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m. SUMMARY AND RECOMMENDATIONS
The purpose of this Report has been to review and evaluate the state
of statistical practice in accounting and auditing. In it, we have
emphasized, (~) Me importance of the problem as one of national interest,
(2) the nonstandard nature of the statistical problem reladve to Be main
body of existing statistical methodology, (3) die lack of adequately reliable
procedures, and (4) the generally scattered and ad hoc nature of the
existing methodology. It is clear Mat much additional research is needed
and it is in Be national interest that this be done. For this reason, He
Report has been directed pnmanly towards researchers and graduate
students, both in statistics and accounting. However, the following
summary and recommendations should be of interest to a much wider
audience within our respective disciplines.
Auditing is an essential activity in a society win advanced capital
markets. In such a society, investors and government officials base
many important decisions on accounting information. Those
decisions affect the welfare of all citizens. Auditing is a costly
activity and statistical procedures can play an important role in
reducing those costs.
· Basic statistical problems in auditing arise when one wishes to
estimate the total population error in an account. Relative to the
main body of statistical methodology, these problems are
nonstandard due to a unique feature of the data; audit data usually
contains mosey zeros! Existing statistical methods do not offer
satisfactory solutions for inferences based on such information.
.
This report's survey of the existing literature and practices points up
several important observations. First of all, statistical methods have
only recently begun to be developed for analyzing this nonstandard
type of data; in the chronological bibliography in Chapter IV, all
but five of the references are dated after 1972. The first significant
contribution was that of Aitchison (19SS) and the key idea of Dollar
Unit Sampling (DUS) was reported by Stringer in 1963.
One of the main factors that serves to retard progress in the
development of new methodology for auditing problems is the high
degree of confidentiality placed upon accounting information. The
resultant lack of good data prevents the characteristics of accounting
populations from being adequately known in all but a limited
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number of cases. ~ order to improve Be quality and applicability of
statistical auditing procedures, it is essential that much more data be
made available by both public and private sectors. ~ particular,
one's confidence in the outcomes of statistical analyses depends
heavily upon the suitability of Me models that have been postulated
for the situations In question. However, We selection of appropn ate
models relies critically upon He availability of adequate data from
such situations. Until there is adequate data available to give
guidance and just~ficabon for mode} selections, there win be less
than the desired confidence in He analyses based upon ~em.
.
.
A survey of existing approaches to the statistical problems of
auditing reveals that one of He most important ideas is that of DUS.
This sampling design selects items from an account with probability
proportional to their book amounts. Items with large book amounts,
therefore, are more likely to be selected than items win smaller
amounts. Since the items with larger book values are considered
relatively more important Han those with smaller book values, DUS
is an appealing sampling design when tile auditor places primary
emphasis on overstatements. The DUS design does have some
limitations, however. For example, items with a zero book amount
will not be selected under this sampling.
The dollar unit sampling design adso permits the auditor to
incorporate into the analysis prior knowledge that the errors are
overstatements and Hat He maximum size of an error of an item is
equal to its book amount. This assumption, when applicable, sets an
upper limit of 1 and a lower limit of O for a DUS error. This ear,
referred to by accountants as tainting, is He ratio of He error amount
to He recorded book amount. Under this assumption, an auditor can
set a conservative upper bound for the population error with a
confidence level at least as large as the stated one. The upper bound
for the population error amount is equal to the it- a) upper bound
for the error rate, multiplied by the known total book amount of the
population. Cox and Snell (1979) provides a theoretical framework
for this method. In this report, it is concluded that this bound based
on attribute sampling theory is the only procedure available that has
a theoretically known sampling distnbution. This means that the
long run performance of aU other currency available procedures
must be investigated by means of simulation. Consequently, it is not
easy to obtain information about the performance of these
procedures in a wider audit situation.
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A significant weakness of the upper bound defined in this way is that
it is far too conservative in Mat the auditor's confidence coefficients
are much larger than intended. A heuristic method, credited to
Swinger, has been widely used and it produces a tighter bound. It is
now about 25 years since me Stringer bound was proposed. In spite
of the fact mat extensive sunulat~on demonstrates that it is far too
conservative, no theoretics justification has as yet been obtained!
This remains an important and interesting open question.
· Several altemative me~ods, mostly heunshc and sometimes totally
ad hoc, have been proposed in recent years and these are reviewed
in this report Based on Innited investigations, the upper bounds set
by some of these procedures are shown to be considerably tighter
than the Swinger bound. Much more research along these fines is
needed. It is also recommended that extensive testing be carried out
using real data in order to evaluate adequately these and other
procedures.
· Sequential methods would seem to be appropn ate for some of these
problems, and yet there is a noticeable lack of such methods in the
relevant literature. This is in spite of the fact that general sequential
methodology is available in statistical monographs directed towards
accounting, for example, Cyert and Davidson (19621. In particular,
simple two-stage sampling schemes could be considered as a
possible way to improve the performance of some of the statistical
procedures.
· Empincal studies indicate Mat negative enters caused by under-
statements are also quite corrunon in auditing populations. Very
little research, however, has been done on the problem of
determining bounds for these cases, and this needs to be corrected.
Note mat DUS may not be an effective sampling design when
understatements are present because items with larger audited
amounts may have smaller chances of selection Man desired.
Except for the procedures that utilize Bayesian mesons, existing
procedures are not effective for setting a good lower bound for
accounting population errors. This failure is extremely senous; one
particularly important situation involves the estimation of the
adjustment of a fien's expense accounts by the Intemal Revenue
Service (IRS). The current IRS procedure is to apply standard
sampling methods such as those used in surveys of human
populations. Investigation of Me perfonnance of these estimators
for certain audit populations indicates that such IRS practice is too
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.
conservative in the sense Hat the IRS is assuming much lower risk
than aBowed in the policy. That is, the actual level of confidence is
substandaBy higher Man the nominal level. Such practice tends to
underestimate the potential tax revenue due the government.
Similar problems also arise in over governmental agencies, e.g., the
Office of hnspector General of the Department of Heady and Human
Services, in their investigation of compliance with government
guidelines of reported expenses by local gove~nents. It is
important that intensive research be carried out for the purpose of
developing more reliable procedures for determining lower
confidence bounds. The financial benefits to the government from
such research should be significant.
The development of valid statistical mesons for seeing confidence
bounds for accounting populations is of nations interest and
importance, in major part because of the considerable economic
benefits mat would accrue to both the public and pr~v ate sectors.
· In developing a methodologies, primary emphasis should be placed
upon the denvation and performance of one sided confidence
intervals and not the two sided confidence intervals commonly
discussed in standard statistical texts. Texts should be revised to
reflect this.
· In this age of widely available high speed computing equipment, it
is reasonable to expect significantly greater use of computer-
intensive statistical methodologies. There is also a need for greater
use of computers in the simulation of performance characteristics of
existing methodologies, particularly as increased data sets become
available to suggest more realistic simulation models.
The survey of the existing literature that is given in Chapter IV
below, reveals that the statistics profession as a whole has not been
heavily involved with the ~rnportant statistical problems Hat arise in
auditing. This may be due in part to the fact that there has not been
adequate nor regular interaction between researchers from the
accounting and the statistics professions.
It is recommended that a series of workshops, conferences and
courses be set up at which theoretical and applied statisticians can
meet and exchange expertise and problems with accountants and
auditors from each of the sectors of gove~Tunent, business and
academia. It would be expected Hat proceedings of some of these
activities would be published wide the purpose of improving the
communication between the two disciplines. There would also be
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important benefits from holding a conference that would bring
researchers together *nm the many diverse areas of applications mat
exist throughout aU of the sciences In which problems of
nonstandard mixtures arise. Several such areas are briefly described
in Chapter ~ above. Primarily, Me exchange of problems and me
transfer of relevant methodologies and references could expedite
progress in an areas.
The initial emphasis of coordinated research activities between the
auditing and statistics professions should focus upon seeking ways
to encourage statisticians to become directly involved in the
auditing environment In this way' statisticians would become more
familiar with the statistical problems in auditing and especially with
the characteristics of the data bases in this sewing. It is also
recommended that accounting firms make audit data available for a
wider research community than its own profession.
Large private accounting finns have bow economic incentives and
resources to carry on research for the purpose of developing better
statistical procedures for their audit problems. However, concerted
efforts must be made to improve me statistical methodologies used
in the public sector. Adequate resources wild need to be available to
make me needed level of research possible.
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