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AUDITING THEORY

Red Sir ug AUDIT SAMPLING (And Other Means of Test ing)

Means for Selecting Items for Testing to Obtain Audit Ev idence: When designing tests of controls and tests of details, the auditor shall determine the means of selecting items for testing that are effective in meeting the purpose of the audit procedure. The means available to the auditor for selecting items for testing are (the auditor may use any one or combination of these): a. Selecting all items (100% examination); b. Selecting specific items; and c. Audit sampling Select ing All Items (100% Examinat ion): Select ing all items – involves examining the entire population of items that make up a class of transactions or account balance 100% examination is: More common for tests of details Unlikely for tests of controls Appropriate when: The population constitutes a small number of large value items There is significant risk (high RMM) and other means do not provide sufficient appropriate audit evidence, or Cost effective – the repetitive nature of a calculation or other process performed automatically by an information system makes a 100% examination cost effective (for example, using computer-assisted audit techniques (CAATs) Select ing Specific Items:

Select ing specific items – judgmental selection of specific items from a population based on the following factors: Auditor’s understanding of the entity Assessed risk of material misstatement Characteristics of the population being tested Specific items that may be selected by the auditor include: High value or key items . The auditor may examine items of high value or items that exhibit some other characteristic (for example, items that are suspicious, unusual, particularly risk-prone or that have a history of error). All items over a certain amount. The auditor may decide to examine items whose values exceed a certain amount so as to verify a lar ge proportion of the total amount of a class of transactions or an account balance. Items to obtain information. The auditor may examine items to obtain information about matters such as the nature of the entity or the nature of transactions. Items to test control activities . The auditor may use judgment to select and examine specific items to determine w hether or not a particular control activity is being performed.

Selecting specific items for examination does not constitute audit sampling and therefore, not subject to sampling risk. The results of audit procedures applied to selected specific items cannot be projected to the entire population; accordingly, selective examination of specific items does not provide audit evidence concerning the remainder of the population.

Audit Sampling:

Audit sampling (sampling) – the application of audit procedures to less than 100% of the items within a population of audit relevance (account balance or class of transactions) such that all sampling units have a chance of selection in order to provide the auditor with a reasonable basis on whi ch to draw conclusions about the entire population Audit sampling is the means that enable the auditor to draw conclusions about the population on the basis of testing a sample draw n from it. Sampling is essential throughout audits as auditors attempt to gather sufficient appropriate evidence in a cost efficient manner. Audit sampling is not required part of any audit procedure because when designing audit procedures, the auditor should determine appropriate means of selecting items for testing. Audit sampling is used for both tests of controls (attributes sampling) and for tests of details of transactions and balances ( variables sampling). In both attributes sampling and variables sampling, the plans may be either non-statistical or statistical. AT – Audit Sampling

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Audit Sampling Ter ms: Populat ion – the entire set of data from which a sample is selected and about which the auditor wishes to draw conclusions Sample – the portion of the population that will be subjected to audit testing Sampling unit – the individual items constituting a population; also known as population item, observation, or elementary unit Representative sample – a sample in which the characteristics of the sample are the same as those of the population Sampling risk – 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. Anomaly – a misstatement or deviation that is demonstrably not representative of misstatements or deviations in a population Confidence level – the mathematical complements of sampling risks; also known as reliability or

confidence Stratificat ion – the process of dividing a population into sub-populations, each of which is a group of

sampling units which have similar characteristics (often monetary value) Tolerable misstatement (in substantive procedures) – 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; it is the maximum total error in a population that the auditor is willing to accept Tolerable rate of deviat ion (in tests of controls) – a rate of deviation from prescribed inter nal control procedures set by the auditor in respect of w hich the auditor seeks to obtain an appropriate level of assurance that the rate of deviation set by the auditor is not exceeded by the actual rate of deviation in the population; it is the maximum rate of deviation from the prescribed control procedure the auditor is willing to accept without changing control risk assessment or planned reliance on internal control Error – either contr ol deviations, when performing tests of contr ol, or misstatements, w hen performing substantive procedures. Total error – either the rate of deviation (in case of tests of control) or total misstatement (in case of substantive procedures) Anomalous error – means an error that arises from an isolated event that has not recurred other than on specifically identifiable occasions and is therefore not representative of errors in the population Expected error – a. Expected error amount – in substantive tests, it is the auditor's best estimate of the amount of error the auditor expects to find in the population b. Expected deviat ion rate – in tests of control, it is the auditor's best estimate of the rate of deviation from a prescribed control procedure in the population

Applicability of Audit Sampling: Where an auditor has no special knowledge about likely misstatements contained in account balances and transactions When the auditor believes that the sample is to be a good representative of the population Inapplicability of audit sampling: Situations w here audit sampling generally do not apply: a. Risk assessment procedures performed to obtain an understanding of internal control. b. Tests of automated application controls when effective general controls are present. (Generally, such contr ols would only be tested once or a few times.) c. Analyses of security and access contr ols, or other controls that do not provide documentar y evidence of performance (e.g., controls related to segregation of duties). d. Some tests related to the operation of the control environment or the accounting system (e.g., examination of the effectiveness of activities performed by those charged with governance). Lists procedures that do not involve sampling: a. Inquir y and obser vation b. Analytical procedures c. Procedures applied to ever y item in a population d. Tests of controls where application is not documented e. Procedures from which the auditor does not intend to extend a conclusion to the remaining item in the account (for example, tracing several transactions through accounting system to obtain understanding) f. Untested balances General Approaches to Audit Sampling: 1. Statistical sampling – an approach to sampling that has the following characteristics: a. Random selection of a sample; and b. Use of probability theor y to evaluate sample results, including measurement of sampling risk

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2.

Statistical sampling applies the law of probability theor y to aid the auditor in designing a sampling plan and evaluating sample results. In statistical sampling, auditors specify the sampling risk they are willing to accept and then calculate the sample size that provides that degree of reliability. Results are evaluated quantitatively. Statistical sampling measures quantitatively the sampling risk (the risk from testing only part of an audit population). Advantages of statistical sampling: Conclusions may be drawn in more precise ways when using statistical sampling because it enables the auditor to: a. Measure the sufficiency of the audit evidence obtained. b. Provide an objective basis for quantitatively evaluating sample results –more objective audit evidence c. Design an efficient sample. d. Quantify/measure sampling risk so as to limit it to an acceptable level. e. Measure reliability (confidence level), precision, and sampling error (sampling risk). Disadvantages of statistical sampling: Danger of accepting statistical evidence at face value without sufficient skepticism Its cost could exceed the benefits Inappropriate it some cases (for example, test of controls that depend on segregation fo duties or otherwise provide no audit trail of documentary evidence) In statistical sampling, random sample selection methods should be used to give all items in the population an equal chance to be included in the sample to be audited.

Non-statistical sampling – a sampling approach that does not have both characteristics of statistical sampling Non-statistical sampling (or judgment sampling) is based solely on the auditor’s judgment. The sample size is not determined mathematically. Auditors rely exclusively on subjective judgment to determine sample size and to evaluate sample results. A properly designed non-statistical sampling application can be as effective as statistical sampling application. One disadvantage is that it can misdirect an auditor to unreliable sampling units. Additional notes on statistical and non-statistical sampling: Statistical sampling is a mathematical approach to inference, whereas non-statistical sampling is a more subjective approach. Conclusions may be drawn in more precise ways when using statistical sampling methods. Both sampling approaches involve judgment in planning, executing the sampling plan, and evaluating the results of the sample. It is acceptable for auditors to use either or combination of statistical and non-statistical sampling. The choice is based primarily on the auditor’s assessment of the relative costs and benefits. Such choice is independent of the selection of audit procedures because audit sampling is merely a means for accomplishing audit procedures. Both sampling approaches can pr ovide sufficient appropriate evidence. Sampling methods are used by auditors in both control testing and substantive testing.

Auditor’s professional judgment: Although statistical sampling aids the auditor in quantitative ways, it is not a substitute for professional judgment. In other wor ds, statistical sampling does not eliminate the need for the auditor’s professional judgment. The auditor must exercise professional judgment in both statistical and non-statistical sampling to: a. Define the population and the sampling unit; b. Select the appropriate sampling method; c. Evaluate the appropriateness of audit evidence; d. Evaluate the nature of deviations or errors; e. Consider sampling risk; and f. Evaluate the results obtained from the sample and project those results to the population. Types of Audit Sampling Plan: Audit sampling is used for both tests of controls (attributes sampling) and for tests of details of transactions and balances (usually, variables sampling). In both attributes sampling and variables sampling, the plans may be either non-statistical or statistical. 1. Attribute sampling – estimates the attribute or quality characteristic of a population Applicable to tests of controls because attribute sampling deals with estimating deviation rate (also called rate of occurrence) from prescribed control procedures that the auditor plans to rely upon 2. Variables sampling – estimates the numerical quantity of a population Applicable to substantive testing because variables sampling deals with peso or monetary amount of misstatement in account balances

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Ordinarily, risk assessment procedures to obtaining understanding of the entity and its environme nt, including internal control, do not involve the use of audit sampling. Audit sampling for substantive procedures applies to tests of details only.

Sampling Risk:

Sampling risk – the possibility that the auditor’s conclusion, based on a sample may be different from the conclusion reached if the entire population were subjected to the same audit procedure. The risk that the sample is not representative of the population and that the auditor's conclusion will be different from the conclusion had the audi tor examined 100% of the population. The possibility that even though a sample is properly chosen, it may not be representative of the population. Sampling risk can be reduced by increasing the sample size. Sampling risk is an inherent part of sampling tha t results from testing less than the entire population. Two Types of Sampling Risk: 1. Risk that affects audit effectiveness and may lead to an inappropr iate audit opinion (“Beta risk” or “Type II error”) – the risk the auditor will conclude that: a. Risk of assessing control risk too low – in case of a test of control, that the assessed control risk is lower than it actually is b. Risk of incorrect acceptance – in case of a substantive test, conclusion that a material error does not exist w hen in fact it does 2. Ris k that affects audit efficiency as it would usually lead to addit ional wor k to establish that initial conclusions were incorrect (“Alpha risk” or “Type I error”) – the risk the auditor will conclude that: a. Risk of assessing control risk too high – in case of a test of control, that the assessed control risk is higher than it actually is b. Risk of incorrect rejection – in case of a substantive test, conclusion that a material error exists when in fact it does not Aspects of Audit Risk(Aspect of detection r isk): Audit risk is a combination of the risk that a material misstatement will occur (inherent risk and control risk) and the risk that it will not be detected by the auditor (detection risk). 1. Sampling r isk – the risk or the possibility that, when a test of controls or a substantive test is restricted to a sample, the auditor's conclusions base on a sample may be different from the conclusions which would have been reached had the tests been applied to all items in the population Sampling risk is the aspect of audit risk and of detection risk that is due to sampling. Aspects of sampling r isk: a. Substant ive testing sampling r isks: 1) Risk of incorrect acceptance – the risk that the auditor will conclude that a material error in an account balance (based on the sample) does not exist when in fact it does (i.e., sample results fail to identify an existing material misstatement). 2) Risk of incorrect rejection – the risk that the auditor will conclude that a material error in an account balance exists w hen in fact it does not (i.e., sample results mistakenly indicate a material misstatement). b. Tests of controls sampling risks: a. Risk of assessing control risk too high or the risk of under reliance (Alpha risk or Type I error) – the risk that the assessed level of contr ol risk (based on the sample) is greater than the true level of control risk (i.e., sample results indicate a greater deviation rate than actually exists in the population). This risk means that the auditor wrongly concludes that the control risk is higher than it actually is. This risk relates to audit efficiency as it w ould lead o additional w ork. If the auditor assesses control risk too high, substantive tests will consequently be expanded beyond the necessary level, leading to audit inefficiency. b. Risk of assessing control risk too low or the risk of over reliance (Beta risk or Type II error) – the risk that the assessed level of control risk (based on the sample) is less than the actual/true level of control risk (i.e., sample results indicate a lower deviation rate than actually exists in the population). This risk means that the auditor wrongly concludes that the contr ol risk is lower than it actually is. This risk relates to audit effectiveness. If the auditor assesses control risk too low, substantive tes ts will not be expanded to the necessar y level to ensure an effective audit. This would more likely lead to an inappropriate audit opinion. Analysis of Sampling Risks:

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Aspects of sampling r isks

Risk of incorrect acceptance

Risk of incorrect rejection

Risk of assessing control risk too low (risk of over reliance) Risk of assessing control risk too high (risk of under reliance)

2.

Auditor’s wrong conclusion Not materially misstated when in fact materially misstated

Effect on audit wor k because of wrong conclusion Performance of less extensive substantive tests

Materially misstated when in fact not materially misstated ↓CR than actual CR – internal control is reliable

Additional wor k (performance of unnecessary more extensive substantive tests) Performance of tests of controls and less extensive substantive tests

↑ CR than actual CR – internal control is not reliable

Additional wor k (because non-performance of tests of controls would lead to the per formance of unnecessary more extensive substantive tests)

Sacrificed Effect iveness of the audit because it may lead to inappropriate opinion due to inappropriate less extensive substantive tests Efficiency of the audit because of unnecessar y additional wor k

Effect iveness of the audit because it may lead to inappropriate opinion due to inappropriate less extensive substantive tests Efficiency of the audit because of unnecessar y additional wor k

Non-sampling risk – the risk that the auditor reaches an erroneous conclusion for any reason not related to sampling risk Examples of non-sampling risk: The auditor might use/select inappropriate audit procedures (audit procedures that are not appropriate to achieve a specific objective) The auditor might misinterpret evidence or the results of audit tests The auditor may fail to recognize an error (for example, failure by the auditor to recognize a misstatement or deviation in documents examined)

Non-sampling risk pertains to all aspects of audit risk that are not due to sampling. It refers to the possibility that auditors will arrive at an erroneous conclusion not because of the chosen sample but due to other factors. Non-sampling risk is always present and cannot be measured. Non-sampling risk can be controlled by adequate planning and super vision of audit wor k and proper adherence to quality control standards.

Sampling r isk and non-sampling risk can affect the components of audit r isk. For example, when performing tests of control, the auditor may find no errors in a sample and conclude that control risk is low, whe n the rate of error in the population is, in fact, unacceptably high (sampling risk). Or there may be errors in the sample which the auditor fails to recognize (nonsampling risk). Types of Statistical Sampling Plans: 1. Attribute sampling – the method used to estimate the rate (%) of occurrence (or exception) of a specific characteristic or attribute Attribute sampling used in tests of controls. In attribute sampling, samples taken to test the operating effectiveness of controls are intended to provide a basis for the auditor to conclude w hether the controls are being applied as prescribed. Attribute sampling generally deals with yes/no questions. For example, "Are time cards properly authorized (i.e., to assure recorded hours were worked)?", or "Are invoices properly voided (e.g., stamped "paid") to prevent duplicate payments?" Commonly used attribute sampling techniques/ models: a. Attribute estimat ion sampling – a statistical sampling plan that uses a fixed sampling plan (for example, testing a single sample) It is used when the auditor wishes to estimate a true but unknow n population deviation rate. b. Discovery sampling – a special type of attribute sampling appropriate w hen the auditor believes the expected population deviation rate is zero or near zero and when the auditor’s objective is to find at least one deviation in the sample if actual population deviation rate

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c.

2.

exceeds or equal a predetermined critical rate (tolerable deviation rate) Discover y sampling should be used to estimate w hether a population co ntains critical deviations. It is used when the auditor is looking for a very critical characteristic or deviations (e.g., fraud). The auditor predeter mines the desired reliability (confidence) level (e.g., 95%) and the maximum acceptable tolerable rate (e.g., 1%), and a table is then used to determine sample size. If no deviations are found in the sample, the auditor can be 95% certain that the rate of deviation in the population does not exceed 1%. If deviations are found, a regular attribute sampling ta ble may be used to estimate the deviation rate in the population, and audit procedures may need to be expanded. Stop-or-go sampling (sequent ial sampling) – is designed to avoid oversampling for attributes by allowing the auditor to stop an audit test before completing all steps It is used when the auditor expects zero or ver y few deviations in the population. It separates the sampling process into several states or steps. After a step, the auditor decides whether to stop or to go on to the next step. In each step, the auditor determines if it is warranted to accept or increase the preliminary level of contr ol risk.

Variables sampling – method used in reaching a conclusion in peso amounts Variables sampling is used in substantive tests. a.

b.

Probability-proportional-to-size (PPS) sampling – sampling technique where the sampling unit is defined as an individual peso in a population PS is a sampling plan that automatically stratifies the population. PPS uses a peso as a sampling unit. Once a peso is selected, the entire account (containing that peso) is audited. PPS is only useful for tests of overstatements (for example, of assets). T hus, it is not appropriate for testing liabilities because understatement is the primary audit consideration. Classical variables sampling – a statistical sampling method used to estimate the numerical measurement of a population, such as a peso value (e.g., accounts receivable balance) The objective of variables sampling is to obtain evidence about the reasonableness of monetar y amounts. The auditor estimates the true value of the population by computing a point estimate of the population and computing a precision inter val around this point estimate. Classical variables sampling measures sampling risk by using the variation of the underlying characteristic of interest. Three commonly used classical variables sampling: 1. Mean- per-unit estimation – a sampling plan that uses the average value of the items in the sample to estimate the true population value by multiplying average sample value by the number of items in population. MPU does not require the book value of the population to estimate true population value. 2. Ratio est imat ion – a sampling plan that uses the ratio of the audited (correct) values/amount to their book values to project the tr ue population value and an allowance for sampling risk Ratio estimation is a highly efficient technique when the calculated audit amounts are approximately proportional to the client's book amounts. 3. Difference estimation – a sampling plan that uses the average difference between the audited (correct) values of items and their book values to project the actual population value. Difference estimation is used instead of ratio estimation when the differences are not nearly proportional to book values. Compar ison of PPS sampling to classical var iables sampling

1. 2. 3. 4. 5. 6.

Advantages of PPS sampling Generally easier to use Size of sample not based on variation of audited amounts Automatically results in a stratified sample Individually significant items are automatically identified Usually results in a smaller sample size if no misstatements are expected Can be easily designed and sample selection can begin before the complete population is available

Advantages of classical var iables 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 balances does not require special sample design considerations 4. Inclusion of negative balances does not require special sample design considerations

Steps in Sampling for Substant ive Testing (Var iables sampling) 1.

Deter mine the objective of the test

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The objective of the test must be to satisfy an audit objective pertaining to a particular account balanc e, that is, to test the reasonableness of a recor ded account balance. For example, the auditor wishes to estimate the value of the client's accounts receivable balance to satisfy valuation audit objective.

2.

Define the populat ion and the sampling unit This is to provide assurance that the audit sample to be selected and examined will satisfy the objective of the test. For example, the population might consist of 5,000 accounts with a recorded book value of P4,500,000. The auditor would examine 100% of acc ounts for w hich potential errors could equal or exceed the tolerable error and w ould exclude those accounts from the population to be sampled. The auditor should consider the completeness of the population in defining the sampling unit. For example, each of the 5,000 accounts is a sampling unit.

3.

Select an appropr iate audit sampling technique Select either non-statistical or statistical sampling. If statistical sampling is used, either probabilityproportional-to-size sampling (PPS) or classical variables techniques may be selected.

4.

Deter mine the sample size Factors to consider in determining sample size for substantive tests of details: a. Acceptable risk of incorrect acceptance b. Acceptable risk of incorrect rejection c. Tolerable error (tolerable misstatement) – maximum amount of errors (or monetar y misstatement) that may exist without causing the account balance or class of transactions to be materially misstated (or maximum amount of error that the auditor is willing to accept) d. Expected error/misstatement (size, frequency, etc.) e. Variation within the population (e.g., an estimate of the standard deviation, or variability, of the population) Summary of relationships between the Increases in Effect on sample size Risk of incorrect Decrease acceptance Risk of incorrect Decrease rejection Tolerable Decrease misstatement (error) Expected Increase misstatement (error)

Variation in the population (standar d deviation) Increase in auditor’s assessment of control risk or inherent risk Reliance on other substantive procedures

Number of items in the population

above factors and the sample size: Explanat ion

This is a sampling risk and sampling risk is reduced by increasing the sample size. This is a sampling risk and sampling risk is reduced by increasing the sample size. The lower the total error that the auditor is willing to accept, the larger the sample size needs to be. The greater the expected amount of error in the population, the larger the sample size needs to be in order to make a reasonable estimate of the actual amount of error in the population. Increases in variation (standard deviation in classical sampling) result in increases in sample size.

Increase

Increase

The higher the auditor’s assessment of inherent risk and control risk, the lar ger the sample size needs to be.

Decrease

Negligible effect

The more the auditor intends to rely on other substantive procedures to reduce to an acceptable level the detection risk, the less assurance the auditor will require from sampling and, therefore, the smaller the sample size can be. The number of items in the population virtually has no effect on sample size unless the population is very small. In other wor ds, population size is not an issue provided the population is large.

5.

Deter mine the sample selection method Generally random number or systematic sampling.

6.

Perfor m the sampling plan Sample items should be selected in such a way that the sample can be expected to be representative of the population (e.g., random sampling). In the same example, an appropriate s ample would consist of individual account balances. Confirmations could then be used to determine the audited values for sample items.

7.

Evaluate the sample results: This includes the following procedure:

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a. b. c. d.

8.

Projecting the sample error. The auditor projects the misstatements found in the sample to the population using one of several methods (e.g., MPU, ratio, difference, etc.). The projected misstatement is applied to the recorded balance to obtain a "point estimate" of the true balance. Considering sampling risk. The auditor must then add an allowance for sampling risk (sometimes called a "precision interval") to this estimate. Considering qualitative information Reaching an overall conclusion In deciding whether to accept the client's book value, the auditor determines whether the recorded book value falls within the acceptable range (i.e., the point estimate +/- the allowance for sampling risk). If so, the book value is fairly stated. The auditor's treatment of items selected for sampling that cannot be located (e.g., are "lost") will depend on their effect on the auditor's evaluation of the sample. If the sample is representative of the population, the auditor generally will make a correct decision regarding w hether the account balance is fairly stated. If the sample is not representative of the population, the auditor will make an incorrect decision, either accepting a materially misstated balance, or rejecting a fairly stated balance.

Document the sampling procedure The auditor must document each step in audit sampling as well as the basis for overall conclusions. Steps in Sampling for Tests of Controls (Attribute sampling)

1.

Define the objectives of the test Tests of controls are designed to test the operating effectiveness of controls. For example, the auditor might test controls for billing systems.

2.

Define the populat ion For tests of controls, the population is the class of transactions being tested. Conclusions based on sample results can be projected only to the population from which the sample was selected.

3.

Define the attribute and dev iation condit ions An attribute (or characteristic) would indicate operation of the inter nal control procedures. A deviation is a departure from the prescribed internal control policy or procedure. For example, i f the prescribed procedure to be tested requires the cancellation of each paid voucher, a paid but uncanceled voucher would constitute a deviation.

4.

Deter mine the sample size The sample size is determined by considering the following factors: a. Risk of assessing control risk too low – inverse relationship with the sample size b. Tolerable deviation rate – inverse relationship with the sample size c. Expected population deviation rate – direct relationship with the sample size Summary of relationships between the above factors and the sample size: Increases in Effect on Explanat ion sample size Risk of assessing Decrease The more assurance the auditor intends to obtain control risk too low from internal controls, the lower the auditor’s assessment of control risk will be, and the larger the sample size will need to be. This is a sampling risk and sampling risk is reduced by increasing the sample size. Tolerable deviation Decrease The lower the rate of deviation that the auditor is rate willing to accept, the lar ger the sample size needs to be. Expected population Increase The higher the rate of deviation that the auditor deviation rate expects, the larger the sample size needs to be so as to be in a position to make a reasonable estimate of the actual rate of deviation. Number of items in Negligible The number of items in the population virtually has no the population effect effect on sample size unless the population is ver y small. In other words, population size is not an issue provided the population is large.

5.

Deter mine the sample selection method Pr incipal sample select ion methods: Appropriate sample selection methods could reduce sampling risk.

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a.

b.

c.

d.

e.

f.

Random- number sampling – this method uses of a computerized random number generator or random number tables Each item in the population has an equal chance and nonzero probability of selection. It is appropriate both for statistical and non-statistical sampling. Systemat ic select ion – the number of sampling units in the population is divided by the sample size to give a sampling interval regar dless of the amount involved (for example 50, and having determined a starting point within the first 50, each 50 th sampling unit thereafter is selected) It involves selecting every nth item from a population of sequentially ordered items. The auditor need to determine that the sampling units within the population are not structured in such a way that the sampling interval corresponds with a particular patter n in the population. It is useful for non-statistical sampling, although it can also be useful for statistical plan if the starting point is selected at random. Haphazard select ion – the auditor selects the sample without following a str uctured technique, but the method is intended to avoid or predictability (for example avoiding difficult to locate items, or always choosing or avoiding the first or last entries on a page) and thus attempt to ensure that all items in the population have a chance of selection Haphazard selection, although may be useful for non-statistical sampling, is not appropriate when using statistical sampling. Block select ion – involves selecting a block(s) of contiguous items from within the population Block selection cannot ordinarily be used in audit sampling because most populations are structured such that items in a sequence can be expected to have similar characteristics to each other, but different characteristics from items elsew here in the population. It often results to excessively high sampling risk. Stratificat ion – grouping of items of similar size and each group is treated as a separate population; it involves subdiving a population into subpopulations or strata For example, assume 1,000 items are stratified into two groups: the 100 largest items will all be examined individually, but sampling techniques will be applied to the remaining 900 items. In this case, the population size for the sampling application would be 900, not 1,000. The primary objective of using stratification as a sampling method is to decrease the effect of variance or variability of items in the total population. Stratification is used when there is a wide range (variability) in the monetary size of items in the population. This method will enable the auditor to direct his efforts towards the items he considers he would potentially contain the greater monetar y error. Value-weighted selection – sets the high-value items as priority to be included in the sample

6.

Perfor m the sampling plan The sampling units selected should be examined for the attributes or quality characteristics of interest and deviations should be documented in the wor king papers.

7.

Evaluate and document results: These include the following: a. Determine the sample dev iat ion rate = Number of deviations obser ved Sample size b. Determine the maximum population dev iation rate (achieved upper dev iation rate) and the

allowance for sampling risk (achieved precision)

c. d.

The maximum dev iation rate is based on the sample size and the number of deviations discovered. The auditor uses standard tables that yield maximum population de viation rates at specified risk of assessing control risk too low. Allowance for sampling risk = Maximum deviation rate – Sample deviation rate When the deviation in the sample is at the expected deviation rate or less, the auditor can continue using his planned assessment of control risk. If it happens to be greater than expected, reassessment of risk is necessar y. Usually, an increase in such should be made. The stronger the internal control, the lower the control risk, the lower the tolerable deviation rate. Consider qualitative consideration (such as the nature of each deviation, its importance, and probable cause) Reach an overall conclusion The overall conclusion relates to assessing control risk after considering all available quantitative and qualitative information.

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Red Sir ug AUDIT SAMPLING (And Other Means of Test ing)

Means for Selecting Items for Testing to Obtain Audit Ev idence: When designing tests of controls and tests of details, the auditor shall determine the means of selecting items for testing that are effective in meeting the purpose of the audit procedure. The means available to the auditor for selecting items for testing are (the auditor may use any one or combination of these): a. Selecting all items (100% examination); b. Selecting specific items; and c. Audit sampling Select ing All Items (100% Examinat ion): Select ing all items – involves examining the entire population of items that make up a class of transactions or account balance 100% examination is: More common for tests of details Unlikely for tests of controls Appropriate when: The population constitutes a small number of large value items There is significant risk (high RMM) and other means do not provide sufficient appropriate audit evidence, or Cost effective – the repetitive nature of a calculation or other process performed automatically by an information system makes a 100% examination cost effective (for example, using computer-assisted audit techniques (CAATs) Select ing Specific Items:

Select ing specific items – judgmental selection of specific items from a population based on the following factors: Auditor’s understanding of the entity Assessed risk of material misstatement Characteristics of the population being tested Specific items that may be selected by the auditor include: High value or key items . The auditor may examine items of high value or items that exhibit some other characteristic (for example, items that are suspicious, unusual, particularly risk-prone or that have a history of error). All items over a certain amount. The auditor may decide to examine items whose values exceed a certain amount so as to verify a lar ge proportion of the total amount of a class of transactions or an account balance. Items to obtain information. The auditor may examine items to obtain information about matters such as the nature of the entity or the nature of transactions. Items to test control activities . The auditor may use judgment to select and examine specific items to determine w hether or not a particular control activity is being performed.

Selecting specific items for examination does not constitute audit sampling and therefore, not subject to sampling risk. The results of audit procedures applied to selected specific items cannot be projected to the entire population; accordingly, selective examination of specific items does not provide audit evidence concerning the remainder of the population.

Audit Sampling:

Audit sampling (sampling) – the application of audit procedures to less than 100% of the items within a population of audit relevance (account balance or class of transactions) such that all sampling units have a chance of selection in order to provide the auditor with a reasonable basis on whi ch to draw conclusions about the entire population Audit sampling is the means that enable the auditor to draw conclusions about the population on the basis of testing a sample draw n from it. Sampling is essential throughout audits as auditors attempt to gather sufficient appropriate evidence in a cost efficient manner. Audit sampling is not required part of any audit procedure because when designing audit procedures, the auditor should determine appropriate means of selecting items for testing. Audit sampling is used for both tests of controls (attributes sampling) and for tests of details of transactions and balances ( variables sampling). In both attributes sampling and variables sampling, the plans may be either non-statistical or statistical. AT – Audit Sampling

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Audit Sampling Ter ms: Populat ion – the entire set of data from which a sample is selected and about which the auditor wishes to draw conclusions Sample – the portion of the population that will be subjected to audit testing Sampling unit – the individual items constituting a population; also known as population item, observation, or elementary unit Representative sample – a sample in which the characteristics of the sample are the same as those of the population Sampling risk – 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. Anomaly – a misstatement or deviation that is demonstrably not representative of misstatements or deviations in a population Confidence level – the mathematical complements of sampling risks; also known as reliability or

confidence Stratificat ion – the process of dividing a population into sub-populations, each of which is a group of

sampling units which have similar characteristics (often monetary value) Tolerable misstatement (in substantive procedures) – 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; it is the maximum total error in a population that the auditor is willing to accept Tolerable rate of deviat ion (in tests of controls) – a rate of deviation from prescribed inter nal control procedures set by the auditor in respect of w hich the auditor seeks to obtain an appropriate level of assurance that the rate of deviation set by the auditor is not exceeded by the actual rate of deviation in the population; it is the maximum rate of deviation from the prescribed control procedure the auditor is willing to accept without changing control risk assessment or planned reliance on internal control Error – either contr ol deviations, when performing tests of contr ol, or misstatements, w hen performing substantive procedures. Total error – either the rate of deviation (in case of tests of control) or total misstatement (in case of substantive procedures) Anomalous error – means an error that arises from an isolated event that has not recurred other than on specifically identifiable occasions and is therefore not representative of errors in the population Expected error – a. Expected error amount – in substantive tests, it is the auditor's best estimate of the amount of error the auditor expects to find in the population b. Expected deviat ion rate – in tests of control, it is the auditor's best estimate of the rate of deviation from a prescribed control procedure in the population

Applicability of Audit Sampling: Where an auditor has no special knowledge about likely misstatements contained in account balances and transactions When the auditor believes that the sample is to be a good representative of the population Inapplicability of audit sampling: Situations w here audit sampling generally do not apply: a. Risk assessment procedures performed to obtain an understanding of internal control. b. Tests of automated application controls when effective general controls are present. (Generally, such contr ols would only be tested once or a few times.) c. Analyses of security and access contr ols, or other controls that do not provide documentar y evidence of performance (e.g., controls related to segregation of duties). d. Some tests related to the operation of the control environment or the accounting system (e.g., examination of the effectiveness of activities performed by those charged with governance). Lists procedures that do not involve sampling: a. Inquir y and obser vation b. Analytical procedures c. Procedures applied to ever y item in a population d. Tests of controls where application is not documented e. Procedures from which the auditor does not intend to extend a conclusion to the remaining item in the account (for example, tracing several transactions through accounting system to obtain understanding) f. Untested balances General Approaches to Audit Sampling: 1. Statistical sampling – an approach to sampling that has the following characteristics: a. Random selection of a sample; and b. Use of probability theor y to evaluate sample results, including measurement of sampling risk

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2.

Statistical sampling applies the law of probability theor y to aid the auditor in designing a sampling plan and evaluating sample results. In statistical sampling, auditors specify the sampling risk they are willing to accept and then calculate the sample size that provides that degree of reliability. Results are evaluated quantitatively. Statistical sampling measures quantitatively the sampling risk (the risk from testing only part of an audit population). Advantages of statistical sampling: Conclusions may be drawn in more precise ways when using statistical sampling because it enables the auditor to: a. Measure the sufficiency of the audit evidence obtained. b. Provide an objective basis for quantitatively evaluating sample results –more objective audit evidence c. Design an efficient sample. d. Quantify/measure sampling risk so as to limit it to an acceptable level. e. Measure reliability (confidence level), precision, and sampling error (sampling risk). Disadvantages of statistical sampling: Danger of accepting statistical evidence at face value without sufficient skepticism Its cost could exceed the benefits Inappropriate it some cases (for example, test of controls that depend on segregation fo duties or otherwise provide no audit trail of documentary evidence) In statistical sampling, random sample selection methods should be used to give all items in the population an equal chance to be included in the sample to be audited.

Non-statistical sampling – a sampling approach that does not have both characteristics of statistical sampling Non-statistical sampling (or judgment sampling) is based solely on the auditor’s judgment. The sample size is not determined mathematically. Auditors rely exclusively on subjective judgment to determine sample size and to evaluate sample results. A properly designed non-statistical sampling application can be as effective as statistical sampling application. One disadvantage is that it can misdirect an auditor to unreliable sampling units. Additional notes on statistical and non-statistical sampling: Statistical sampling is a mathematical approach to inference, whereas non-statistical sampling is a more subjective approach. Conclusions may be drawn in more precise ways when using statistical sampling methods. Both sampling approaches involve judgment in planning, executing the sampling plan, and evaluating the results of the sample. It is acceptable for auditors to use either or combination of statistical and non-statistical sampling. The choice is based primarily on the auditor’s assessment of the relative costs and benefits. Such choice is independent of the selection of audit procedures because audit sampling is merely a means for accomplishing audit procedures. Both sampling approaches can pr ovide sufficient appropriate evidence. Sampling methods are used by auditors in both control testing and substantive testing.

Auditor’s professional judgment: Although statistical sampling aids the auditor in quantitative ways, it is not a substitute for professional judgment. In other wor ds, statistical sampling does not eliminate the need for the auditor’s professional judgment. The auditor must exercise professional judgment in both statistical and non-statistical sampling to: a. Define the population and the sampling unit; b. Select the appropriate sampling method; c. Evaluate the appropriateness of audit evidence; d. Evaluate the nature of deviations or errors; e. Consider sampling risk; and f. Evaluate the results obtained from the sample and project those results to the population. Types of Audit Sampling Plan: Audit sampling is used for both tests of controls (attributes sampling) and for tests of details of transactions and balances (usually, variables sampling). In both attributes sampling and variables sampling, the plans may be either non-statistical or statistical. 1. Attribute sampling – estimates the attribute or quality characteristic of a population Applicable to tests of controls because attribute sampling deals with estimating deviation rate (also called rate of occurrence) from prescribed control procedures that the auditor plans to rely upon 2. Variables sampling – estimates the numerical quantity of a population Applicable to substantive testing because variables sampling deals with peso or monetary amount of misstatement in account balances

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Ordinarily, risk assessment procedures to obtaining understanding of the entity and its environme nt, including internal control, do not involve the use of audit sampling. Audit sampling for substantive procedures applies to tests of details only.

Sampling Risk:

Sampling risk – the possibility that the auditor’s conclusion, based on a sample may be different from the conclusion reached if the entire population were subjected to the same audit procedure. The risk that the sample is not representative of the population and that the auditor's conclusion will be different from the conclusion had the audi tor examined 100% of the population. The possibility that even though a sample is properly chosen, it may not be representative of the population. Sampling risk can be reduced by increasing the sample size. Sampling risk is an inherent part of sampling tha t results from testing less than the entire population. Two Types of Sampling Risk: 1. Risk that affects audit effectiveness and may lead to an inappropr iate audit opinion (“Beta risk” or “Type II error”) – the risk the auditor will conclude that: a. Risk of assessing control risk too low – in case of a test of control, that the assessed control risk is lower than it actually is b. Risk of incorrect acceptance – in case of a substantive test, conclusion that a material error does not exist w hen in fact it does 2. Ris k that affects audit efficiency as it would usually lead to addit ional wor k to establish that initial conclusions were incorrect (“Alpha risk” or “Type I error”) – the risk the auditor will conclude that: a. Risk of assessing control risk too high – in case of a test of control, that the assessed control risk is higher than it actually is b. Risk of incorrect rejection – in case of a substantive test, conclusion that a material error exists when in fact it does not Aspects of Audit Risk(Aspect of detection r isk): Audit risk is a combination of the risk that a material misstatement will occur (inherent risk and control risk) and the risk that it will not be detected by the auditor (detection risk). 1. Sampling r isk – the risk or the possibility that, when a test of controls or a substantive test is restricted to a sample, the auditor's conclusions base on a sample may be different from the conclusions which would have been reached had the tests been applied to all items in the population Sampling risk is the aspect of audit risk and of detection risk that is due to sampling. Aspects of sampling r isk: a. Substant ive testing sampling r isks: 1) Risk of incorrect acceptance – the risk that the auditor will conclude that a material error in an account balance (based on the sample) does not exist when in fact it does (i.e., sample results fail to identify an existing material misstatement). 2) Risk of incorrect rejection – the risk that the auditor will conclude that a material error in an account balance exists w hen in fact it does not (i.e., sample results mistakenly indicate a material misstatement). b. Tests of controls sampling risks: a. Risk of assessing control risk too high or the risk of under reliance (Alpha risk or Type I error) – the risk that the assessed level of contr ol risk (based on the sample) is greater than the true level of control risk (i.e., sample results indicate a greater deviation rate than actually exists in the population). This risk means that the auditor wrongly concludes that the control risk is higher than it actually is. This risk relates to audit efficiency as it w ould lead o additional w ork. If the auditor assesses control risk too high, substantive tests will consequently be expanded beyond the necessary level, leading to audit inefficiency. b. Risk of assessing control risk too low or the risk of over reliance (Beta risk or Type II error) – the risk that the assessed level of control risk (based on the sample) is less than the actual/true level of control risk (i.e., sample results indicate a lower deviation rate than actually exists in the population). This risk means that the auditor wrongly concludes that the contr ol risk is lower than it actually is. This risk relates to audit effectiveness. If the auditor assesses control risk too low, substantive tes ts will not be expanded to the necessar y level to ensure an effective audit. This would more likely lead to an inappropriate audit opinion. Analysis of Sampling Risks:

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Aspects of sampling r isks

Risk of incorrect acceptance

Risk of incorrect rejection

Risk of assessing control risk too low (risk of over reliance) Risk of assessing control risk too high (risk of under reliance)

2.

Auditor’s wrong conclusion Not materially misstated when in fact materially misstated

Effect on audit wor k because of wrong conclusion Performance of less extensive substantive tests

Materially misstated when in fact not materially misstated ↓CR than actual CR – internal control is reliable

Additional wor k (performance of unnecessary more extensive substantive tests) Performance of tests of controls and less extensive substantive tests

↑ CR than actual CR – internal control is not reliable

Additional wor k (because non-performance of tests of controls would lead to the per formance of unnecessary more extensive substantive tests)

Sacrificed Effect iveness of the audit because it may lead to inappropriate opinion due to inappropriate less extensive substantive tests Efficiency of the audit because of unnecessar y additional wor k

Effect iveness of the audit because it may lead to inappropriate opinion due to inappropriate less extensive substantive tests Efficiency of the audit because of unnecessar y additional wor k

Non-sampling risk – the risk that the auditor reaches an erroneous conclusion for any reason not related to sampling risk Examples of non-sampling risk: The auditor might use/select inappropriate audit procedures (audit procedures that are not appropriate to achieve a specific objective) The auditor might misinterpret evidence or the results of audit tests The auditor may fail to recognize an error (for example, failure by the auditor to recognize a misstatement or deviation in documents examined)

Non-sampling risk pertains to all aspects of audit risk that are not due to sampling. It refers to the possibility that auditors will arrive at an erroneous conclusion not because of the chosen sample but due to other factors. Non-sampling risk is always present and cannot be measured. Non-sampling risk can be controlled by adequate planning and super vision of audit wor k and proper adherence to quality control standards.

Sampling r isk and non-sampling risk can affect the components of audit r isk. For example, when performing tests of control, the auditor may find no errors in a sample and conclude that control risk is low, whe n the rate of error in the population is, in fact, unacceptably high (sampling risk). Or there may be errors in the sample which the auditor fails to recognize (nonsampling risk). Types of Statistical Sampling Plans: 1. Attribute sampling – the method used to estimate the rate (%) of occurrence (or exception) of a specific characteristic or attribute Attribute sampling used in tests of controls. In attribute sampling, samples taken to test the operating effectiveness of controls are intended to provide a basis for the auditor to conclude w hether the controls are being applied as prescribed. Attribute sampling generally deals with yes/no questions. For example, "Are time cards properly authorized (i.e., to assure recorded hours were worked)?", or "Are invoices properly voided (e.g., stamped "paid") to prevent duplicate payments?" Commonly used attribute sampling techniques/ models: a. Attribute estimat ion sampling – a statistical sampling plan that uses a fixed sampling plan (for example, testing a single sample) It is used when the auditor wishes to estimate a true but unknow n population deviation rate. b. Discovery sampling – a special type of attribute sampling appropriate w hen the auditor believes the expected population deviation rate is zero or near zero and when the auditor’s objective is to find at least one deviation in the sample if actual population deviation rate

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c.

2.

exceeds or equal a predetermined critical rate (tolerable deviation rate) Discover y sampling should be used to estimate w hether a population co ntains critical deviations. It is used when the auditor is looking for a very critical characteristic or deviations (e.g., fraud). The auditor predeter mines the desired reliability (confidence) level (e.g., 95%) and the maximum acceptable tolerable rate (e.g., 1%), and a table is then used to determine sample size. If no deviations are found in the sample, the auditor can be 95% certain that the rate of deviation in the population does not exceed 1%. If deviations are found, a regular attribute sampling ta ble may be used to estimate the deviation rate in the population, and audit procedures may need to be expanded. Stop-or-go sampling (sequent ial sampling) – is designed to avoid oversampling for attributes by allowing the auditor to stop an audit test before completing all steps It is used when the auditor expects zero or ver y few deviations in the population. It separates the sampling process into several states or steps. After a step, the auditor decides whether to stop or to go on to the next step. In each step, the auditor determines if it is warranted to accept or increase the preliminary level of contr ol risk.

Variables sampling – method used in reaching a conclusion in peso amounts Variables sampling is used in substantive tests. a.

b.

Probability-proportional-to-size (PPS) sampling – sampling technique where the sampling unit is defined as an individual peso in a population PS is a sampling plan that automatically stratifies the population. PPS uses a peso as a sampling unit. Once a peso is selected, the entire account (containing that peso) is audited. PPS is only useful for tests of overstatements (for example, of assets). T hus, it is not appropriate for testing liabilities because understatement is the primary audit consideration. Classical variables sampling – a statistical sampling method used to estimate the numerical measurement of a population, such as a peso value (e.g., accounts receivable balance) The objective of variables sampling is to obtain evidence about the reasonableness of monetar y amounts. The auditor estimates the true value of the population by computing a point estimate of the population and computing a precision inter val around this point estimate. Classical variables sampling measures sampling risk by using the variation of the underlying characteristic of interest. Three commonly used classical variables sampling: 1. Mean- per-unit estimation – a sampling plan that uses the average value of the items in the sample to estimate the true population value by multiplying average sample value by the number of items in population. MPU does not require the book value of the population to estimate true population value. 2. Ratio est imat ion – a sampling plan that uses the ratio of the audited (correct) values/amount to their book values to project the tr ue population value and an allowance for sampling risk Ratio estimation is a highly efficient technique when the calculated audit amounts are approximately proportional to the client's book amounts. 3. Difference estimation – a sampling plan that uses the average difference between the audited (correct) values of items and their book values to project the actual population value. Difference estimation is used instead of ratio estimation when the differences are not nearly proportional to book values. Compar ison of PPS sampling to classical var iables sampling

1. 2. 3. 4. 5. 6.

Advantages of PPS sampling Generally easier to use Size of sample not based on variation of audited amounts Automatically results in a stratified sample Individually significant items are automatically identified Usually results in a smaller sample size if no misstatements are expected Can be easily designed and sample selection can begin before the complete population is available

Advantages of classical var iables 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 balances does not require special sample design considerations 4. Inclusion of negative balances does not require special sample design considerations

Steps in Sampling for Substant ive Testing (Var iables sampling) 1.

Deter mine the objective of the test

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The objective of the test must be to satisfy an audit objective pertaining to a particular account balanc e, that is, to test the reasonableness of a recor ded account balance. For example, the auditor wishes to estimate the value of the client's accounts receivable balance to satisfy valuation audit objective.

2.

Define the populat ion and the sampling unit This is to provide assurance that the audit sample to be selected and examined will satisfy the objective of the test. For example, the population might consist of 5,000 accounts with a recorded book value of P4,500,000. The auditor would examine 100% of acc ounts for w hich potential errors could equal or exceed the tolerable error and w ould exclude those accounts from the population to be sampled. The auditor should consider the completeness of the population in defining the sampling unit. For example, each of the 5,000 accounts is a sampling unit.

3.

Select an appropr iate audit sampling technique Select either non-statistical or statistical sampling. If statistical sampling is used, either probabilityproportional-to-size sampling (PPS) or classical variables techniques may be selected.

4.

Deter mine the sample size Factors to consider in determining sample size for substantive tests of details: a. Acceptable risk of incorrect acceptance b. Acceptable risk of incorrect rejection c. Tolerable error (tolerable misstatement) – maximum amount of errors (or monetar y misstatement) that may exist without causing the account balance or class of transactions to be materially misstated (or maximum amount of error that the auditor is willing to accept) d. Expected error/misstatement (size, frequency, etc.) e. Variation within the population (e.g., an estimate of the standard deviation, or variability, of the population) Summary of relationships between the Increases in Effect on sample size Risk of incorrect Decrease acceptance Risk of incorrect Decrease rejection Tolerable Decrease misstatement (error) Expected Increase misstatement (error)

Variation in the population (standar d deviation) Increase in auditor’s assessment of control risk or inherent risk Reliance on other substantive procedures

Number of items in the population

above factors and the sample size: Explanat ion

This is a sampling risk and sampling risk is reduced by increasing the sample size. This is a sampling risk and sampling risk is reduced by increasing the sample size. The lower the total error that the auditor is willing to accept, the larger the sample size needs to be. The greater the expected amount of error in the population, the larger the sample size needs to be in order to make a reasonable estimate of the actual amount of error in the population. Increases in variation (standard deviation in classical sampling) result in increases in sample size.

Increase

Increase

The higher the auditor’s assessment of inherent risk and control risk, the lar ger the sample size needs to be.

Decrease

Negligible effect

The more the auditor intends to rely on other substantive procedures to reduce to an acceptable level the detection risk, the less assurance the auditor will require from sampling and, therefore, the smaller the sample size can be. The number of items in the population virtually has no effect on sample size unless the population is very small. In other wor ds, population size is not an issue provided the population is large.

5.

Deter mine the sample selection method Generally random number or systematic sampling.

6.

Perfor m the sampling plan Sample items should be selected in such a way that the sample can be expected to be representative of the population (e.g., random sampling). In the same example, an appropriate s ample would consist of individual account balances. Confirmations could then be used to determine the audited values for sample items.

7.

Evaluate the sample results: This includes the following procedure:

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a. b. c. d.

8.

Projecting the sample error. The auditor projects the misstatements found in the sample to the population using one of several methods (e.g., MPU, ratio, difference, etc.). The projected misstatement is applied to the recorded balance to obtain a "point estimate" of the true balance. Considering sampling risk. The auditor must then add an allowance for sampling risk (sometimes called a "precision interval") to this estimate. Considering qualitative information Reaching an overall conclusion In deciding whether to accept the client's book value, the auditor determines whether the recorded book value falls within the acceptable range (i.e., the point estimate +/- the allowance for sampling risk). If so, the book value is fairly stated. The auditor's treatment of items selected for sampling that cannot be located (e.g., are "lost") will depend on their effect on the auditor's evaluation of the sample. If the sample is representative of the population, the auditor generally will make a correct decision regarding w hether the account balance is fairly stated. If the sample is not representative of the population, the auditor will make an incorrect decision, either accepting a materially misstated balance, or rejecting a fairly stated balance.

Document the sampling procedure The auditor must document each step in audit sampling as well as the basis for overall conclusions. Steps in Sampling for Tests of Controls (Attribute sampling)

1.

Define the objectives of the test Tests of controls are designed to test the operating effectiveness of controls. For example, the auditor might test controls for billing systems.

2.

Define the populat ion For tests of controls, the population is the class of transactions being tested. Conclusions based on sample results can be projected only to the population from which the sample was selected.

3.

Define the attribute and dev iation condit ions An attribute (or characteristic) would indicate operation of the inter nal control procedures. A deviation is a departure from the prescribed internal control policy or procedure. For example, i f the prescribed procedure to be tested requires the cancellation of each paid voucher, a paid but uncanceled voucher would constitute a deviation.

4.

Deter mine the sample size The sample size is determined by considering the following factors: a. Risk of assessing control risk too low – inverse relationship with the sample size b. Tolerable deviation rate – inverse relationship with the sample size c. Expected population deviation rate – direct relationship with the sample size Summary of relationships between the above factors and the sample size: Increases in Effect on Explanat ion sample size Risk of assessing Decrease The more assurance the auditor intends to obtain control risk too low from internal controls, the lower the auditor’s assessment of control risk will be, and the larger the sample size will need to be. This is a sampling risk and sampling risk is reduced by increasing the sample size. Tolerable deviation Decrease The lower the rate of deviation that the auditor is rate willing to accept, the lar ger the sample size needs to be. Expected population Increase The higher the rate of deviation that the auditor deviation rate expects, the larger the sample size needs to be so as to be in a position to make a reasonable estimate of the actual rate of deviation. Number of items in Negligible The number of items in the population virtually has no the population effect effect on sample size unless the population is ver y small. In other words, population size is not an issue provided the population is large.

5.

Deter mine the sample selection method Pr incipal sample select ion methods: Appropriate sample selection methods could reduce sampling risk.

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a.

b.

c.

d.

e.

f.

Random- number sampling – this method uses of a computerized random number generator or random number tables Each item in the population has an equal chance and nonzero probability of selection. It is appropriate both for statistical and non-statistical sampling. Systemat ic select ion – the number of sampling units in the population is divided by the sample size to give a sampling interval regar dless of the amount involved (for example 50, and having determined a starting point within the first 50, each 50 th sampling unit thereafter is selected) It involves selecting every nth item from a population of sequentially ordered items. The auditor need to determine that the sampling units within the population are not structured in such a way that the sampling interval corresponds with a particular patter n in the population. It is useful for non-statistical sampling, although it can also be useful for statistical plan if the starting point is selected at random. Haphazard select ion – the auditor selects the sample without following a str uctured technique, but the method is intended to avoid or predictability (for example avoiding difficult to locate items, or always choosing or avoiding the first or last entries on a page) and thus attempt to ensure that all items in the population have a chance of selection Haphazard selection, although may be useful for non-statistical sampling, is not appropriate when using statistical sampling. Block select ion – involves selecting a block(s) of contiguous items from within the population Block selection cannot ordinarily be used in audit sampling because most populations are structured such that items in a sequence can be expected to have similar characteristics to each other, but different characteristics from items elsew here in the population. It often results to excessively high sampling risk. Stratificat ion – grouping of items of similar size and each group is treated as a separate population; it involves subdiving a population into subpopulations or strata For example, assume 1,000 items are stratified into two groups: the 100 largest items will all be examined individually, but sampling techniques will be applied to the remaining 900 items. In this case, the population size for the sampling application would be 900, not 1,000. The primary objective of using stratification as a sampling method is to decrease the effect of variance or variability of items in the total population. Stratification is used when there is a wide range (variability) in the monetary size of items in the population. This method will enable the auditor to direct his efforts towards the items he considers he would potentially contain the greater monetar y error. Value-weighted selection – sets the high-value items as priority to be included in the sample

6.

Perfor m the sampling plan The sampling units selected should be examined for the attributes or quality characteristics of interest and deviations should be documented in the wor king papers.

7.

Evaluate and document results: These include the following: a. Determine the sample dev iat ion rate = Number of deviations obser ved Sample size b. Determine the maximum population dev iation rate (achieved upper dev iation rate) and the

allowance for sampling risk (achieved precision)

c. d.

The maximum dev iation rate is based on the sample size and the number of deviations discovered. The auditor uses standard tables that yield maximum population de viation rates at specified risk of assessing control risk too low. Allowance for sampling risk = Maximum deviation rate – Sample deviation rate When the deviation in the sample is at the expected deviation rate or less, the auditor can continue using his planned assessment of control risk. If it happens to be greater than expected, reassessment of risk is necessar y. Usually, an increase in such should be made. The stronger the internal control, the lower the control risk, the lower the tolerable deviation rate. Consider qualitative consideration (such as the nature of each deviation, its importance, and probable cause) Reach an overall conclusion The overall conclusion relates to assessing control risk after considering all available quantitative and qualitative information.

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