller sizes.

Explain sampling risk and non-sampling risk? 

Sampling risk

Sampling risk is the possibility that the sample may not be representative of population. As a result, the auditor’s conclusions based on the entire sample may be different from what would have been the conclusions had the auditor verified entire population.

Sample risk for tests of controls

For test of control two types of sampling risk exist

1. Risk of over reliance 
Risk of over reliance is the risk that the auditor assesses control risk too low than it actually is. The risk is quite serious as the auditor will inappropriately reduce substantive procedures. As a result, the audit effectiveness is reduced.

2. Risk of under reliance
Risk of under reliance is the risk that the auditor assesses control risk (based on sample selected) to be too high than it actually is As a result it affects audit efficiency because the auditor will unnecessarily perform more substantive testing than is necessary.

Sampling risk for substantive procedures

For substantive procedures, two.types of risks exist.

1. Risk of incorrect acceptance (beta risk)
It is the risk that sample results will indicate that an account balance is not materially misstated when, in fact, it is materially misstated. In such a case the effectiveness of audit is impaired as it may lead to inappropriate audit opinion.

2. Risk of incorrect rejection (alpha risk)
It is the risk that sample results will indicate that an account balance is materially misstated when, in fact it is not misstated. This risk will affect audit efficiency because unnecessarily additional procedures will be performed

Nonsampling risk

Non sampling risk arises due to following reasons:

a) Audit procedures applied may not be relevant to the purpose test
b) Failure to recognize misstatement in the documents
c) Misinterpretation of a fact
d) Reliance on the responses of another party.

State the difference between tolerable misstatement and tolerable rate of deviation? 

In the context of sampling, tolerable misstatement is the application of materiality  to individual accounts.

For example, if total assets Rs. 700,000 include inventories Rt 200,000, and the materiality is 2% of total assets, materiality level is Rs. 14,000. Tolerable misstatement for inventories is Rs. 4,000 (2% of Rs. 14,000).

Tolerable rate of deviation is the maximum rate of deviation auditor will accept and still conclude that the internal controls are effectively operating.

Tolerable rate of deviation is the maximum rate of deviation auditor will accept and still conclude that the internal controls are effectively operating.

Discuss matters to be considered in designing a sample? 

Sample designing involves
– Purpose of the test
– Population from where sample is to be drawn
– Audit procedure to achieve objective
– Identification of misstatement or deviation

For example:

Purpose of test : To detect overstatement of accounts payable

Population: Suppliers invoices recorded during few days before end of accounting period

Audit procedure: Compare suppliers’ invoices with GRNs

Possible misstatement: Those suppliers’ invoices which are not supported by GRNs

If the purpose of test is to detect understatement of accounts payable:

Purpose of test: To detect understatement of accounts payable

Population: Goods received notes issued during a few days before end of accounting Population Period.

Audit procedure: Compare GRNs with suppliers’ invoices

Possible misstatement: Those GRNs where related invoices have not been recorded in purchase day book.

Note that the population from which sample is drawn and audit procedure should be relevant purpose of test.

If the purpose of test is to ensure that dummy payables have not been recorded, the sample will be drawn from accounts payable recorded by the client to ensure their validity. The validity is verified by ensuring that the goods have been received before the end of accounting period as evidenced by GRN.

If the purpose is to detect understatement of accounts payable, the list of recorded payables is not a relevant population because we are more interested in searching for unrecorded liabilities rather than the liabilities which have already been recorded by the client. The purpose of the test will be achieved if we compare GRNs (for which goods have been received) to suppliers invoices to ensure that liabilities have been set up for such goods.

Discuss sampling methods? 


1. Stratification is a technique of dividing population into sub population.

2. The sub population is generally based on monetary values

3. The technique is used in test of details and is particularly appropriate to detect overstatement of assets.

4. By using small sample size which covers large values in an account, audit efficiency and audit effectiveness are increased.

5. Generally, all items over book value of tolerable misstatement are tested. Systematic selection method may be used on remaining items.

6. Class intervals are called strata

7. The sample results are evaluated for each stratum separately.

8. Stratification reduces variability within the population.


1. Value weighted selection or monetary unit sampling involves computing sampling interval by dividing sample size with population value.

2. The population is made up of fixed monetary units.
3. First item is selected randomly, other items selected are those which contain that monetary unit.
4. The method is useful to detect overstatement of asset or revenues
5. Value weighted technique makes sure that all items above the monetary units are selected. Small balances stand a lower chance of being selected.
6. This technique is more appropriate when the population consists
of small number of high value items.


1. Systematic selection involves dividing population units by the sample size and selecting every nth item. The first item is selected randomly.
2. The method is quite simple to apply
3. Auditor’s bias is reduced
4. The bias can further be avoided but taking two starting numbers
5. The technique can be used even if the documents are not sequentially numbered
6. Auditor this technique all items whether high value or low value have an equal chance of being selected.
7. Under this technique all items whether high value or low value have an equal chance of being selected.


1. Random number tables contain rows and columns. Such rows and columns are absolutely arbitrary.
2. The numbers are meaningless

3. The auditor should use the random number table of the same digits as contained in the population.
4. The auditor reads the column and selects a starting point and marks the sampling unit to be selected.
5. The selection is complete when the desired sample size has been identified.
6. The starting point is selected randomly
7. If the same number is selected twice, the duplicate number can be ignored without increasing size.
8. The method avoids auditor’s bias and all sampling units have a chance of being selected.
9. The numbers can be read top to bottom or right to left.


1. In block selection, all items contained in the particular blocks are verified.
2. The blocks normally- consist of numeric sequence or specificy months. For example, an auditor may select following blocks of sales invoices:


All invoices in the above blocks will be verified. Further sampling is not advisable.

3. The blocks may also consist of particular months. For example, sales invoices issued during March, June, and August 2013.

4. Block sampling is not encouraged as all items in the population do not have a chance of being selected.


  1. Items are selected on arbitrary basis
  2. However the auditor should avoid bias, as much as possible so that the sample should be representative of population.
  3. This method should not be widely used because it does not have any basis.

Discuss projection of misstatement?

Projection of misstatement is an estimate of the most likely amount of monetary misstatement in a population.


Projected misstatement is compared with tolerable misstatement. If the projected misstatement is less than tolerable misstatement, the auditor will conclude that the account balance is reasonable. If the projected misstatement is close to tolerable misstatement, the risk of material misstatement in the account is too high. In such a case their auditor request the client to correct the identified misstatements or perform additional audit procedures.

The auditor should also evaluate qualitative evaluation of misstatements For example, if the misstatements identified indicate existence of fraud the auditor will be more. concerned than misstatements resulting from clerical errors.

Discuss some factors that would affect sample size for tests of control? 

1. The auditor intends to place more reliance on int control in order to reduce substantive procedures

A large sample for test of control is required to provide more assurance that controls are effectively operating.

2. The auditor’s tolerable rate of deviation is relatively low

If tolerable rate of deviation is low, a large sample size is required to confirm that the deviations are not excessive.

3. High expected rate of deviation

A low expected rate of deviation may require a low sample size; a higher expected rate of deviation requires selection of large sample size. However, if expected rate of deviation is unacceptably high, no test of controls need be performed as the auditor would not place any reliance on internal control.

Increase in desired level of assurance

Same as in (l) above

State the matters to be considered in evaluation cause and nature of deviation?

The auditor should consider following qualitative aspects in evaluating and nature of deviations.

– Whether the deviation is anomaly or repetitive?
– Whether the deviation is intentional or unintentional?
– Whether the deviation is due to override of control by mangement?
– Inexperienced employee?
– Human error?
– Misunderstanding?
– Whether the deviation directly affects financial statements?

Posted on November 3, 2015 in AUDIT SAMPLING

Share the Story

Back to Top