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E Y  f 00414 ^ ^ J ^IV niura & I 0 ' ^ Pa • Li t o ^ ^ ^ ^B PILOT (Netherlands) 3 Editor: H. Volten RA General Director, NIVRA Statistical Sampling in Auditing An Interim Report by the Subcommittee on Statistical Sampling of the Auditing Committee NEDERLANDS INSTITUUT VAN REGISTERACCOUNTANTS MENSINGE 2 / AMSTERDAM / THE NETHERLANDS b troduction The purpose of PILOT (Netherlands) is to provide information — for the benefit of foreign colleagues and other interested parties  about the Dutch accountancy profession. In welcoming the present contribution in the field of auditing, I should like to clarify that, contrary to practice in many countries, NIVRA has not issued auditing standards. The Rules of Conduct and Professional Practice of Registeraccountants (see PILOT 1) contain the general criterion: "A registeraccountant shall make no statement on the outcome of his activities unless his expert knowledge and the work done by him provide a sound basis for his statement." Traditionally, there has never been any doubt that to provide a sound basis the auditor's work should include a wide and basically unrestricted field of activities: independent checks, balancing, confirmations, inventory taking, etc. A common approach to audit work by the profession in The Netherlands is based, firstly, on a high degree of uniformity in teaching. Secondly, NIVRA's Auditing Committee keeps developments under review and, where necessary, initiates discussion. The interim report of its Subcommittee on Statistical Sampling, published as PILOT 3, provides a sample of this attitude. The Editor Price on. 15. (Subscribers Dfi. 10.) September 1977 PILOT (Netherlands) 3 Editor: H. Volten RA General Director, NIVRA Statistical Sampling in Auditing An Interim Report by the Subcommittee on Statistical Sampling of the Auditing Committee NEDERLANDS INSTITUUT VAN REGISTERACCOUNTANTS MENSINGE 2 / AMSTERDAM / THE NETHERLANDS Contents Chapter page I Introduction II Statistical Conditions for the Application of Sampling III Application in the Audit 1. Introduction 2. The applicability of sampling in auditing 3. Acceptability of sampling in auditing 4. The size of the sample 5. Finding errors in the sample 3 5 5 5 8 11 14 I Introduction The first few pages of the Interim Report have not been reproduced here. They give a short introduction to some statistical concepts, such as: — precision and reliability; — acceptance and estimation sampling. The Interim Report then continues as follows: II Statistical Conditions for the Application of Sampling In order to draw a mathematically sound conclusion from a sample the following conditions must be met: a. the population should be defined; b. the population should be differentiated into individual elements, each of which has an equal significance to the conclusion to be drawn; c. all elements should have an equal probability of being selected for the sample. The meaning of the three conditions is explained more fully hereafter. Re a. Defining the population The purpose of the sample is to draw a conclusion with respect to the entire population. In order to be able to form a meaningful conclusion it is, therefore, necessary to define the population in such a way that the elements which do belong and those which do not belong to the population are thereby established. The objective of the examination is the basis for defining the population. Re b. Differentiation of the population into elements of equal significance In order to draw a conclusion regarding the entire population from the characteristics of the elements observed in the sample, the condition must be met that the population is differentiated into individual elements, each of which has an equal significance to the conclusion to be drawn. For if the elements differ among themselves as to significance and are thus not equally important to the conclusion, there is a risk that the sample will produce a distorted picture of the population. 3 Re c. Equal probability for all elements By virtue of the condition that all elements should have an equal probability of being selected in the sample, the influence is eliminated of all such causes as could have led to those elements with distinct features appearing in disproportionately large or small measure. So as to give all elements an equal probability the selection must be determined solely on a random basis whereby the conscious or unconscious preferences of the person making the selection is eliminated and coincidence of any classification in the population with an analogous classification in the sample is avoided. Such a selection is known as random selection or aselect choice. 4 Ill Application in the Audit 1. Introduction Based upon the statistical conditions for the application of sampling as formulated and described in the foregoing section, it should first be determined whether these conditions impede the use of sampling in auditing. If not, the next question to be answered would be whether the demands to be made of the audit render sampling improper or subject to certain restrictions. 2. The applicability of sampling in auditing The statistical conditions discussed earlier concern: a. definition of the population; b. differentiation of the population into elements of equal significance; c. equal probability of selection for aU elements. Re a. Definition of the population The fairly obvious requirement that the population must be defined does, however, present certain problems in auditing. What is the population, anyway? If one wishes to establish whether the records reflect transactions properly, the population is formed by the records to be examined. This creates a practical problem in those instances where the records have not been written up to the actual time of commencing the examination, as is often the case with physical stocktaking. If one wishes to establish that the records are complete, the extent of the population is unknown; it is the object of the examination. Then sampling is only possible if a link is made with another population, the extent of which is known or the completeness of wliich has been otherwise established.*) In this way the completeness of, for instance, the sales records can be determined on the basis of delivery records, thus these latter records form the required defined population. The condition that the population must be defined does therefore not signify an obstacle but indeed sometimes a restriction to the application of sampling in auditing. *) This type of examination is called: "relationship check". 5 Re b. Differentiation of the population into elements of equal significance This strict statistical requirement has, for a very long time, made it impossible for sampling to be applied in auditing. The object of an audit is often to obtain the basis for an opinion on an amount included in annual accounts whilst the population to be examined comprises items frequently of a largely variable size which thus have a largely variable significance for the conclusion. A. van Heerden solved this problem by defining the units of such populations as being the guilders and not the items. The guilders have an equal significance for the conclusion whereby the required condition is met. This means that in the selection each guilder must have an equal probability of being selected in the sample; the possibility that an item is drawn into the sample is then greater for a large item than it is for a small one. The possibility of a relatively large item being selected in the sample quickly approaches 100%. The objection put forward by Prof. Dr. S. Kleerekoper, of the disproportionately large risk run by the auditor of an occasional fraudulent item not being detected, is met in this way, at least for material items. This approach is not only of considerable significance to the examination of pretended total amounts but can also be important to forming an opinion on the functioning of internal control. If, in any one case, the size of the items dealt with, whether or not correct, is deemed to be irrelevant to the latter opinion, then the selection can be directed towards the items. Should, however, the importance of good internal control be considered proportionate to the size of the related items, then every unit of value (e.g. guilder) should obtain an equal probability of being selected. Re c. Equal probability of selection for all elements In carrying out an examination the auditor is confronted with the possibility that potential errors are not spread through the population in a random manner. It is, therefore, essential to allow chance to determine the units to be examined. For if every unit has an equal probability of being selected in the sample, the consequences of the phenomenon that errors are not randomly spread throughout the population will be neutralised. The requirement for random selection resulting therefrom presents practical problems in auditing — as it does in many other fields — yet does not create any fundamental impediment to the apphcation of sampling. Theoretically, the selection based upon random numbers is preferred 6 because in that way it is established that the condition requiring equal probability for all units is satisfied with the greatest possible certainty. Inasmuch as this procedure can be cumbersome, other methods of selection are applied in auditing, such as the method whereby the interval between two units to be selected is limited yet varies according to chance. It follows from the foregoing that the conditions around the drawing of a statisticaUy justifiable conclusion from the sample do not impede the application of sampling in auditing. It would seem, at this point, useful to discuss a number of other circumstances which are sometimes considered as obstructions to the application of sampling such as the occurrence of — errors and/or fraud, and — partial populations of varying nature or origin. Errors and/or fraud The aim of sampling, that is to say the drawing of a conclusion regarding one or more features of the population to be examined, can be achieved by estabhshing whether or to what extent the selected units have these features. An error is such a feature and whether or not the feature occurs is precisely the objective of the test. In auditing this means that the possible occurrence of errors does not, statistically, create any obstruction to the use of sampUng as an audit technique. This also holds good for the possible occurrence of fraud, insofar as this is detectable by means of the audit techniques applied to the individual units; if the latter is not the case then the fraud will not be established, even with a complete detailed examination. Yet, if a fraud, in principle detectable by means of a detailed examination, assumes a significant size, it will be found when sampling with a measure of probability related to the size of the sample. The same considerations apply with respect to internal control. Insofar as the effective operation thereof can be estabhshed by the auditor, he can also draw a conclusion based upon sampling. However, insofar as the internal control lies beyond the expertise and technical possibilities of the auditor, neither a complete detailed examination nor a sample can result in a conclusion. The possibility that the internal control has not operated satisfactorily is thus no obstacle to the apphcation of sampling. The system of internal control requires, of course, to be such that it is evident whether the individual elements have, or have not, been subjected to internal control (e.g. whether or not initiaUed). Certainty as to the existence of such a system can be obtained by the 7 examination of a limited number of items per sort of transaction from which, of course, no statistically justified conclusions can be drawn regarding the operation of the system. If the system appears not to satisfy his requirements, the auditor must ask himself whether he can, in principle, express an unqualified opinion; in this case the choice of a complete or a sample examination is irrelevant. Subpopulations The population to be examined can consist of elements of differing origin, or of an otherwise differing nature; the population can comprise subpopulations differing from each other. If, however, the desired conclusion regarding the feature to be examined is significant for the entire population then the occurrence of such subpopulations is no obstacle to the apphcation of sampUng. There is, of course, a limitation because the conclusion which can be drawn for the entire population is not simply applicable to the subpopulations individually. Consequently, the conclusion formed on the examination by sample of purchases is not, as such, applicable to, for example, the investments in fixed assets or power expenses included therein. A sample of the total purchases is not always meaningful because there are often different requirements set for the examination of these subpopulations. The sample must then be aimed at the individual subpopulations. The same applies if one wishes, by way of sample, to judge the operation of the internal control with respect to, for example, the acts of individual executives: the findings with respect to the totality do not apply to the activities of the executives individuaUy. It is indeed possible to draw separate conclusions about the subpopulations from the sample applied to the total population, though frequently with such low precision or reliability, that the conclusions have no practical significance. 3. Acceptability of sampling in auditing The following observations are aimed at the apphcation of sampling to the examination of financial statements. In special investigations, the extent to which the following arguments and conclusions are apphcable will have to be assessed case by case. The examination of the financial statements embraces a balanced whole of subexaminations of the different sets of data from which the financial statements are prepared. Each subexamination must produce a conclusion which contributes to a balanced whole and which must often serve as a starting point for other subexaminations. 8 Such a subexamination can often, dependent on the specific circumstances, be technically carried out in a variety of ways. Naturally, such a procedure will be followed as involves the least expense. If a completely exact examination aimed dhectly at the total amount of a set of data (direct check of total) is possible, then, in general, the investigation will not be directed at the individual elements of the set of data. The completely exact direct check of a total is, however, only possible in certain instances. When variances are small the direct check of a total is applied with less than complete exactitude. The degree of certainty to be obtained with this approach decreases as precision decreases. Indeed, the auditor is often faced with situations where, with this approach, the required certainty cannot be achieved. In that case, the examination must be directed at the individual elements of the set of data; this can be done completely or by sample. For the time being the certainty regarding the object of the subexamination which the auditor may have obtained by other means will be ignored; its effect will be dealt with in the next section. A sample differs from the complete detailed examination in the two characteristics described earlier: a loss of precision and a measure of risk*). This does not, however, mean that a complete detailed examination also gives complete certainty; if the accumulated information comprises a large number of elements, it is almost impossible for all these elements to be investigated with a total alertness more than superficially. If only part of the elements is investigated, the selected items receive full attention and the likelihood of possible errors going undetected is reduced. This in itself, however, is insufficient reason not to investigate the remaining elements at all. Additional arguments are necessary to be able to decide on this. An important consideration is that with regard to the decisions usually made on the basis of financial statements, absolute precision is hardly ever a requirement; it is the "view" which financial statements give that matters. It is for that reason that the certainty to be given by the auditor can be confined to what is relevant to "a true and fair view". In this light some loss of precision in the audit is acceptable. It is clear that acceptance of some loss of precision with the rejection of any risk of an incorrect conclusion means no material reduction of the extent of the examination. The desirability of arriving at a reduction of activities is, however, in itself no justification for acceptance of that risk. The risk which remains after carrying out a sample is, however, not vague *) "Risk" in this context is the complement of reliability. 9 or unknown in extent; it can be quantified, but more important is that the risk of an incorrect conclusion decreases as the error in the accumulated information increases. Although this largely removes a substantial objection, it does not yet justify the use of sampling. Sampling has yet another characteristic and this is decisive for the problem under consideration. Every time the sample is extended by an equal number of elements, the reduction of the risk, with a constant precision, lessens continually until a point is reached where further extension adds very little certainty. Then such an extension is no longer economically justifiable: the related costs yield scarcely any more benefit in the form of additional certainty. Now there is positively no rational interest, either of the party being examined or of society, which is served by the incurring of expense against which hardly any benefit accrues; the auditor can reasonably be expected to avoid such expense. These — economic — considerations lead to the acceptance of sampling in auditing; more than that, the complete detailed examination will frequently, on these grounds, have to be rejected. The consequence of the foregoing would be that the extent of the sample would have to be objectively determined by comparing the additional expense with the additional benefit. An interesting attempt thereat has been made by A. van Heerden (see A. van Heerden, Samphng as as tool for auditing, Maandblad voor Accountancy en Bedrijfseconomie, December 1961)*). The problem here is how the (additional) benefit of sampling can be expressed in the same value as the (additional) costs, namely in money. Van Heerden writes that the additional benefit of the extension of the sample lies in the reduction in uncertainty so achieved. He values this uncertainty at the product of the amount about which there is still uncertainty and the measure of uncertainty on this point (the risk percentage). He puts the additional benefit at the reduction in the uncertainty so quantified when extending the sample by one element from the accumulated information. He fixes the additional expense at the amount the client should be charged for this extension. The additional benefit reduces continually with further extension of the sample (diminishing returns); the additional expense is assumed to remain the same. The optimum sample size has been reached the moment these two quantities are equal. Van Heerden has developed a formula therefor; *) Also introduced as a national paper at the 9th International Congress of Accountants, Paris 1967. 10 i»c{1!'q' because of the mathematical peculiarities of the problem, however, only the maximum justifiable sample size is determinable. This maximum holds good only if it can be assumed that the benefit of the sample cannot go beyond the amount regarding which uncertainty is being removed. It is conceivable that the benefit of the detection of shortcomings in the operation of the internal control is greater than the aforementioned amount because in this way a further deterioration will be prevented. Thus the thoughts in the committee are also divergent regarding the acceptability of the premises of Van Heerden's formula and the possibility of objective determination of the sample size. Apart from economic factors, the application of sampling has been stimulated by developments in accounting organisation. As the significance thereof for the quality of accounting for business activities increased, so it became more important for the auditor to pay attention to the many facets of accounting organisation. Sampling, in this case, serves his purpose. On the one hand it is definitely not necessary for a number of facets to be completely checked within the scope of an examination of the financial statements, on the other, the application of sampling allows for a greater depth of investigation, thereby favourably influencing the quality of the work. 4. The size of the sample The objective determination of the maximum justifiable sample size as discussed in the foregoing paragraph is based on the supposition that certainty is obtained solely from sampling. However, in addition to sampling, the auditor utihses other audit techniques which also provide some specific certainty. This has not been taken into account when weighing cost against benefits. This leads to the question whether there are any grounds for reducing the maximum size referred to above. This question can, differently worded, also be put if the earlier mentioned comparison is not considered acceptable and the size of the sample is consequently based on subjectively selected criteria. The question then is what other audit procedures may play a part in the respective considerations. Now with these other audit procedures two purposes could be aimed at, viz. certainty in respect of — the organisation and  the information. Two objects have to be distinguished in the audit procedures aimed at the organisation: the existence and the operation of the system. 11 As measures aimed at the existence are mentioned: inventory of structures and procedures, completion of questionnaires, as well as depth checks and similar forms of partial observation. Sampling, however, is not among them: sampling is aimed at a conclusion which should apply to the whole of the information, and accordingly should have a larger size than the partial observation with which the existence of a system is estabhshed. The latter objective is often already achieved by the examination of the recording of one or a few events or transactions. In this connection, therefore, application of sampling is only efficient for the examination of the operation of the system (comphance tests). How should an examination of the operation of the system affect the size of the sample directed at the correctness and/or completeness of the information? This question does not seem to be very relevant, the opinions on the information and on the organisation being, in fact, hardly detachable: the certainty on the information is, to a large extent, arrived at by establishing that the organisation has led to the required internal control procedures having been carried out. It is quite natural that both objectives should be pursued with the same sample (dualpurpose tests). Then the question remains of what effect the conclusions from the examination of the existence of the system have on the size of the sample, which is aimed at the information (substantive tests). This examination may well have led to the conclusion that, having regard to the existing system of structures and procedures, the chance of materially incorrect information must be considered small. Now it is the auditor's duty to obtain certainty as to that information. The establishment of the fact that the organisation in respect of design of the system meets high standards does not quite provide that certainty, because this does not yet prove that the system has, in fact, been operating adequately all the time; parts of the system may have failed temporarily or occasionaUy, and there could have been outside interference. An examination of the information itself is therefore necessary, but often the auditor aheady has an expectation in respect of the results of the examination, on the basis of his observation and judgement of the design of the system and of his experience with the operation of the system in previous periods. Could the size of the sample be reduced on the basis of this expectation? In other words, could the auditor under these circumstances decide to accept less precision or a greater risk? Statistical methods have been pubhshed whereby an existing expectation in respect of events material to the examination could be combined with the computation of the precision and the risk from the sample (the 12 socalled Bayesian statistics). The precision would then be higher or the risk smaller than would result from the sample without considering the expectation. This expectation has therefore to be quantified, which as a matter of fact can only be on a subjective basis, so that also the certainty acquired is subjective. There seems to be no proof as yet of this statistical technique being also applicable in the present situation where it is the confirmation of the expectation that should be provided by the sample. Within the committee there are doubts in this respect. Similar considerations are also applicable in respect of reducing the size of the sample on the basis of other auditing procedures which are directly aimed at the information, such as review of the figures, budget control, reconciliations, techniques which are aimed directly at the total amount of the information to be examined. In the cases where the certainty provided by such techniques is adequate, a detailed examination is required. No solution has, as yet, been found to the problem of how the certainty already acquired could be expressed in the statistical concepts of precision and risk, and accordingly could be taken into account when establishing the size of the sample. However, the auditor may have come to the conclusion, on the basis of the examination of the system and from the application of other auditing procedures to the information to be examined, that the chance of materially incorrect information may be considered very small. It is then, for his purposes, sufficient to establish that the quality of the organisation and of the information did not remain considerably below expectations. This means that the auditor could arrive at the conclusion that he could accept a greater risk in this subexamination which then leads to a decrease in the size of the sample. Also past experience could have an effect on this. A line of thought which is reminiscent of the aforementioned socalled Bayesian statistics can be found in Appendix B to Statement on Auditing Procedure No. 54 (Journal of Accountancy, March 1973) of the American Institute of Certified Public Accountants (later included in Statements on Auditing Standards, section 320 B). A formula is propagated there to determine the reliability level to be apphed in sampling, where both the opinion on the internal control and the auditing procedures aimed at the information (substantive tests) are taken into account; the related precision is to be derived from that which in a certain case is to be considered to be "material". 13 The reliability level is then derived from the formula: s=1  7^zn~' ^'^^'^^^y S = rehability level for substantive tests; R = combined reliability level deshed; C = reliance assigned to internal accounting control and to other relevant factors (other auditing procedures). Here, accordingly, the combination of the conclusions from various examinations is accepted, without further proof indeed. Apart from the fact that these examinations have different objectives, and, consequently, produce different conclusions, the determination of factor C is so highly subjective, that this could only be called "quasi objectivity". The committee wiU make a further study of the question whether the above approach means an actual contribution to the solution of the problem of the objective determination of the sample size. 5. Finding errors in the sample Generally experience shows that a very small percentage of errors occurs in the information to which sampling could be applied during the audit. Therefore the size of the sample is often chosen in such a way that the information could be accepted if not a single error is found; viz. this leads to the smallest possible sample size in that case. However, the problem arises of what to do if an error is found when carrying out a sample. Now the definition of what is to be considered as an error is dependent on the purpose of the (sub)examination. As stated before a distinction should be made between the certainty about: — the operation of the organisation (compliance tests); — the correctness and/or the completeness of the information (substantive tests). In respect of the operation of the organisation it is to be considered an error, if an instruction in respect of organisation, more specially of internal control, appears to have been disregarded, irrespective of the consequences. Generally a number of internal control procedures are appUed when effecting transactions or during events to which the information to be audited relates. Therefore often a number of categories of errors 14 relatmg to the organisation is to be distinguished, which should be considered separately. Only one criterion appUes to the information: the correct presentation of related transactions or events. If an error in the information to be audited appears to have been corrected later, then in respect of the conclusion on the information it is not to be considered an error. It could even imply a strengthening of the positive opinion on the organisation, viz. if the error appears to have been corrected within the scope of internal control. The incorrect presentation of a transaction could appear directly by comparison with the item with which it is checked, e.g. a voucher. However, there could also be an indirect indication of an error e.g. if it appears that the voucher was not subject to the prescribed measures of internal control. In the latter case the auditor should obtain the actual certainty as to the correct presentation of this transaction in another way; the formal certainty which is obtained by carrying out a measure of internal control afterwards will generaUy not do. In the event of a purchase invoice not having been initialled for price checking, the actual certainty as to the purchase price could for instance be obtained by the observation that the same article was purchased earlier and later at approximately the same price, which in both cases appears to have been subject to internal control. When an error is found, two questions arise, viz. how this error could arise  in spite of internal control  and to what extent similar enors could occur in the information. For the answers to these two questions it is important whether the error is of a systematic or an occasional nature; this apphes both to a shortcoming in the operation of the organisation and to an incorrect presentation of events or transactions. The systematic character of an error sometimes already appears from the frequency with which it is found in the sample, whereas in other cases it will not become apparent untU the examination into the cause of the error has been carried out. A systematic error in the operation of an organisation arises e.g. due to misinterpretation or misappUcation of an internal control procedure. Incorrect interpretation of a principle of valuation may lead to a systematic error in the information; the same applies to fraud. In all these cases the total amount or the total number of enors in the information can be estabhshed by examining under what combination of circumstances the systematic error occurs, and by further establishing to what elements of the information this combination of circumstances has been apphcable. Extension of the size of the sample is then generally not efficient because 15 the selection must be made at random; once the system of the error is known, it is often more efficient to direct the examination at those elements where an error is expected. When the total amount of the systematic error has been so established, the remaining information can be accepted, provided no further occasional errors have been found. For occasional errors the total amount cannot be established in this way; it can only be estabhshed by a complete detailed examination carried out with faultless precision. Having regard to the purpose of the examination, this procedure wiU mostly not be considered, because it is not necessary to know the total amount exactly. When despite an occasional error the presentation of the transaction proves to be correct, then this error is only significant to the opinion on the operation of the organisation. In this case it is certainly not necessary to know exactly the number of "derailments" of the organisation; an indication of the level of errors with a certain precision and a certain risk is sufficient for the purpose of the examination, which is judging whether the operation of the organisation should be improved. An estimation of the level of errors for each category by means of mathematical methods ("estimation sampling") could well serve this purpose. It is to be recommended to record this level regularly and to follow its development systematically. There is, however, no point in extending the sample when finding the aforementioned errors. It is, however, another matter if the presentation of a transaction occasionaUy proves not to be correct or, if in the case of shortcomings found in the operation of the internal control, no certainty could otherwise be obtained that despite this the presentation is correct; in principle this leads to an adverse opinion or a disclaimer of opinion with regard to the information. The auditor can protect himself against unjustified rejection of the information when finding one occasional error by adopting a twostage sampling plan. If not more than one error is found in the first stage of the sample, the required level of reliability could be reached after aU by extending the sample in such a way that, on finding no error in the second stage, precision and risk are equal to those of the original sample if no error is found. If, however, in the second stage again one or more errors are found, further extension is to no avail. Moreover, the chance to find more errors is great: one then runs the risk of reaching the same unsatisfactory conclusion with more certainty and more expense. The same apphes if in the first stage more than one error is found. 16 In these cases the auditor has to act according to chcumstances. A complete reprocessing of the information by the client is naturally to be preferred, but wiU not always be possible. To support his final opinion the auditor could calculate a probable upper limit of the amount of errors in the total information on the basis of the number of errors in the sample. He could then come to the conclusion that this amount does not justify a disclaimer of opinion or an adverse opinion on the financial statements. It is not, however, acceptable to decrease the standards on insufficient grounds under the pressure of circumstances. It is conceivable that the auditor did also take into account, when estabhshing the size of the sample, the need of management for having the information provided, checked. Now in many cases management will require greater precision than is considered necessary for the financial statements. In considering the probable upper hmit of the amount of the enors the auditor could come to the conclusion that the financial statements could be accepted, but that the information does not meet the more extensive needs of management. A too strict definition of errors leads to unnecessary work; the same apphes to too strict standards for precision and risk. In determining these standards a clear picture should be formed of the objectives to be reached by the examination. As stated, no complete treatment of ah the problems related to the apphcation of statistical samphng has been given in the foregoing; this Interim Report is intended rather to guide the discussions. In addition to comments in the professional magazines, individual comments in writing are invited by the committee. 17 ( Publications available: Act on annual accounts of enterprises Dfl. 27.50 'Accountantsdag'1976 Storms about norms Dfl. 10.— Financial standards in national, regional and international perspective (authors: Drs. I. Kleerekoper, Sh Henry Benson, John C. Burton, Dr. KarlHeinz Forster) PILOT (Neth.) series: 1. — Rules of Conduct and Professional Practice of Register Dfl. 15. accountants — Le Code des Devoirs Professionels des Registeraccountants — Die Verhaltens und Berufsregeln fur Registeraccountants 2. The Audhor's Report in The Netheriands Dfl. 15. (Statements with discussion points) by A.B. Frielink RA PILOT (Neth.) in preparation: • Registeraccountants Act • Automatic data processing and auditing procedures • Considerations on the act on annual accounts prepared by the Tripartite Study Group (TSG) • The education of registeraccountants B IO fa, 3CL
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Titel  Statistical sampling in auditing : an interim report by the Subcommittee on Statistical Sampling of the Auditing Committee 
Auteur  Nederlands Instituut van Registeraccountants, Amsterdam 
Jaartal  1977 
Collectienaam  NIVRA, UBVU gedigitaliseerd 
PPN  353451320 
Toegangsgegevens (URL)  http://imagebase.ubvu.vu.nl/getobj.php?ppn=353451320 
Signatuur origineel  EY.00414. 
Transcript  E Y  f 00414 ^ ^ J ^IV niura & I 0 ' ^ Pa • Li t o ^ ^ ^ ^B PILOT (Netherlands) 3 Editor: H. Volten RA General Director, NIVRA Statistical Sampling in Auditing An Interim Report by the Subcommittee on Statistical Sampling of the Auditing Committee NEDERLANDS INSTITUUT VAN REGISTERACCOUNTANTS MENSINGE 2 / AMSTERDAM / THE NETHERLANDS b troduction The purpose of PILOT (Netherlands) is to provide information — for the benefit of foreign colleagues and other interested parties  about the Dutch accountancy profession. In welcoming the present contribution in the field of auditing, I should like to clarify that, contrary to practice in many countries, NIVRA has not issued auditing standards. The Rules of Conduct and Professional Practice of Registeraccountants (see PILOT 1) contain the general criterion: "A registeraccountant shall make no statement on the outcome of his activities unless his expert knowledge and the work done by him provide a sound basis for his statement." Traditionally, there has never been any doubt that to provide a sound basis the auditor's work should include a wide and basically unrestricted field of activities: independent checks, balancing, confirmations, inventory taking, etc. A common approach to audit work by the profession in The Netherlands is based, firstly, on a high degree of uniformity in teaching. Secondly, NIVRA's Auditing Committee keeps developments under review and, where necessary, initiates discussion. The interim report of its Subcommittee on Statistical Sampling, published as PILOT 3, provides a sample of this attitude. The Editor Price on. 15. (Subscribers Dfi. 10.) September 1977 PILOT (Netherlands) 3 Editor: H. Volten RA General Director, NIVRA Statistical Sampling in Auditing An Interim Report by the Subcommittee on Statistical Sampling of the Auditing Committee NEDERLANDS INSTITUUT VAN REGISTERACCOUNTANTS MENSINGE 2 / AMSTERDAM / THE NETHERLANDS Contents Chapter page I Introduction II Statistical Conditions for the Application of Sampling III Application in the Audit 1. Introduction 2. The applicability of sampling in auditing 3. Acceptability of sampling in auditing 4. The size of the sample 5. Finding errors in the sample 3 5 5 5 8 11 14 I Introduction The first few pages of the Interim Report have not been reproduced here. They give a short introduction to some statistical concepts, such as: — precision and reliability; — acceptance and estimation sampling. The Interim Report then continues as follows: II Statistical Conditions for the Application of Sampling In order to draw a mathematically sound conclusion from a sample the following conditions must be met: a. the population should be defined; b. the population should be differentiated into individual elements, each of which has an equal significance to the conclusion to be drawn; c. all elements should have an equal probability of being selected for the sample. The meaning of the three conditions is explained more fully hereafter. Re a. Defining the population The purpose of the sample is to draw a conclusion with respect to the entire population. In order to be able to form a meaningful conclusion it is, therefore, necessary to define the population in such a way that the elements which do belong and those which do not belong to the population are thereby established. The objective of the examination is the basis for defining the population. Re b. Differentiation of the population into elements of equal significance In order to draw a conclusion regarding the entire population from the characteristics of the elements observed in the sample, the condition must be met that the population is differentiated into individual elements, each of which has an equal significance to the conclusion to be drawn. For if the elements differ among themselves as to significance and are thus not equally important to the conclusion, there is a risk that the sample will produce a distorted picture of the population. 3 Re c. Equal probability for all elements By virtue of the condition that all elements should have an equal probability of being selected in the sample, the influence is eliminated of all such causes as could have led to those elements with distinct features appearing in disproportionately large or small measure. So as to give all elements an equal probability the selection must be determined solely on a random basis whereby the conscious or unconscious preferences of the person making the selection is eliminated and coincidence of any classification in the population with an analogous classification in the sample is avoided. Such a selection is known as random selection or aselect choice. 4 Ill Application in the Audit 1. Introduction Based upon the statistical conditions for the application of sampling as formulated and described in the foregoing section, it should first be determined whether these conditions impede the use of sampling in auditing. If not, the next question to be answered would be whether the demands to be made of the audit render sampling improper or subject to certain restrictions. 2. The applicability of sampling in auditing The statistical conditions discussed earlier concern: a. definition of the population; b. differentiation of the population into elements of equal significance; c. equal probability of selection for aU elements. Re a. Definition of the population The fairly obvious requirement that the population must be defined does, however, present certain problems in auditing. What is the population, anyway? If one wishes to establish whether the records reflect transactions properly, the population is formed by the records to be examined. This creates a practical problem in those instances where the records have not been written up to the actual time of commencing the examination, as is often the case with physical stocktaking. If one wishes to establish that the records are complete, the extent of the population is unknown; it is the object of the examination. Then sampling is only possible if a link is made with another population, the extent of which is known or the completeness of wliich has been otherwise established.*) In this way the completeness of, for instance, the sales records can be determined on the basis of delivery records, thus these latter records form the required defined population. The condition that the population must be defined does therefore not signify an obstacle but indeed sometimes a restriction to the application of sampling in auditing. *) This type of examination is called: "relationship check". 5 Re b. Differentiation of the population into elements of equal significance This strict statistical requirement has, for a very long time, made it impossible for sampling to be applied in auditing. The object of an audit is often to obtain the basis for an opinion on an amount included in annual accounts whilst the population to be examined comprises items frequently of a largely variable size which thus have a largely variable significance for the conclusion. A. van Heerden solved this problem by defining the units of such populations as being the guilders and not the items. The guilders have an equal significance for the conclusion whereby the required condition is met. This means that in the selection each guilder must have an equal probability of being selected in the sample; the possibility that an item is drawn into the sample is then greater for a large item than it is for a small one. The possibility of a relatively large item being selected in the sample quickly approaches 100%. The objection put forward by Prof. Dr. S. Kleerekoper, of the disproportionately large risk run by the auditor of an occasional fraudulent item not being detected, is met in this way, at least for material items. This approach is not only of considerable significance to the examination of pretended total amounts but can also be important to forming an opinion on the functioning of internal control. If, in any one case, the size of the items dealt with, whether or not correct, is deemed to be irrelevant to the latter opinion, then the selection can be directed towards the items. Should, however, the importance of good internal control be considered proportionate to the size of the related items, then every unit of value (e.g. guilder) should obtain an equal probability of being selected. Re c. Equal probability of selection for all elements In carrying out an examination the auditor is confronted with the possibility that potential errors are not spread through the population in a random manner. It is, therefore, essential to allow chance to determine the units to be examined. For if every unit has an equal probability of being selected in the sample, the consequences of the phenomenon that errors are not randomly spread throughout the population will be neutralised. The requirement for random selection resulting therefrom presents practical problems in auditing — as it does in many other fields — yet does not create any fundamental impediment to the apphcation of sampling. Theoretically, the selection based upon random numbers is preferred 6 because in that way it is established that the condition requiring equal probability for all units is satisfied with the greatest possible certainty. Inasmuch as this procedure can be cumbersome, other methods of selection are applied in auditing, such as the method whereby the interval between two units to be selected is limited yet varies according to chance. It follows from the foregoing that the conditions around the drawing of a statisticaUy justifiable conclusion from the sample do not impede the application of sampling in auditing. It would seem, at this point, useful to discuss a number of other circumstances which are sometimes considered as obstructions to the application of sampling such as the occurrence of — errors and/or fraud, and — partial populations of varying nature or origin. Errors and/or fraud The aim of sampling, that is to say the drawing of a conclusion regarding one or more features of the population to be examined, can be achieved by estabhshing whether or to what extent the selected units have these features. An error is such a feature and whether or not the feature occurs is precisely the objective of the test. In auditing this means that the possible occurrence of errors does not, statistically, create any obstruction to the use of sampUng as an audit technique. This also holds good for the possible occurrence of fraud, insofar as this is detectable by means of the audit techniques applied to the individual units; if the latter is not the case then the fraud will not be established, even with a complete detailed examination. Yet, if a fraud, in principle detectable by means of a detailed examination, assumes a significant size, it will be found when sampling with a measure of probability related to the size of the sample. The same considerations apply with respect to internal control. Insofar as the effective operation thereof can be estabhshed by the auditor, he can also draw a conclusion based upon sampling. However, insofar as the internal control lies beyond the expertise and technical possibilities of the auditor, neither a complete detailed examination nor a sample can result in a conclusion. The possibility that the internal control has not operated satisfactorily is thus no obstacle to the apphcation of sampling. The system of internal control requires, of course, to be such that it is evident whether the individual elements have, or have not, been subjected to internal control (e.g. whether or not initiaUed). Certainty as to the existence of such a system can be obtained by the 7 examination of a limited number of items per sort of transaction from which, of course, no statistically justified conclusions can be drawn regarding the operation of the system. If the system appears not to satisfy his requirements, the auditor must ask himself whether he can, in principle, express an unqualified opinion; in this case the choice of a complete or a sample examination is irrelevant. Subpopulations The population to be examined can consist of elements of differing origin, or of an otherwise differing nature; the population can comprise subpopulations differing from each other. If, however, the desired conclusion regarding the feature to be examined is significant for the entire population then the occurrence of such subpopulations is no obstacle to the apphcation of sampUng. There is, of course, a limitation because the conclusion which can be drawn for the entire population is not simply applicable to the subpopulations individually. Consequently, the conclusion formed on the examination by sample of purchases is not, as such, applicable to, for example, the investments in fixed assets or power expenses included therein. A sample of the total purchases is not always meaningful because there are often different requirements set for the examination of these subpopulations. The sample must then be aimed at the individual subpopulations. The same applies if one wishes, by way of sample, to judge the operation of the internal control with respect to, for example, the acts of individual executives: the findings with respect to the totality do not apply to the activities of the executives individuaUy. It is indeed possible to draw separate conclusions about the subpopulations from the sample applied to the total population, though frequently with such low precision or reliability, that the conclusions have no practical significance. 3. Acceptability of sampling in auditing The following observations are aimed at the apphcation of sampling to the examination of financial statements. In special investigations, the extent to which the following arguments and conclusions are apphcable will have to be assessed case by case. The examination of the financial statements embraces a balanced whole of subexaminations of the different sets of data from which the financial statements are prepared. Each subexamination must produce a conclusion which contributes to a balanced whole and which must often serve as a starting point for other subexaminations. 8 Such a subexamination can often, dependent on the specific circumstances, be technically carried out in a variety of ways. Naturally, such a procedure will be followed as involves the least expense. If a completely exact examination aimed dhectly at the total amount of a set of data (direct check of total) is possible, then, in general, the investigation will not be directed at the individual elements of the set of data. The completely exact direct check of a total is, however, only possible in certain instances. When variances are small the direct check of a total is applied with less than complete exactitude. The degree of certainty to be obtained with this approach decreases as precision decreases. Indeed, the auditor is often faced with situations where, with this approach, the required certainty cannot be achieved. In that case, the examination must be directed at the individual elements of the set of data; this can be done completely or by sample. For the time being the certainty regarding the object of the subexamination which the auditor may have obtained by other means will be ignored; its effect will be dealt with in the next section. A sample differs from the complete detailed examination in the two characteristics described earlier: a loss of precision and a measure of risk*). This does not, however, mean that a complete detailed examination also gives complete certainty; if the accumulated information comprises a large number of elements, it is almost impossible for all these elements to be investigated with a total alertness more than superficially. If only part of the elements is investigated, the selected items receive full attention and the likelihood of possible errors going undetected is reduced. This in itself, however, is insufficient reason not to investigate the remaining elements at all. Additional arguments are necessary to be able to decide on this. An important consideration is that with regard to the decisions usually made on the basis of financial statements, absolute precision is hardly ever a requirement; it is the "view" which financial statements give that matters. It is for that reason that the certainty to be given by the auditor can be confined to what is relevant to "a true and fair view". In this light some loss of precision in the audit is acceptable. It is clear that acceptance of some loss of precision with the rejection of any risk of an incorrect conclusion means no material reduction of the extent of the examination. The desirability of arriving at a reduction of activities is, however, in itself no justification for acceptance of that risk. The risk which remains after carrying out a sample is, however, not vague *) "Risk" in this context is the complement of reliability. 9 or unknown in extent; it can be quantified, but more important is that the risk of an incorrect conclusion decreases as the error in the accumulated information increases. Although this largely removes a substantial objection, it does not yet justify the use of sampling. Sampling has yet another characteristic and this is decisive for the problem under consideration. Every time the sample is extended by an equal number of elements, the reduction of the risk, with a constant precision, lessens continually until a point is reached where further extension adds very little certainty. Then such an extension is no longer economically justifiable: the related costs yield scarcely any more benefit in the form of additional certainty. Now there is positively no rational interest, either of the party being examined or of society, which is served by the incurring of expense against which hardly any benefit accrues; the auditor can reasonably be expected to avoid such expense. These — economic — considerations lead to the acceptance of sampling in auditing; more than that, the complete detailed examination will frequently, on these grounds, have to be rejected. The consequence of the foregoing would be that the extent of the sample would have to be objectively determined by comparing the additional expense with the additional benefit. An interesting attempt thereat has been made by A. van Heerden (see A. van Heerden, Samphng as as tool for auditing, Maandblad voor Accountancy en Bedrijfseconomie, December 1961)*). The problem here is how the (additional) benefit of sampling can be expressed in the same value as the (additional) costs, namely in money. Van Heerden writes that the additional benefit of the extension of the sample lies in the reduction in uncertainty so achieved. He values this uncertainty at the product of the amount about which there is still uncertainty and the measure of uncertainty on this point (the risk percentage). He puts the additional benefit at the reduction in the uncertainty so quantified when extending the sample by one element from the accumulated information. He fixes the additional expense at the amount the client should be charged for this extension. The additional benefit reduces continually with further extension of the sample (diminishing returns); the additional expense is assumed to remain the same. The optimum sample size has been reached the moment these two quantities are equal. Van Heerden has developed a formula therefor; *) Also introduced as a national paper at the 9th International Congress of Accountants, Paris 1967. 10 i»c{1!'q' because of the mathematical peculiarities of the problem, however, only the maximum justifiable sample size is determinable. This maximum holds good only if it can be assumed that the benefit of the sample cannot go beyond the amount regarding which uncertainty is being removed. It is conceivable that the benefit of the detection of shortcomings in the operation of the internal control is greater than the aforementioned amount because in this way a further deterioration will be prevented. Thus the thoughts in the committee are also divergent regarding the acceptability of the premises of Van Heerden's formula and the possibility of objective determination of the sample size. Apart from economic factors, the application of sampling has been stimulated by developments in accounting organisation. As the significance thereof for the quality of accounting for business activities increased, so it became more important for the auditor to pay attention to the many facets of accounting organisation. Sampling, in this case, serves his purpose. On the one hand it is definitely not necessary for a number of facets to be completely checked within the scope of an examination of the financial statements, on the other, the application of sampling allows for a greater depth of investigation, thereby favourably influencing the quality of the work. 4. The size of the sample The objective determination of the maximum justifiable sample size as discussed in the foregoing paragraph is based on the supposition that certainty is obtained solely from sampling. However, in addition to sampling, the auditor utihses other audit techniques which also provide some specific certainty. This has not been taken into account when weighing cost against benefits. This leads to the question whether there are any grounds for reducing the maximum size referred to above. This question can, differently worded, also be put if the earlier mentioned comparison is not considered acceptable and the size of the sample is consequently based on subjectively selected criteria. The question then is what other audit procedures may play a part in the respective considerations. Now with these other audit procedures two purposes could be aimed at, viz. certainty in respect of — the organisation and  the information. Two objects have to be distinguished in the audit procedures aimed at the organisation: the existence and the operation of the system. 11 As measures aimed at the existence are mentioned: inventory of structures and procedures, completion of questionnaires, as well as depth checks and similar forms of partial observation. Sampling, however, is not among them: sampling is aimed at a conclusion which should apply to the whole of the information, and accordingly should have a larger size than the partial observation with which the existence of a system is estabhshed. The latter objective is often already achieved by the examination of the recording of one or a few events or transactions. In this connection, therefore, application of sampling is only efficient for the examination of the operation of the system (comphance tests). How should an examination of the operation of the system affect the size of the sample directed at the correctness and/or completeness of the information? This question does not seem to be very relevant, the opinions on the information and on the organisation being, in fact, hardly detachable: the certainty on the information is, to a large extent, arrived at by establishing that the organisation has led to the required internal control procedures having been carried out. It is quite natural that both objectives should be pursued with the same sample (dualpurpose tests). Then the question remains of what effect the conclusions from the examination of the existence of the system have on the size of the sample, which is aimed at the information (substantive tests). This examination may well have led to the conclusion that, having regard to the existing system of structures and procedures, the chance of materially incorrect information must be considered small. Now it is the auditor's duty to obtain certainty as to that information. The establishment of the fact that the organisation in respect of design of the system meets high standards does not quite provide that certainty, because this does not yet prove that the system has, in fact, been operating adequately all the time; parts of the system may have failed temporarily or occasionaUy, and there could have been outside interference. An examination of the information itself is therefore necessary, but often the auditor aheady has an expectation in respect of the results of the examination, on the basis of his observation and judgement of the design of the system and of his experience with the operation of the system in previous periods. Could the size of the sample be reduced on the basis of this expectation? In other words, could the auditor under these circumstances decide to accept less precision or a greater risk? Statistical methods have been pubhshed whereby an existing expectation in respect of events material to the examination could be combined with the computation of the precision and the risk from the sample (the 12 socalled Bayesian statistics). The precision would then be higher or the risk smaller than would result from the sample without considering the expectation. This expectation has therefore to be quantified, which as a matter of fact can only be on a subjective basis, so that also the certainty acquired is subjective. There seems to be no proof as yet of this statistical technique being also applicable in the present situation where it is the confirmation of the expectation that should be provided by the sample. Within the committee there are doubts in this respect. Similar considerations are also applicable in respect of reducing the size of the sample on the basis of other auditing procedures which are directly aimed at the information, such as review of the figures, budget control, reconciliations, techniques which are aimed directly at the total amount of the information to be examined. In the cases where the certainty provided by such techniques is adequate, a detailed examination is required. No solution has, as yet, been found to the problem of how the certainty already acquired could be expressed in the statistical concepts of precision and risk, and accordingly could be taken into account when establishing the size of the sample. However, the auditor may have come to the conclusion, on the basis of the examination of the system and from the application of other auditing procedures to the information to be examined, that the chance of materially incorrect information may be considered very small. It is then, for his purposes, sufficient to establish that the quality of the organisation and of the information did not remain considerably below expectations. This means that the auditor could arrive at the conclusion that he could accept a greater risk in this subexamination which then leads to a decrease in the size of the sample. Also past experience could have an effect on this. A line of thought which is reminiscent of the aforementioned socalled Bayesian statistics can be found in Appendix B to Statement on Auditing Procedure No. 54 (Journal of Accountancy, March 1973) of the American Institute of Certified Public Accountants (later included in Statements on Auditing Standards, section 320 B). A formula is propagated there to determine the reliability level to be apphed in sampling, where both the opinion on the internal control and the auditing procedures aimed at the information (substantive tests) are taken into account; the related precision is to be derived from that which in a certain case is to be considered to be "material". 13 The reliability level is then derived from the formula: s=1  7^zn~' ^'^^'^^^y S = rehability level for substantive tests; R = combined reliability level deshed; C = reliance assigned to internal accounting control and to other relevant factors (other auditing procedures). Here, accordingly, the combination of the conclusions from various examinations is accepted, without further proof indeed. Apart from the fact that these examinations have different objectives, and, consequently, produce different conclusions, the determination of factor C is so highly subjective, that this could only be called "quasi objectivity". The committee wiU make a further study of the question whether the above approach means an actual contribution to the solution of the problem of the objective determination of the sample size. 5. Finding errors in the sample Generally experience shows that a very small percentage of errors occurs in the information to which sampling could be applied during the audit. Therefore the size of the sample is often chosen in such a way that the information could be accepted if not a single error is found; viz. this leads to the smallest possible sample size in that case. However, the problem arises of what to do if an error is found when carrying out a sample. Now the definition of what is to be considered as an error is dependent on the purpose of the (sub)examination. As stated before a distinction should be made between the certainty about: — the operation of the organisation (compliance tests); — the correctness and/or the completeness of the information (substantive tests). In respect of the operation of the organisation it is to be considered an error, if an instruction in respect of organisation, more specially of internal control, appears to have been disregarded, irrespective of the consequences. Generally a number of internal control procedures are appUed when effecting transactions or during events to which the information to be audited relates. Therefore often a number of categories of errors 14 relatmg to the organisation is to be distinguished, which should be considered separately. Only one criterion appUes to the information: the correct presentation of related transactions or events. If an error in the information to be audited appears to have been corrected later, then in respect of the conclusion on the information it is not to be considered an error. It could even imply a strengthening of the positive opinion on the organisation, viz. if the error appears to have been corrected within the scope of internal control. The incorrect presentation of a transaction could appear directly by comparison with the item with which it is checked, e.g. a voucher. However, there could also be an indirect indication of an error e.g. if it appears that the voucher was not subject to the prescribed measures of internal control. In the latter case the auditor should obtain the actual certainty as to the correct presentation of this transaction in another way; the formal certainty which is obtained by carrying out a measure of internal control afterwards will generaUy not do. In the event of a purchase invoice not having been initialled for price checking, the actual certainty as to the purchase price could for instance be obtained by the observation that the same article was purchased earlier and later at approximately the same price, which in both cases appears to have been subject to internal control. When an error is found, two questions arise, viz. how this error could arise  in spite of internal control  and to what extent similar enors could occur in the information. For the answers to these two questions it is important whether the error is of a systematic or an occasional nature; this apphes both to a shortcoming in the operation of the organisation and to an incorrect presentation of events or transactions. The systematic character of an error sometimes already appears from the frequency with which it is found in the sample, whereas in other cases it will not become apparent untU the examination into the cause of the error has been carried out. A systematic error in the operation of an organisation arises e.g. due to misinterpretation or misappUcation of an internal control procedure. Incorrect interpretation of a principle of valuation may lead to a systematic error in the information; the same applies to fraud. In all these cases the total amount or the total number of enors in the information can be estabhshed by examining under what combination of circumstances the systematic error occurs, and by further establishing to what elements of the information this combination of circumstances has been apphcable. Extension of the size of the sample is then generally not efficient because 15 the selection must be made at random; once the system of the error is known, it is often more efficient to direct the examination at those elements where an error is expected. When the total amount of the systematic error has been so established, the remaining information can be accepted, provided no further occasional errors have been found. For occasional errors the total amount cannot be established in this way; it can only be estabhshed by a complete detailed examination carried out with faultless precision. Having regard to the purpose of the examination, this procedure wiU mostly not be considered, because it is not necessary to know the total amount exactly. When despite an occasional error the presentation of the transaction proves to be correct, then this error is only significant to the opinion on the operation of the organisation. In this case it is certainly not necessary to know exactly the number of "derailments" of the organisation; an indication of the level of errors with a certain precision and a certain risk is sufficient for the purpose of the examination, which is judging whether the operation of the organisation should be improved. An estimation of the level of errors for each category by means of mathematical methods ("estimation sampling") could well serve this purpose. It is to be recommended to record this level regularly and to follow its development systematically. There is, however, no point in extending the sample when finding the aforementioned errors. It is, however, another matter if the presentation of a transaction occasionaUy proves not to be correct or, if in the case of shortcomings found in the operation of the internal control, no certainty could otherwise be obtained that despite this the presentation is correct; in principle this leads to an adverse opinion or a disclaimer of opinion with regard to the information. The auditor can protect himself against unjustified rejection of the information when finding one occasional error by adopting a twostage sampling plan. If not more than one error is found in the first stage of the sample, the required level of reliability could be reached after aU by extending the sample in such a way that, on finding no error in the second stage, precision and risk are equal to those of the original sample if no error is found. If, however, in the second stage again one or more errors are found, further extension is to no avail. Moreover, the chance to find more errors is great: one then runs the risk of reaching the same unsatisfactory conclusion with more certainty and more expense. The same apphes if in the first stage more than one error is found. 16 In these cases the auditor has to act according to chcumstances. A complete reprocessing of the information by the client is naturally to be preferred, but wiU not always be possible. To support his final opinion the auditor could calculate a probable upper limit of the amount of errors in the total information on the basis of the number of errors in the sample. He could then come to the conclusion that this amount does not justify a disclaimer of opinion or an adverse opinion on the financial statements. It is not, however, acceptable to decrease the standards on insufficient grounds under the pressure of circumstances. It is conceivable that the auditor did also take into account, when estabhshing the size of the sample, the need of management for having the information provided, checked. Now in many cases management will require greater precision than is considered necessary for the financial statements. In considering the probable upper hmit of the amount of the enors the auditor could come to the conclusion that the financial statements could be accepted, but that the information does not meet the more extensive needs of management. A too strict definition of errors leads to unnecessary work; the same apphes to too strict standards for precision and risk. In determining these standards a clear picture should be formed of the objectives to be reached by the examination. As stated, no complete treatment of ah the problems related to the apphcation of statistical samphng has been given in the foregoing; this Interim Report is intended rather to guide the discussions. In addition to comments in the professional magazines, individual comments in writing are invited by the committee. 17 ( Publications available: Act on annual accounts of enterprises Dfl. 27.50 'Accountantsdag'1976 Storms about norms Dfl. 10.— Financial standards in national, regional and international perspective (authors: Drs. I. Kleerekoper, Sh Henry Benson, John C. Burton, Dr. KarlHeinz Forster) PILOT (Neth.) series: 1. — Rules of Conduct and Professional Practice of Register Dfl. 15. accountants — Le Code des Devoirs Professionels des Registeraccountants — Die Verhaltens und Berufsregeln fur Registeraccountants 2. The Audhor's Report in The Netheriands Dfl. 15. (Statements with discussion points) by A.B. Frielink RA PILOT (Neth.) in preparation: • Registeraccountants Act • Automatic data processing and auditing procedures • Considerations on the act on annual accounts prepared by the Tripartite Study Group (TSG) • The education of registeraccountants B IO fa, 3CL 
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