PertanikaJ. Soc. Sci. & Hum. 4(2): 175-184 (1996)ISSN: 0128-7702

© Penerbit Universiti Pertanian Malaysia

Sarn.pling Size and Auditors' Judgern.ents: A Sirn.ulation

MOHAMAD ALI ABDUL-HAMID, SHAMSER MOHAMED and ANNUAR MD-NASSIRDepartment of Accounting and FinanceFaculty of Economics and Management

U niversiti Pertanian Malaysia43400 UPM Serdang, Selangor, Malaysia

Keywords: audit sa:mpling, audit assurance, error tainting, si:mulation

ABSTRAK

Auditor gunapakai teknik-teknik kos efektif dan efisyen untuk mendapatkan bukti-bukti yang membanrumereka didalam memberi pendapat keatas penyata kewangan. Salah satu teknik audit yang lazimdigunakan ialah persampelan dan di UK auditor menggunakan saiz sampel sekecil 25 item. Kajian inimenggunakan teknik simulasi Monte Carlo untuk menentukan samada pendapat auditor berdasarkanpelbagai saiz sampel dan aras ralat adalah dibawah paras ketepatan bolehterima. Keputusan kajianmendapati firma-firma yang menggunakan saiz sampel yang kurang daripada 25 item tidak cukup besaruntuk memberi pelan persampelan yang berjaya kecuali pada tahap nilai ralat yang rendah. Untukmemperbaiki pelan persampelan dan kualiti audit, adalah dicadangkan saiz sampel minimum hendaklahmelebihi 50 item.

ABSTRACT

Auditors usually seek cost-effective and efficient techniques to accumulate evidence in an effort tu expresstheir opinions on financial statements. One such technique is audit sampling, and in the United Kingdomauditors use sample sizes as small as 25 items. This study uses the Monte Carlo simulation technique todetermine whether an auditor's opinion using both different sample size and error levels is within anacceptable degree of accuracy. The results suggest that samples of fewer than 50 items are not large enoughto provide a successful sampling plan unless the error value is very low. To improve the sampling plan andthe quality of the audit, the sample size should, therefore, be increased to more than 50 items.

INTRODUCTION

The high cost of audit sampling in recentyears has forced auditors to reduce the size ofaudit samples. To be cost-effective, auditsamples have been reduced significantly, asreported in the literature (Mohamad-Ali1993), where a sample of 25 items was usedto test accounting populations of severalthousand items. However, a small auditsample is subject to the possibility of a lackof credibility and accuracy, in terms of givinga true and fair view of the accounts beingaudited. This study tests whether smallsamples do provide the auditor with thedegree of assurance he needs to state theaccounts under audit give a "true and fair"view of the financial condition of thecompany.

An auditor faces the challenge of twoconflicting objectives in gathering evidentialmatter. First, the collection of excessiveevidence at the expense of the client maylead him to seek the services of a more cost­efficient auditor. Second, the auditor issubject to litigation if the client perceivesthat the auditor had the means, but did notgive the most reasonable opinion. Therefore,an auditor needs to maintain a balancebetween controlling the cost of evidencegathering and the possible consequences ofexpressing an opinion based on inadequatedata.

One way of determining an optimal sizeof audit sample is to use a well-testedstatistical formula. In a recent survey

Mohamad Ali Abdul-Hamid, Shamser Mohamed and Annuar Md-Nassir

TABLE IFrequency distribution and major characteristics

of book values

distribution of the generated book and errorvalues are shown in Table 1 and 2 respec­tively.

l Neter and Loebbecke's (1975) study consists of Popula­tions I, 2, 3 and 4. The Neter and Loebbecke populationsare well known in the audit sampling literature and havebeen widely used by other researchers for comparing theperformance of alternative sampling techniques (forexample, see Frost and Tamura (1982)).

Class Book Amount ($) Number ofAccounts

1 0 <x:::: 90 1,0702 90 <x:::: 230 7153 230 < x:::: 400 4504 400 < x:::: 650 3375 650 < x:::: 1,500 4556 1,500 < x:::: 3,500 4097 3,500 < x:::: 5,000 1498 5,000 < x :::: 10,000 2389 10,000 < x:::: 25,000 210

4,033

POPULATIONS USED IN THIS STUDY

In order to generate a series of book andaudited values several elements in thesimulated accounting population need to bespecified and explained.

First, to generate the distribution patternof values (the skewness) in this study, theactual elements found in audited accountingpopulations were sampled (taken from Popu­lation 4 of Neter and Loebbecke's (1975)study1 of accounting population parameters).Population 4 consists of 4033 trade debtors'accounts and contains only one-sided errorsowed to a large US manufacturer. Table 1illustrates a frequency distribution of thesebook values representing the trade debtors'accounts. It shows that the distribution isskewed to the right, implying smaller numberof items of high value in the populationsuggests larger number of errors are expectedin small value items.

Total

SOUTce: Neter and Loebbecke (1975) p. 26

RESEARCH DESIGN

This study utilized the Monte Carlo simula­tion technique to examine problems with astochastic or probabilistic basis (Hammerselyand Handscomb 1964). Principally, a com­puter program is used to generate a series ofbook values and error values. These errorvalues are seeded into the book values tobecome the accounting population, which islater used to generate a series of matchingaudited values. The book values and the errorvalues are taken from a series of actual bookand error values noted by auditors. The

(Mohamad-Ali 1993) it was found that theuse of statistical sampling is on the increase,with 43% using statistical sampling techni­ques at some stage of their audit proceduresand the majority of medium-sized accountingfirms stating that they drew a minimumsample size of25 items from an account underaudit. On average, most firms stipulated asample size of 20-40 units per accountaudited. Another study (McRae 1982) notedthat statistical sample sizes in the UK appearto be significantly smaller than those in NorthAmerica, with most firms in the UK imposinga minimum sample size of 25 units and amaximum of 100 units.

Although statistical sampling has been inuse as an effective audit tool for more thanforty years, there is little published evidenceon the issue of sample size. The lack ofresearch on this important practical problemis possibly due to the cost of carrying out aproper test on a large population of data. Totest the accuracy of the sample on an actualpopulation of accounts is time consuming andcostly as every item in the population must bechecked for error.

One possible solution to this problem is todevelop a computer program which cangenerate a series of book and audited values(any differences being an error), thus simu­lating the audit of a real accounting popula­tion. This study attempts to determinewhether an auditor's opinion on the sampledpopulation is likely to be within an acceptabledegree of accuracy when the auditor usesvarying audit sample sizes.

176 PertanikaJ. Soc. Sci. & Hum. Vol. 4 No.2, 1996

Sampling Size and Auditors' Judgements: A Simulation

TABLE 2Tainting percentages: a classification by relative size of the item in error

Audited Items

Tainting

0- 1%> 1 - 10%> 10 - 20%> 20 - 99%

100%> 100%

Source: McRae (1982)

Exceeding $10,000

35%33%

5%17%10%0%

100%

$2,000-$10,00

19.0%25.0%12.0%19.0%23.5%

1.5%

100.0%

Less than $2,000

3%17%19%21%37%

3%

100%

Second, there are errors of principle andoperational errors (Taylor 1974). Opera­tional errors can be classified further, intoprocedural errors and errors of value. Thisstudy is concerned with measuring accidentalerrors of value, which are also referred to assubstantive errors; most are monetary errors(McRae 1982). We have ignored deliberateor fraudulent errors in our simulation becausethe pattern and incidence of such errors arelikely to be very different from those ofaccidental errors and therefore require aseparate research study.

The error rate is defined as the propor­tion of errors in a population. Thus an errorrate of 20% means that out of a totalpopulation of 100 items, 20 items are inerror. The error rate in most accountingpopulations is very low; however, the accep­table level of error varies from sample tosample. For example, Jones (1947) suggeststhat error rates below 0.3% are "acceptable"and below 0.9% are considered to be "fair"in clerical work. Vance (1950) used 0.5% asan acceptable rate and 3% as an unaccep­table error rate in clerical work. The NationalAudit Office in the UK applies an unaccep­table upper error rate of 2.5% to their auditwork on government accounts.

In this study we use three error rates, 1,2.5 and 5% and define these errors as low,medium and high, and seed them into thepopulation via our simulation program.'2

Third, the value of the errors and thepattern of distribution of the errors are

summarized in Table 2. The term "taint­ing" used in audit sampling describes theratio between the value of an error and thevalue of the item in error. For example, anitem of$60 containing a $15 error is said to be25% "tainted". In actual practice theprobability of finding a given tainted percen­tage appears to be influenced by the relativesize of the items in error (McRae 1982). Thisstudy classifies the tainting percentage intothree groups following McRae's study, that is,audited items exceeding $10,000, those lessthan $2,000 and those between $2,000 and$10,000.

THE SIMULATION

The simulation program consists of twointerrelated BASIC programs. The firstprogram generates 4033 random numbersand stores them on data files. The numbersbetween 0 and n are generated by using theformula INT[THETA*LOG(RND)], whereINT and RND are BASIC functions standingfor integer and random number respectively.The second program uses the data insertedinto the data file by the first program. Table 3describes the simulation in detail.

2 According to Neter and Loebbecke's study the number ofitems in the population is 4033. Thus to make the processsimpler, the error items are set to be 50, 100 and 200 errorsrespectively, that is, for example 2.5% of 4033 is 100(rounded to ten). This approach creates three populations tobe tested.

PertanikaJ. Soc. Sci. & Hum. Vol. 4 No.2, 1996 177

Mohamad Ali Abdul-Hamid, Shamser Mohamed and Annuar Md-Nassir

TABLE 3The simulation process

STEPS

I . Generate the file holding the popula­tion

2. Population generation

3. Sampling selection

4. Estimate audit value

5. Decision taken

6. Repeat

DESCRIPTION

The intention is to generates 100 files with each file containing4033 items.

Within this step we generate a population of 4033 values. Thevalues generated correspond to the book and audited values ofeach item. The program creates a set of audited values byseeding error values into population of book values.

A sample in now extracted from each population using themonetary unit sampling (MUS) procedure as describedbelow:

a) Create a cumulative book value for each population ofaccounts.

b) Randomly select a number = y between I and thesampling interval within the cumulated value. We shallcall this sampling interval (SI).

c) Select the account whose cumulative book values index isjust > Y + SI = X.

d) Repeat C, by X + SI = X2

Estimate the total audited value of all 4033 accounts based onthe samples of 25, 50 and 100 items sampled using the MUSprocedure.

Decide whether the total audited book value is to be acceptedor rejected based on level of tolerable errors.

Repeat Steps 2, 3, 4 and 5 for 100 runs. This step will measurethe probability that the confidence levels claimed by theauditor using this procedure are reasonably accurate.

AUDIT SAMPLING PROCEDURE

Monetary unit sampling (MUS) is a com­monly used statistical procedure for expres­sing an opinion on the validity of the accountsaudited from evidence collected from asample. Mohamad-Ali's (1993) andMcRae's (1982) surveys suggest that over90% of applications of statistical sampling usesome form of MUS. The MUS procedureused in this study is a simplified version of theDUS (dollar unit sampling) method de­scribed in Leslie et al. (1980). This procedureis outlined in Table 4.

This method divides the total populationvalue into equal dollar segments. A dollarunit, sometimes called the "hit" dollar, isthen systematically selected from each seg-

ment. Thus a sampling interval is calculatedas follows: Sf = BV/n, where BV is the bookvalue and n is the sample size. In our case letus say BV = $600,000 and n = 88, then thesampling interval is $6,818 ($600,000/88).The initial step in the sampling selectionprocess is to pick a random number between 1and 6,818. The auditor then selects the valueitem that contains every 6,8l8th dollarthereafter in the population. Assuming a5,000 random number start, the four sampleitems selected are as shown in Table 4. Itshould be noted that though we are samplingindividual monetary units in single dollars,the results concern the entire value associatedwith the "hit" dollar.

178 PertanikaJ. Soc. Sci. & Hum. Vol. 4 0.2,1996

Sampling Size and Auditors' Judgements: A Simulation

TABLE 4Systematic selection procedure in MUS sampling

Logical Book Cumulative Numbers I terns selected forunit values values selected audit

I 1,200 1,2002 6,043 7,243 5,000 6,0433 2,190 9,4334 3,275 12,708 11,818 3,2755 980 13,688

6 1,647 15,3357 4,260 19,595 18,636 4,2608 480 20,075

9 7,150 27,225 25,454 7,150

600,000 600,000

EVALUATING THE RESULTS OF THEMUS SAMPLE

The next stage is to evaluate the results of thesampling procedure. Here the auditor con­siders (I) the projected error value deter­mined by the sample, (2) the degree of errorallowed for sampling risk, and (3) the uppererror limit determined by the sample. Item(3) is calculated from items (1) and (2). Theevaluation process now differs depending onwhether any errors are found in the sample.

Sample Selection with No Errors Found

The error results found in the sample are usedto estimate the error in the total population.When no errors are discovered in the samplethe allowance for sampling risk will equal theupper error limit, which is equal to or lessthan the level of tolerable error specified indesigning the sample. Therefore the auditorcan ordinarily conclude, without makingadditional calculations, that the book valueof the population is not overstated by morethan the level of tolerable error at thespecified risk of incorrect acceptance.

When no errors are found in the sample,the sampling risk factor consists of basicprecision (BP). The amount is obtained bymultiplying the reliability factor (RF) for zeroerrors at the specified risk of incorrectacceptance by the sampling interval (Sf). In

the case under discussion, let us say that therequired level of confidence is 95%) thus RF = 3.0(derived from the Poisson distribution), thenthe basic precision is $20,454 (computed as:BP = RF x Sf = 3.0 x $6,818 = $20,454).Since the projected error is zero, this amountis also equal to the upper error limit, which isless than the $30,000 tolerable error specifiedin the sample design. Thus, the auditor maynow state that the book value for thepopulation is not overstated by more than$20,454 at the 5% risk of incorrect accep­tance.

Sample Selection with Some Errors Found

If some errors are found in the sample, theauditor must calculate both the projectederror value in the population and theallowance for sampling risk in order todetermine the upper error limit for over­statement errors. The upper error limit isthen compared with the tolerable error.

Projected Population Error

A projected error amount for the populationis estimated by first calculating the error foreach sampled unit containing an error andthen adding these errors for the entirepopulation. The projected error is calculatedas follows:

PertanikaJ. Soc. Sci. & Hum. Vol. 4 No.2, 1996 179

Mohamad Ali Abdul-Hamid, Shamser Mohamed and Annuar Md-Nassir

TABLE 5Determination of projected error

Book Value(EV)

9502,5005,300

8,750

Book Value( AV)

855o

5,035

5,890

Tainting Percentage(TP = (EV-AV)jEV

10100

5

Projected Error(TP x Sf)

6826,818

341

7,841

Tainting percentage

Projected error

(book value - auditvalue)jbook valuetainting percentage xsampling interval

• Multiply the ranked projected errorsby the appropriate factor and sumthe products.

Table 6 illustrates the first step.

To illustrate, let's assume that the debt­ors' accounts reveal the following errors as inTable 5. The total error in the sample is$2,860 ($8,750 - $5,890) and the total pro­jected error in the population is $7,841.

Allowance for Sampling Risk

The allowance for sampling risk of samplescontaining errors has two components: (1)basic precision, and (2) an incrementalallowance resulting from the errors. Thecalculation of basic precision (RF x Sf) isthe same as explained previously for a samplewith no errors. Thus, in the case studied theamount of this component is again $20,454.

The calculation of the incrementalallowance involves the following steps:

• Determine the appropriate incremen­tal change in the reliability factor.

• Rank the projected errors from thehighest to lowest.

The data in the first two columns are thespecified risk of incorrect acceptance (5 % inthis illustration). Each entry in the thirdcolumn is the incremental reliability factor.The values in the last column are obtained bysubtracting one from each value in the thirdcolumn. The second and third steps are illus­trated in Table 7, which has the projectederrors in the first column (taken from Table5) and incremental reliability factors in thesecond column (taken from Table 6).

The incremental allowance for samplingrisk is the product of columns one and two,and the incremental allowances for theprojected errors are then summed to deter­mine the total incremental allowance, whichis $5,580 in this example. The total allowancefor sampling risk is the sum of basic precisionand incremental allowance for projectederrors. For example, in the case understudy, the total allowance is computed to be$26,034, which is estimated as follows:

TABLE 6

Incremental change in reliability factor minus one 5% risk of incorrect acceptance

Number ofOverstatement

Error

oI234

Reliability Factor(RF)

3.004.746.307.759.15

IncrementalChange in RF

1.741.561.451.40

IncrementalChange in RF

Minus One

.74

.56

.45

.40

180 PertanikaJ. Soc. Sci. & Hum. Vol. 4 No.2, 1996

Sampling Size and Auditors' Judgements: A Simulation

TABLE 7Incremental allowance for sampling risk

RankedProjected Errors

$ 6,818682341

Incremental Change inReliability Factor Minus One

.74

.56

.45

Incremental Allowancefor Sampling Risk

$ 5,045382153

$ 5,580

Upper error limit for overstatementerrors. The upper error limit equals the sumof the projected errors plus the allowance forsampling risk, that is, $33,875 ($7841 +$26,034). Thus, the auditor may concludethat there is a 5% risk that the book value isoverstated by $33,875 or more.

The figure thus calculated is thencompared with the tolerable error for theitem under consideration. If the upper errorlimit is less than the tolerable error theauditor can accept the population. If theopposite is true, the auditor may adjust theupper error limit for any error found(assuming that the client agrees to theadjustment) to determine whether thatreduces the upper error limit to below thetolerable error. If the upper error limitremains above the tolerable error the auditorshould carry out such procedures as are laiddown by the audit firm to deal with such asituation.

Generally, if the upper error limit is lessthan the tolerable error, the sample resultssupport the conclusion that the populationbook value is not mis-stated by more than thetolerable error at the specified risk of incorrectacceptance. In the case under review, theupper error limit exceeds the tolerable errorof $30,000 specified in designing the sample.Thus, in this case, the population should berejected.

Basic precisionIncremental allowance for

projected errorsTotal allowance for sampling

risk

$20,454

5,580

$26,034

HYPOTHESES TO BE TESTED

In this study, the simulation model usedtested the following hypotheses:

HI Auditor's conclusion on the population audited:using a lOO-sample sizeThe hypothesis tested is that thissampling plan, using a sample size of100 items, accepts the populationcorrectly over 90% of the time at alllevels of error rate: 1, 2.5 and 5%.

H2 Auditor's conclusion on the population audited:using a 50-sample size

The hypothesis tested is that thissampling plan, using a sample size of50 items, accepts the population cor­rectly over 90% of the time at all levelsof error rate: 1,2.5 and 5%.

H3 Auditors conclusion on the population audited:using a 25-sample size

The hypothesis tested is that thissampling plan using a sample size of25 items, accepts the population cor­rectly over 90% of the time at all levelsof error rate: 1, 2.5 and 5%.

The various sample sizes used in testingthese hypotheses are based on the researchconducted in the UK which used sample sizesof 25 and 50 items to test large populations3

under audit. The error value found in

3 We assume that all accounting populations audited usingsampling consist of several hundred and usually severalthousand items.

Pertanika J. Soc. Sci. & Hum. Vol. 4 No.2, 1996 181

Mohamad Ali Abdul-Hamid, Shamser Mohamed and Annuar Md-Nassir

TABLE 8Auditor's conclusion on the population

Sample

Size 1%

Error Rate

5%

100

5025

Accept Reject Accept Reject

100 a 96 492 8 63 37

55 45 19 81

Accept

956418

Reject

536

82

accounting populations is reported to be 0.5­5%. An auditor is likely to reject anaccounting population thought to containan error value exceeding 1%. The hypothesesabove are intended to ascertain whetherpopulations containing an error value ofvarious magnitudes are likely to be rejectedby an auditor using sample sizes of 100, 50and 25 units.

RESULTS AND DISCUSSION

A simulation test was carried out to ascertainwhether the sampling sizes used by auditorsare likely to result in correct conclusionsbeing drawn by the auditor on the accept­ability of the population under audit, giventhree error levels and sample sizes.

The end product of the audit is either toreject or to accept the population underaudit. If the upper error limit generated bythe sample is less than the tolerable error, thesample results support the prior hypothesisthat the population book value is not mis­stated by more than the tolerable error.

The simulation results are then comparedwi th the actual data to ascertain thereliability of the auditor's conclusions. Table8 shows the auditor's conclusions based on thevarious sample sizes and the percentage oftimes the auditor would accept or reject eachparticular population under the variousconditions stated. The auditor's conclu~ionis that the population book value under auditis, or is not, in error by more than thetolerable error at the specified degree of risk.

If the level of correct decision as toacceptance or rejection generated by oursimulation lies below the 90% level (the

auditor makes a wrong decision more than10% of the time) then the audit proceduresused would seem to be inadequate. Forexample, the audit testing procedure istelling the auditor to reject the populationunder audit when he should be accepting thepopulation.4

The audit sampling plans using a samplesize of 100 accepted the audited populationsthat should have been accepted over 90% ofthe time at all levels of error rate. Thesampling plans using sample sizes of 25 and50 units provided very different results.

With the error rate at 1% a samplingplan with a sample size of 50 accepts thepopulation correctly more than 90% of thetime. However, at an error rate of2.5 and 5%a sampling plan of 50 provides acceptancesfar below 90% that is, it only accepts thepopulation (the correct decision) 63% and64% of the time respectively. The samplingplan based on a sample size of 25 produces anincorrect decision at all levels of error rate,that is, it produces the correct decision lessthan 90% of the time at all levels.

These findings suggest that firms usingsamples of fewer than 50 units for auditingaccounting populations with low error rateshave an unacceptably low probability ofarriving at a correct conclusion on thequality of the population under audit and soshould increase their minimum sample sizeper population audited to at least 50 units,and preferably 100 units. The auditor is too

4 If an Auditor rejects a population he should accept this iscalled Alpha risk. If an Auditor accepts a population heshould reject this is called Beta risk.

182 PertanikaJ. Soc. Sci. & Hum. Vol. 4 No.2, 1996

Sampling Size and Auditors' Judgements: A Simulation

IMPLICATIONS FOR THE AUDITORS

TABLE 9Summary of results of simulation analysis

*at error rate of 1%,2.5% and 5%, it is significantly above95%+ at error rate of 1%, the hypothesis is accepted

Since the study covered only one accountingpopulation, namely debtors, with a relativelylow number of simulation runs (100), theconclusions drawn are largely tentative.Nevertheless, the results suggest that anauditor using any form of sampling shouldbe concerned about the validity of theconclusions drawn from the sample whenthe sample size is below 50 units perpopulation sampled. The findings suggestthat audit samples below 50 are not largeenough to mitigate alpha and beta risk.

To further validate the findings of thisstudy, it is suggested that a larger number ofaccounting populations with other errordistributions and larger simulation runs arecollected and tested. It might also be useful to

Accepted +Rejected in part *R~jected

Accept/Reject

tently if the sample size is in the region of 100random items. With samples of 50 randomitems the results vary somewhat, but forsamples of 25 random items, the results areconsistently negative. Since many earlierresearchers (McRae 1982; Maysmor-Gee etal. 1984; Mohamad-Ali 1993) used fewer than50 sample items per population audited (onaverage), the findings of this study shouldalert them in their future audit work. Hope­fully, the size of their audit samples in thefuture would be increased to at least 50 itemsand preferably 100 items per populationaudited. This is based on the assumptionthat the populations under audit consist ofseveral thousand items, though these resultsmight also be true for very small accountingpopulations consisting of a few hundreditems.

Hypothesis IHypothesis 2Hypothesis 3

Hypothesis

CONCLUSION

The objective of this study was to ascertainwhether the different sample sizes drawn byaudit firms do provide the auditor with anacceptable level of assurance as to the qualityof the population under audit. The auditorsmust design a cost-effective sampling plan whichwill minimize both alpha and beta risk, that isan assurance that populations which shouldbe rejected are not accepted, and vice-versa.

The simulation was based on an actualaccounting distribution taken from Neter andLoebbecke (1975) Population 4. The samplesizes used were 25, 50 and 100 random itemswith a required confidence level set at 90 %.The findings are summarized in Table 9.

The results show that within the range ofsample sizes normally used by auditors inpractice, namely 25-100 units per populationaudited, the procedures only work consis-

often rejecting populations he should accept,thus requiring needless extra audit work byboth the auditor and the auditee.

However, in practice there are certainother qualitative issues that need to beconsidered in reaching an overall conclusionon accepting or rejecting an accountingpopulation under audit. These qualitativefactors might influence the auditor's conclu­sions derived from the audit sampling plan. Itmust also be noted that in this study thesimulation was applied only to debtors'account of one particular industry.

However, the type of industry is unlikelyto affect the conclusions since the statisticalparameters of accounting distributions do notvary much between industries (Neter andLoebbecke 1975). The level of skewnessattached to debtor distributions is similar tothat attached to most other accountingdistributions such as creditors and inven­tory. The rate of error and the distribution oftotal error are unlikely to vary in aninventory distribution compared to a debt­or's or creditor's distribution. Therefore, wedoubt if this parameter variation would havemuch effect on our conclusions as to thevalidity of the decisions to be drawn byauditors from small audit samples.

Pertanika J. Soc. Sci. & Hum. Vol. 4 No.2, 1996 183

Mohamad Ali Abdul-Hamid, Shamser Mohamed and Annuar Md-Nassir

run the simulation using other estimators,such as the so-called (MEST) boundssuggested by McCray (1980).

ACKNOWLEDGEMENTS

We thank Prof McRae (Maybank Professorat Department of Accounting and Finance,Faculty of Economics and Management,UPM) for his objective review of the paperand Dr. Ali Mamat of Computer ScienceDepartment, UPM for his computer assis­tance in the programming.

REFERENCES

FROST, P.A. and H. TAMURA. 1982. Jackknifedratio estimation in statistical auditing. Journalof Accounting Research 20: 103-120.

HAMMERSELY, J.M. and D.C. HANDSCOMB.1964. Monte Carlo Method. London: Methuen.

JONES, H.L. Sampling plans for verifying clericalwork. Industrial Quality Control 3(4): 5-11.

LESLIE, D.A, AD. TEITLEBAUM and D. ANDER­SON. 1980. Dollar Unit Sampling. Coop, Clarke& Pitman.

MAYSMOR-GEE, C., J. CRAMER and J.STANTOCKI. 1984. The audit process in theUnited Kingdom. City of Birmingham Poly­technic.

MCCRAY, JH. 1980. A quasi-bayesian audit riskmodel for dollar unit sampling AccountingReview 151: 35-51.

MCRAE, T.W. 1982. A study of the application ofstatistical sampling to external auditing.ICAEW.

MOHAMAD-ALI, A.H. 1993. A study of auditmethod: a study of the audit technique usedby medium sized accounting firms in Eng­land. Ph.D. dissertation, University of Brad­ford.

NETER,J andJK. LOEBBECKE. 1975. Behaviourof major estimators in sampling accountingpopulations. New York: AICPA

TAYLOR, R.G. 1974 Error analysis in audit tests.Journal of Accountanry 148: 78-82.

VANCE, L.L. 1950. Auditing use of probabilities inselecting and interpreting test checks. Journalof Accountanry 88(3): 21-25.

(Received 11 January 1995)

184 PertanikaJ. Soc. Sci. & Hum. Vol. 40 No.2, 1996