Audit Sampling

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What is Audit Sampling?

Applying a procedure to less than 100% of a population

To estimate some characteristic of the population Qualitative Quantitative

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Advantages of Statistical Sampling

Design efficient samples Measure sufficiency of evidence Objectively evaluate sample results

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Selection of Random Sample

Random number tables Random number generators Systematic selection

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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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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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Sampling Risks--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 ThanAuditors’ Conclusion Tolerable Rate Tolerable RateFrom the Sample Is:

Deviation Rate Exceeds Tolerable Rate

Deviation Rate Is Less Than Tolerable Rate

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Audit Sampling for Tests of Controls

Determine the objective of the test Define the attributes and deviation conditions Define the population to be sampled Choose an audit sampling technique Specify:

The risk of assessing control risk too low The tolerable deviation rate

Estimate the population deviation rate Determine the sample size Select the sample Test the sample items Evaluate the sample results Document the sampling procedure

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Sampling Risks--Substantive Tests

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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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

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Factors Affecting Sample Size

Risk of incorrect rejection Risk of incorrect acceptance Tolerable misstatement Characteristics of the population

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Population Variability—Why it Matters

Item Population A Population B 1 2,100 8,000 2 2,100 25 3 2,100 2,000 4 2,100 400 5 2,100 75

Mean 2,100 2,100

Standarddeviation -0- 3,395

The variability determines how much information each of the items in the population tells you about the other items in the population.

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Determining Sample Size--MPU

Sample size =

risksamplingforallowancePlannedSDEstxcoefrejIncorrectxsizePop ....

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Determining Sample Size--MPU Sampling

Planned allowancefor sampling risk =

Tolerable misstatement______________________

1 + Incorrect acceptance coef. Incorrect rejection coef.

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Variables Sampling Illustration--MPU

Adjusted allowance for sampling risk =

Tolerable _ (Population size * Incorrect acceptance coef. * Sample stan. dev.) misstatement Sample size

This formula “adjusts” the allowance for sampling risk to consider the standard deviation of the audited values in the sample. It holds the risk of incorrect acceptance at its planned level.

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Variables Sampling Illustration--MPU

Using the text example with a standard deviation of audited values of $16

Adjusted allowance for sampling risk =

Tolerable _ (Population size * Incorrect acceptance coef. * Sample stan. dev.) misstatement Sample size

= $364,000 _ ($100,000 * 1.64 * $16)

225 = $189,067 We would still “accept” the book balance because the $6,250,000 (book

value) falls within this interval

Estimate of total + Adjusted allowanceaudited value for sampling risk $6,100,000 + $189,067 [$5,910,933 to $6,289,067]

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Nonstatistical Variables Sampling Illustration

Plan Sample: Population:

Size = 363 items Book value = $200,000

Tolerable misstatement = $10,000 Risk assessments:

Inherent and control risk = Slightly below maximum Other substantive tests = Moderate

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Nonstatistical Sampling--Determination of Sample Size

Sample size = Population book value X Reliability factor Tolerable misstatement

= $200,000 X 2.0 = 40 items $10,000

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Nonstatistical Sampling--Evaluation of Sample Results

Sample results: 40 accounts in sample $350 net overstatement $60,000 book value of sample items

Projected misstatement:

= [Sample net misstatement] X Book value of population [ Book value of sample ] = [ $350 ] X $200,000 [$60,000]

= $1,167

Since the projected misstatement is only 11.7 percent ($1,167/$10,000) of tolerable misstatement, it is likely that the auditors would conclude that the account balance is materially correct.

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PPS Sampling Illustration

Population book value = $6,250,000 Other Information:

Tolerable misstatement = $364,000 Sampling risk--Incorrect acceptance = 5% Expected misstatement = $50,000

Use Figures 9-14 and 9-15 to obtain a “reliability factor” and an “expansion factor.”

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PPS Sample Size Computation

Sample size =

Recorded amount of population * Reliability factor

Tolerable misstatement - (Expected misstatement * Expansion factor)

= $6,250,000 * 3.0 = 66 $364,000 - ($50,000 * 1.6)

Sampling interval = Book value of the population Sample size

= $6,250,000 = $95,000 (approximately) 66

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PPS Evaluation of Results

Upper Limit on misstatement = Projected misstatement + Basic precision (Rel. factor x interval) + Incremental allowance