Audit sampling

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Audit Sampling

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Audit Sampling Defined

SAS No. 39 defines audit sampling as the application of an audit procedure to less than 100 percent of the items within an account balance or class of transactions for the purpose of evaluating some characteristic of the balance or class (AU 350.01).

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Advantages of Statistical Sampling

Design efficient samples Measure sufficiency of evidence Objectively evaluate sample results

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Requirements of Audit Sampling Plans

When planning the sample consider:» The relationship of the sample to the relevant audit objective» Materiality or the maximum tolerable misstatement or deviation

rate» Allowable sampling risk» Characteristics of the population

Select sample items in such a manner that they can be expected to be representative of the population

Sample results should be projected to the population Items that cannot be audited should be treated as

misstatements or deviations in evaluating the sample results Nature and cause of misstatements or deviations should be

evaluated

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Selection of Random Sample

Random number tables Random number generators Systematic selection Haphazard Selection

Note that these methods are often used in conjunction with a stratification process.

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Terminology

Sampling risk» Risk of assessing CR too high / Risk of

incorrect rejection» Risk of assessing CR too low / Risk of

incorrect acceptance

Precision (allowance for sampling risk)

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Types of Statistical Sampling Plans

Attributes sampling» Discovery sampling

Classical variables sampling Probability-proportional-to-size sampling

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Attribute Sampling Applied To Tests Of Controls

Attribute sampling is a statistical method used to estimate the proportion of a characteristic in a population.

The auditor is normally attempting to determine the operating effectiveness of a control procedure in terms of deviations from the prescribed internal control.

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Sampling Risk for Tests of Controls

CorrectDecision

Incorrect Decision

(Risk of Assessing Control Risk

Too High)

IncorrectDecision

(Risk of AssessingControl Risk

Too Low)

Correct Decision

True State of Population

Deviation Rate Deviation Rate Exceeds Is Less Than

Auditors’ Conclusion Tolerable Rate Tolerable RateFrom the Sample Is:

Deviation Rate Exceeds Tolerable Rate

Deviation Rate Is Less Than Tolerable Rate

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Attribute Sampling for Tests of Controls

Determine the objective of the test Define the attributes and deviation conditions Define the population to be sampled Specify:

» The risk of assessing control risk too low» The tolerable deviation rate» The estimated population deviation rate

Determine the sample size Select the sample Test the sample items Evaluate the sample results Document the sampling procedure

Planning

Performance

Evaluation

Documentation

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Discovery Sampling

A modified case of attributes sampling Purpose is to detect at least one deviation (i.e.

critical deviations) Useful in fraud detection Auditor risk and deviation assessments:

» Risk of assessing control risk too low (i.e. 5%)» Tolerable rate (normally set very low, i.e. < 2%)» Expected deviation rate is generally set at 0

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Nonstatistical Attributes Sampling

Determination of required sample size» Must consider risk of assessing control risk too low

and tolerable deviation rate» Need not quantify the risks

Evaluation of results» Compare tolerable deviation rate to sample

deviation rate. Assuming appropriate n:– If SDR somewhat less than TDR, then conclude that risk

of assessing control risk too low is set appropriately.– If SDR approaches TDR it becomes less likely that PDR

< TDR– Must use professional judgment

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Audit Sampling for Substantive Tests

Determine the objective of the test Define the population and sampling unit Choose an audit sampling technique Determine the sample size Select the sample Test the sample items Evaluate the sample results Document the sampling procedure

Planning

Performance

Evaluation

Documentation

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Audit Sampling for Substantive Tests

Sampling Risk

True State of Population

Misstatement in Misstatement in Account Exceeds Account Is Less

Auditors’ Conclusion Tolerable Amount Than Tolerable From the Sample Is: Amount

Misstatement inAccount Exceeds Tolerable Amount

Misstatement inAccount Is LessThan TolerableAmount

CorrectDecision

Incorrect Decision

(Risk of Incorrect Rejection)

IncorrectDecision

(Risk of Incorrect Acceptance)

Correct Decision

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Risk of Incorrect Acceptance (RIA)

Modification of audit risk model:

AR = IR x CR x DRDR comprised of two types of substantive procedures,

each with an associated type of risk: Risk associated with AP and other procedures that do not

involve audit sampling (AP) Risk associated with procedures involving audit sampling (RIA)

AR = IR x CR x AP x RIA

RIA = AR /(IR x CR x AP)

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Classic Variables Sampling

Mean per-unit estimation Difference and Ratio Estimation

» Appropriate when differences between audited and book values are frequent

» Difference estimation is most appropriate when the size of the misstatements does not vary significantly in comparison to book value

» Ratio estimation is most appropriate when the size of misstatements is nearly proportional to the book values of the items.

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Mean Per-unit (MPU) EstimationDetermining the Sample Size

N = population size

Ur = incorrect rejection coefficient (Table 9-8)

SDE = estimated population standard deviation

A = planned allowance for sampling risk

2

A

SDUNn Er

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Mean Per-unit (MPU) EstimationDetermining the Sample Size

N

)Xx( 2

Standard deviation

1

)( 2

n

Xxs

Population SD

Sample SD

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MPU Estimation Determining the Sample Size

Calculation of planned allowance for sampling risk (A):

r

a

UUTM

A

1

TM = tolerable misstatement

Ua = Incorrect acceptance coefficient (Table 9-8)

Ur = incorrect rejection coefficient (Table 9-8)

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MPU Estimation Adjusted Allowance for Sampling

Risk

Calculation of adjusted allowance for sampling risk (A´):

TM = Tolerable misstatementUa = Incorrect acceptance coefficient (Table 9-8)SDC = Sample (calculated) standard deviation n = sample size

n

SDUNTMA Ca

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MPU Estimation

Estimated total audited value = Mean audited value x Number of accounts

Acceptance interval

= Estimated total audited value +/- Adjusted allowance for sampling risk

Projected misstatement = Estimated total audited value – Book value of

population

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Nonstatistical Variables Sampling

PBV = population book value

RF = reliability factor (based on auditors’ combined assessment of inherent and control risk and the risk that other substantive procedures will fail to detect misstatements) (Table 9-13).


TM

RFPBVn

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Nonstatistical Variables Sampling

PBVSBV

SNMPM

PM = projected misstatement

SNM = sample net misstatement

SBV = sample book value


Test: compare PM to TM.

Rule-of-thumb: if PM exceeds 1/3 of TM, PM “becoming too high”

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Probability-proportional-to-size (PPS) Sampling

Applies the theory of attributes sampling to estimate the total dollar amount of misstatement in a population.

Population is defined by the individual dollars comprising the population’s book value ($1 = 1 item).

Relatively easy to use and often results in smaller sample sizes than classical variables approaches.

Assumptions underlying PPS sampling:» Expected misstatement rate in the population is small.» Amount of misstatement in physical unit should not exceed

recorded BV of the item.» PPS focuses on overstatements.

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PPS SamplingDetermination of Sample Size

)(0

EFEMTM

RFPBVn


RF = reliability factor (Table 9-14)


EM = expected misstatement

EF = expansion factor (Table 9-15)

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PPS SamplingSample Selection

Systematic selection is generally used with PPS sampling:

n

PBVSI

SI = sampling interval


n = sample size

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PPS SamplingEvaluation of Sample Results

IABPPMULM

ULM = upper limit on misstatement

PM = projected misstatement

BP = basic precision

IA = incremental allowance

Allowance for sampling risk

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Projected misstatement (PM) If BV < SI, PM = TF x SI

TF = tainting factor = (BV – AV) / BV» BV = book value» AV = audit value

If BV > SI, PM = actual misstatement

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Allowance for sampling risk Basic precision = SI x RF0

Incremental allowanceIf no misstatements in sample found, IA = 0If misstatements found:

For misstatements in which BV < SI, rank order projected misstatements from largest to

smallest, multiply by corresponding incremental factor (from Table 9-14) and sum to calculate IA.

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Compare ULM to TM: If ULM < TM, conclude that population is not

misstated by more than TM at the specified level of sampling risk.

If ULM > TM, conclude that the sample results do not provide enough assurance that the population misstatement is less than the TM and balance adjustment may be warranted.

Audit sampling

Economy & Finance

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