Chapter 9 Audit Sampling 1

What is Audit Sampling? Applying a procedure to less than 100% of a population To estimate some characteristic of the population Qualitative Quantitative

Advantages of Statistical Sampling Design efficient samples Measure sufficiency of evidence Objectively evaluate sample results 2

Selection of Random Sample Random number tables Random number generators Systematic selection 3

Random Number Table

Types of Statistical Sampling Plans Attributes sampling Discovery sampling Classical variables sampling Probability-proportional-to-size sampling 4

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 5 5

Sampling Risks--Tests of Controls Actual Extent of Operating Effectiveness of the Control Procedure is Adequate Inadequate The Test of Controls Sample Indicates: Extent of Operating Effectiveness is Adequate Effectiveness Inadequate Correct Decision Incorrect Decision (Risk of Assessing Control Risk Too High) Incorrect Decision (Risk of Assessing Control Risk Too Low) Correct Decision 6 6

Audit 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 Estimate the population deviation rate Determine the sample size Select the sample Test the sample items Evaluate the sample results Document the sampling procedure 7 7

Sampling Risks--Substantive Tests The Population Actually is Not Materially Materially Misstated Misstated The Substantive Procedure Sample Indicates Misstatement in Account Exceeds Tolerable Amount Account Is Less Than Tolerable Amount Correct Decision Incorrect Decision (Risk of Incorrect Rejection) Incorrect Decision (Risk of Incorrect Acceptance) Correct Decision 8 8

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 9 9

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 Standard deviation -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. 2 11

Factors Affecting Sample Size

Determining Sample Size--MPU 2

Determining Sample Size--MPU Sampling Planned allowance for sampling risk Tolerable misstatement ______________________ = Incorrect acceptance coef. 1 + Incorrect rejection coef. 12

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. 4 13

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 allowance audited value for sampling risk $6,100,000 + $189,067 [$5,910,933 to $6,289,067]

Acceptance Interval Figure 9-12

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 8 15

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 9 16

Nonstatistical Sampling--Evaluation of 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. 10 17

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.” 6 18

PPS Sample Size Computation 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 7 19

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

Calculation of Upper Limit on Misstatement