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An empirical investigation of the auditor's decision to project errors.

SUMMARY

Statement on Auditing Standards No. 39 requires that auditors project to the population being sampled the dollar errors in tests of details of balances. This study uses an archival approach to examine auditors' sample error projection decisions for inventory and accounts receivable errors from audits conducted by three large accounting firms. This archival approach provides a rich environment for describing the auditor's sample projection decision.

We suggest that sample evaluation consists of both error quantification and error resolution. Consistent with previous experimental research, auditors often fail to quantify errors by projecting them to the population. The decision to project an error is related to several factors, including the materiality of the error, direction of the error, type of test, and audit firm characteristics. Error immateriality was the most common documented reason for not projecting an error. Although most errors were small in relation to planning materiality, failure to project seemingly immaterial amounts may increase audit risk by an unacceptable amount, especially if sampling risk is not considered. The auditors in our study did not explicitly consider sampling risk in making error projections. Consistent with previous research, error containment was also associated with the decision to not project errors. We suggest that this strategy is used for large errors as part of the auditor's resolution of the error. Professional standards indicate that auditors should consider qualitative aspects of errors (AU [section] 350.27), but do not address whether error containment is appropriate. The results of this study suggest the need for further guidance and additional research in the use of error containment, and of the consideration of sampling risk in the evaluation of errors.

Key Words: Error projection, Audit sampling, Error containment, SAS No. 39.

Data Availability: Data used in this study are available on request. The data were provided on condition of anonymity; the audit firms and clients will not be identified.

Audit sampling in tests of details of balances is widely used in gathering evidence for the auditor's decision on the fairness of client financial statements. When sampling is used, SAS No. 39 (AICPA 1981) indicates that the auditor should estimate the total error in the population by projecting sample errors to the population. Failure to project errors lowers the estimate of the total error, which could cause the auditor to improperly issue an unqualified opinion on the financial statements. Previous experimental research demonstrates that auditors have a propensity to not project errors considered to be "unique" (Burgstahler and Jiambalvo 1986). Dusenbury et al. (1994) found that the error projection decision is related to the containment of errors to well-defined sub-populations and to the perceived frequency of the error. (1)

We examine auditors' projection decisions using an archival approach based on data drawn from audit workpapers for 64 audits from the offices of three large accounting firms (two Big 6 firms and one regional firm) located in different geographic regions. In addition to validating the results of previous empirical research using a range of sampling applications, we develop an expanded description of the auditor's error evaluation decision as a two-stage process that depends on several error and firm characteristics.

Error projection is used in the first stage to quantify errors, and error containment is a strategy used in the second stage to resolve large errors. Error projection is related to error materiality, error direction, type of test, and audit firm characteristics. As expected, auditors are less likely to project immaterial errors, and errors which reduce net income. Auditors are more likely to project errors arising from tests with high error rates, especially for tests with a specific objective for a well-defined population. Auditors from a firm in which error projection was structured in standard computerized working papers were more likely to project errors. In addition, we find that auditors rarely quantify sampling risk when projecting errors. The results of the study suggest the need for additional guidance on error projection, error containment, and the consideration of sampling risk.

The paper is organized as follows. The next section discusses the auditor's error projection decision and previous error projection research. The third section describes the research design and data collection procedures. The results and implications are discussed in the fourth section. The final section is the summary and conclusion.

THE ERROR PROJECTION DECISION

SAS No. 39 indicates the auditor should project the misstatement results of the sample to the items from which the sample was selected. The projected misstatement should be compared to tolerable misstatement for the account balance, and appropriate consideration should be given to sampling risk (AU [section] 350.26). The auditor should also consider the qualitative nature of any errors (AU [section] 350.27).

Previous Error Projection Research

Burgstahler and Jiambalvo (1986) were the first to note the apparent propensity of auditors to not project certain types of errors. They provided auditors with a set of seven accounts receivable cases, and found that auditors frequently did not project the errors on the basis that the errors were "unique." Dusenbury et al. (1994) built upon the concept of error uniqueness, and found that the error projection decision is related to the containment of errors to well-defined sub-populations, and the perceived frequency of the error.

One purpose of this study is to test the validity of the results in Burgstahler and Jiambalvo (1986) and Dusenbury et al. (1994) using actual auditor decisions based on archival data involving a range of sampling applications. Cushing and Ahlawat (1996) suggest that auditors are more involved with their responsibilities in real world audit settings than in experimental settings. Auditor involvement in an experimental setting is subject to numerous constraints that are not present in a real audit setting. "Hence the cognitive efforts that auditors employ in making the judgments and decisions for which they are responsible is likely to be much greater in the 'real-world' than in an experimental setting" (Cushing and Ahlawat 1996, 121).

Laboratory experiments such as those performed by Burgstahler and Jiambalvo (1986) and Dusenbury et al. (1994) are useful because of their ability to increase internal validity by separating the "research situation from the life around the laboratory by eliminating the many extraneous influences" (Kerlinger 1986, 367). "Internally valid research should be reproducible by other authors under different settings and for different samples" (Abdel-khalik and Ajinkya 1979, 47). The convergence between two methods enhances our belief that the results are valid and not a methodological artifact (Bouchard 1976). The triangulation of research using different methodologies and researchers to study the same phenomenon lends more robustness to the theory (Jick 1979). In addition to validating the experimental results in previous research, the archival approach may be useful to auditors and auditing standard setters in providing an estimate of the extent to which errors are not projected, and in understanding the circumstances surrounding the decision to not project an error.

Use of Error Containment to Resolve Errors

Burgstahler and Jiambalvo (1986) argue that isolation of errors is rarely appropriate because errors in the sample proxy for unknown errors in the population and leads to a biased estimate of errors in the population. Wheeler et al. (1997) question this normative model and contend that a biased estimator (i.e., unique errors not projected) is more precise than an unbiased estimator when the unique error rate and sample size are sufficiently small.

The AICPA (1983) Audit Sampling Guide does not specifically comment on the appropriateness of containment procedures; however, it notes that audit sampling differs from traditional sampling applications in other fields. "Rather than using the sample to estimate an unknown, the auditor's objective is generally to corroborate the accuracy of certain client data.... In addition, the evidence obtained from each audit test is just one element of the total evidence the auditor obtains.... Therefore, an auditor plans and evaluates a sample with the knowledge that the overall conclusion about the population characteristic of interest will be based on more than the results of that audit sample" (AICPA 1983, 11-12).

One purpose of this study is to provide evidence on the circumstances in which auditors have contained errors, and the nature of the containment procedures. We believe that the treatment of errors is appropriately divided into two stages--an error quantification stage, and an error resolution stage. Containment of errors is not used to avoid error projection per se, but is used to resolve large errors. If the auditor has already determined that the error is material and plans to contain the error to a sub-population, then the error is not projected.

The use of error containment is inconsistent with the normative argument in Burgstahler and Jiambalvo (1986). However, error containment is not used to completely avoid error projection, but to ex post stratify the sample for subsequent testing and error projection. While the population should be specified in advance, the sample may contain items which belong in a separate population (Guy et al. 1994, 20-21). Error containment may be appropriate if the error arises from unique characteristics of the sub-population. The AICPA (1983)Audit Sampling Guide indicates that evidence from the sample is just one element of the auditor's total evidence set. In addition to information from the sample, the auditor's conclusion about the appropriateness of the financial statements is also based on evidence related to, among other things, the adequacy of internal controls and inherent risk factors.

Error projection is used to quantify the materiality of an error. Usually, projected errors are not individually material, and are resolved by placing the projected error on a summary of proposed audit adjustments that are ultimately not recorded in the financial statements. However, when projected errors exceed tolerable error, quantification alone is not sufficient. The auditor must ultimately express an opinion on the financial statements and must, therefore, pursue additional courses of action which may include: (1) perform tests in specific areas (containment); (2) increase the sample size; (3) adjust the account balance; (4) have the client fix the population; and (5) not issue an unqualified opinion (Arens and Loebbecke 1997, 491-492).

For many large errors, containment is likely to be a plausible course of action. Issuing a qualified opinion is usually not desirable, and the auditor would ask the client to fix the population only in cases in which the errors are pervasive. An adjustment is feasible for the actual detected errors, but discussions with auditors indicate that clients will rarely approve adjustments for projected amounts. The remaining options are an increase in sample size, or increased tests in specific areas. A general increase in sample size can be used to lower the total projected error, but may be costly if the initial projected error is large. Also, an unrestricted increase in sample size ignores the information provided by the detected error. The normative model proposed by Burgstahler and Jiambalvo (1986) suggests that nearly all errors should be projected. However, the normative model does not provide guidance on how the auditor should resolve large differences. The archival data set used in the current study allows us to provide evidence on how auditors actually resolve large errors.

Additional Factors Affecting the Auditor's Error Projection Decision

If an error is contained to resolve an error, we find that auditors may not quantify the error by projecting it to the population. In addition, we consider the effect of error frequency, error materiality, error direction, and audit firm task structure on the projection decision.

Error Frequency

The purpose of audit sampling is to estimate the extent of error in the population. When the auditor concludes to isolate an error, s/he assumes that it is highly unlikely that similar errors exist in the population. Burgstahler and Jiambalvo (1986) identify error frequency as one factor that may be associated with the decision to isolate an error. Dusenbury et. al (1994) manipulate error frequency by distinguishing between errors and irregularities. They argue that errors are more likely to be projected than irregularities because errors occur more frequently.

Dusenbury et al. (1994) suggest that a useful extension of their research is to explore less extreme relative error frequencies than errors compared to irregularities. Consistent with prior research we measure error frequency by type of audit test across many audits (Coakley and Loebbecke 1985; Kreutzfeldt and Wallace 1986; Ham et al. 1987). Although material financial statement errors resulting in adjustment to the financial statements are relatively rare events (Ashton 1991), individually immaterial errors are likely to be more frequent, and they provide a basis for auditors to assess error frequency.

Materiality of the Error

Materiality is an important consideration in all audit decisions. Although AU [section] 350.26 indicates that errors should be projected, in practice auditors may not project or contain small errors. However, at the time an error projection is made, the auditor often does not know whether material errors exist in other segments of the audit. Because individual errors detected in an audit often are not material, it is important to understand how materiality of the error affects the projection decision.

Both projection and containment require further effort and documentation on the part of the auditor. Applying the auditor's concept of materiality, we expect this effort to be reserved for those items that are perceived as potentially material. (2) While the ultimate materiality of an error depends on the total of errors in the aggregate, auditors may be less likely to project errors deemed to be immaterial.

A nonprojected error is classified as immaterial if the auditor documented in the workpapers that the decision to not project the error was based on lack of materiality. We assessed the actual materiality of the error as the ratio of the projected error to planning materiality. We computed the projected amount for these errors since the auditors did not make an error projection.

Error Direction

Closely related to error materiality is the direction of the error. Audit risk for asset accounts arises primarily from the risk of over-statement errors. As a result, auditors may treat overstatement errors differently than understatement errors. For example, DeFond and Jiambalvo (1991) find that very few corrections of prior year earnings involve understatement errors. (3)

Firm Structure

Hermanson (1995) found that auditors from structured audit firms are more likely to project errors than those from less structured firms. We examine firm structure at both the firm level (Cushing and Loebbecke 1986; Kinney 1986) and at the task level (Prawitt 1995). The two Big 6 firms included in our study did not differ in structure at the firm level (Kinney 1986). However, after reviewing sample audits from each firm, it became clear that one firm (Firm C) took a much more structured approach to the error projection task. For this firm, error projection was built in to computerized audit working papers in a standardized format. Accordingly, we consider this firm as structured and the remaining two firms as unstructured in considering task-level firm structure.

Consideration of Sampling Risk in Evaluating Errors

SAS No. 39 also indicates that the auditor should consider sampling risk when projecting errors. "If the total projected misstatement is less than the tolerable misstatement for the account balance or class of transactions, the auditor should consider the risk that such a result might be obtained even though the true monetary misstatement for the population exceeds tolerable misstatement" (AU [section] 350.26). Because failure to project errors increases the risk that an account balance will be accepted as fairly stated when it is not, we also gather information on sampling methods and the consideration of sampling risk.

In summary, the current study examines whether the results of prior experiments (Burgstahler and Jiambalvo 1986; Dusenbury et al. 1994) are robust across a wide range of audits, sampling applications, and types of errors that auditors encounter in practice. We develop an expanded description of the auditor's error projection decision in which error containment is used to resolve errors, and identify additional factors affecting the auditor's error projection decision. We also provide evidence regarding auditor consideration of sampling risk.

RESEARCH DESIGN

Data for this study were collected from the accounts receivable and inventory workpapers for a total sample of 64 audits conducted by two Big 6 firms and one large regional public accounting firm for fiscal year 1993 or 1994. Each office was located in a different geographic region of the U.S. We believe that the benefits of examining actual audit decisions outweigh the potential loss of generality, and that the errors and auditor decisions in our data set are indicative of the types that auditors encounter.

We collected data from audit workpapers at each audit firm's office. We agreed not to disclose the names of the firms or their clients, but otherwise were not restricted in our data collection procedures. We focused on "middle market" clients since discussions with firm representatives indicated that such audits were more likely to include errors. Firm representatives selected audit working papers for fiscal year 1993 or 1994 on the basis of their availability in the office at the time of our visit. Selected clients had accounts receivable and/or inventory, and were primarily manufacturers or distributors. Though the clients were selected by a firm representative, there was no indication that there was any attempt to screen out clients or otherwise restrict our access to data. Of 64 clients in the sample, 13 (20 percent) were publicly traded and 51 (80 percent) were not publicly traded. The average client had $53 million in sales and $37 million in assets. Selected audit clients were included in our sample only once; we did not include multiple years for any audit clients.

We reviewed the inventory and accounts receivable workpapers for each sample company. Previous research (Burgstahler and Jiambalvo 1986; Dusenbury et al. 1994) has used laboratory cases based on errors in accounts receivable. We include inventory tests as well as accounts receivable because inventory has more sampling applications and is more likely to include errors (Icerman and Hillison 1991). For each sampling application, data were collected on the number of errors, the extent of any containment procedures, error size, error direction, planning materiality, and whether the error was projected or isolated.

RESULTS

Panel A of table 1 provides data on the sampling applications, including applications in which errors were detected, the number of errors projected and not projected, and the number of nonprojected errors in which immateriality and containment were used to justify the decision to not project the error. The 238 sampling applications yielded 117 tests (49 percent) with error, an indication that errors are common in many sampling applications. Most errors occurred in inventory price tests, followed by inventory test counts and confirmation of accounts receivable. Cutoff and other tests have relatively few errors. (4)
TABLE 1
Frequency and Disposition of Errors
                                              Tests
                                              With
                                             Errors

                 Col. 1   Col. 2   Col. 3    Col. 4

                                   No. of
                  Mean             Tests     No. of
Sampling         Sample   No. of    With     Errors
Application       Size    Tests    Errors   Projected

Panel A: All Observations

Accounts
Receivable:
  Confirmation     22       61       25        14
  Other             6        3       0          0

  Inventory:
  Test Counts      55       67       36        23
  Price Tests      26       67       47        40
  Cutoff Tests     16       33        6         0
  Other            12        7        3         1

  Total                    238      117        78

Percent                              49%       67%

                  Tests
                   With
                  Errors           Errors Not Projected

                  Col. 5       Col. 6      Col. 7      Col. 8

                                Non-        Non-
                  No. of     projected    projected     Non-
                  Errors     Immaterial   Contained   projected
Sampling            Not        Errors      Errors       Other
Application      Projected       (a)         (b)       Errors

Panel A: All Observations

Accounts
Receivable:
  Confirmation      11            4           3           4
  Other              0            0           0           0

  Inventory:
  Test Counts       13            6           3           4
  Price Tests        7            5           2           0
  Cutoff Tests       6            2           3           1
  Other              2            1           0           1

  Total             39           18          11          10

Percent             33%         46%          28%         26%

                                         Tests
                                          With
                                         Errors

             Col. 1   Col. 2   Col. 3    Col. 4

                               No. of
              Mean             Tests     No. of
             Sample   No. of    With     Errors
Audit Firm    Size    Tests    Errors   Projected

Panel B: Firm Differences

Firm A         21      110       31        14
Firm B         36       68       42        25
Firm C         43       60       44        39

Total                  238      117        78

% Firm A                         28%       45%
% Firm B                         62%       60%
% Firm C                         73%       89%

Overall %                        49%       67%

              Tests
               With
              Errors            Errors Not Projected

              Col. 5       Col. 6      Col. 7      Col. 8

                            Non-        Non-
              No. of     projected    projected     Non-
              Errors     Immaterial   Contained   projected
                Not        Errors      Errors       Other
Audit Firm   Projected      (a)          (b)       Errors

Panel B: Firm Differences

Firm A          17          13            3           1
Firm B          17           3            6           8
Firm C           5           2            2           1

Total           39          18           11          10

% Firm A        55%         76%          18%          6%
% Firm B        40%         18%          35%         47%
% Firm C        11%         40%          40%         20%

Overall %       33%         46%          28%         26%

Column Descriptions:

1 Average number of items in sample for that type of test.

2 Number of separate tests for each type of sampling
application.

3 Number of tests from column 2 in which errors were
identified.

4 Number of tests with errors from column 3 that were
projected.

5 Number of tests with errors from column 3 that were not
projected.

6 Number of tests not projected from column 5 based on
immateriality.

7 Number of tests not projected from column 5 because the
error was contained.

8 Number of tests not projected from column 5 that did not use
containment or immateriality as justification for not projecting
the error.

(a) For these errors, the auditor documented in the working
papers that the error was not projected because it was
immaterial.

(b) For these errors, the auditor performed additional
procedures that suggested that the error could be contained to a
sub-population or that the error was unique.


Consistent with Burgstahler and Jiambalvo (1986) we find that auditors often do not project errors from samples to the population, although the projection rate in our sample is higher than for the experimental cases in their study. Errors were projected in 78 cases (67 percent) in this study, compared to a reported projection rate of 35 percent across the experimental cases in Burgstahler and Jiambalvo (1986). (5)

Of the 39 cases in which errors were not projected, "lack of materiality" was used as an explanation for not projecting in 18 cases; error containment was used in 11 cases. In the remaining ten cases, the auditors did not project an error, and did not specifically justify the decision based on immateriality, containment procedures, or other factors. The use of containment procedures to justify the decision to not project an error is consistent with the primary findings of Dusenbury et al. (1994) that auditors use containment procedures as a justification for not projecting errors. Description of the contained errors and a discussion of the use of containment procedures follows a discussion of other factors affecting the projection decision.

Additional Factors Affecting the Projection Decision

Firm Differences

Panel B of table 1 provides information on the frequency and disposition of errors by audit firm. Firm A had lower error rates than Firm B and Firm C. Firm A also had the lowest rate of projection, and auditors from this firm most frequently used immateriality to explain the decision to not project the error.

Firm B had relatively high error and projection rates. Errors were projected in 25 out of 42 cases (60 percent), and auditors were somewhat more likely to use containment procedures. Auditors in this firm were also somewhat more likely to not project an error without specifically arguing that the error was immaterial. This happened most frequently for inventory test counts, and usually involved relatively small errors in test counts.

Firm C had relatively high error rates, and projected almost all errors. The error projection rate for this firm was significantly higher than for the other two firms ([chi square] = 15.32; p < .001). This firm took a more structured approach to error projection than the other two firms. Error projection computations were standardized in computerized audit workpapers, and auditors projected even extremely small audit differences.

These results indicate firm differences in sample sizes, and in frequency of error projection, even between firms considered to be roughly equivalent in terms of structure. One factor that may influence the frequency of projection by auditors is the relative ease of making the projection. As firms increasingly use computerized working papers, they may be more likely to project errors if this is facilitated by the working paper program. Firm differences in error projection may also reflect differences in training.

Type of Test Differences

Table 2 summarizes the error and projection rates by type of test. There are significant differences in error rates ([chi square] = 26.56; p < .01) and projection rates ([chi square] = 22.10; p < .01). There is a high correlation between the error rate and projection rate for each type of test. Both inventory test counts and inventory price tests have higher error rates and rates of projection than accounts receivable confirmations; cutoff tests have low error and projection rates.
TABLE 2
Error and Projection Rates by Type of Test

                        No. of     Number      Error
Type of Test            Tests    With Errors   Rate

Accounts receivable
  confirmation            61         25        41.0%
Inventory test counts     67         36        53.7
Inventory price tests     67         47        70.1
Cutoff tests              33          6        18.2
Other tests               10          3        30.0
Total                    238         117       49.0%

                         Number     Projection
Type of Test            Projected      Rate

Accounts receivable
  confirmation             14         56.0%
Inventory test counts      23         63.9
Inventory price tests      40         85.1
Cutoff tests                0          0.0
Other tests                 1         33.3
Total                      78         67.0%

[chi square] test of difference in error rates:
[chi square] = 26.56; p < .01

[chi square] test of difference in projection rates:
[chi square] = 22.10; p < .01

(Excludes tests in "other" category.)


The relation between error and projection rates is consistent with the argument that auditors are more likely to project frequently occurring errors. In addition to differences in error rates, the tests have other characteristics that may affect the rate of projection. Inventory price tests are a very specific test for a well-defined population. Inventory test counts are a very specific test, but it may not be easy to define the errors in dollar terms at the time the observation occurs. Inventory test counts also test client controls over the observation, in addition to providing substantive evidence. Accounts receivable confirmations are applied to a well-defined population, but address multiple objectives. Although cutoff tests are very specific, the fact that the dollar population is not well-specified may reduce the likelihood of error projection. Additional guidance may be needed on projecting errors from populations that are not well-defined, such as cutoff tests or inventory test counts.

Materiality of Projected and Nonprojected Errors

Table 3 provides descriptive information on the size of the errors. Values of the projected error, and the projected error as a percentage of the planning materiality set by the auditors are reported for projected and nonprojected errors. (6) For nonprojected errors, these values are also reported for errors which the auditor concluded were immaterial, errors which the auditor contained, and other nonprojected errors.
TABLE 3
Materiality of Projected and Nonprojected Errors

                                   No.
                                Positive
Error Classification     n      (Percent)

Projected Errors       78 (c)      54
                                 (69.2)

Not Projected (a)      29 (b)      20
                                 (69.0)

Not Projected--        13           9
Immaterial                       (69.2)

Not Projected--         8           6
Contained                        (75.0)

Not Projected--         8           5
Other                            (62.5)

                         Error Direction Not
                           Considered (all
                         errors recorded as
                          positive amounts)
                             Median Mean
                             (std. dev.)

                                     Estimated
                                    Proj. Error/
                       Est. Proj.     Planning
Error Classification     Error      Materiality

Projected Errors          $11,600       .078
                           51,340       .224
                        (118,525)      (.477)

Not Projected (a)          13,400       .110
                           64,050       .302
                         (95,801)      (.473)

Not Projected--             5,100       .018
Immaterial                 27,680       .091
                         (39,503)      (.167)

Not Projected--           118,600       .389
Contained                 130,300       .536
                        (106,563)      (.483)

Not Projected--            10,700       .160
Other                      56,900       .410
                        (123,082)      (.674)

                          Error Direction Not
                         (errors recorded as
                         positive and negative
                         amounts) Median Mean
                              (st. dev.)

                                     Estimated
                                    Proj. Error/
                       Est. Proj.     Planning
Error Classification     Error      Materiality

Projected Errors           $4,750       .031
                           40,210       .125
                        (122,799)      (.512)

Not Projected (a)           6,600       .040
                            1,380       .002
                        (115,865)      (.564)

Not Projected--             1,200       .012
Immaterial                 26,120       .084
                         (40,633)      (.172)

Not Projected--            36,600       .218
Contained                   7,480       .140
                        (175,201)      (.735)

Not Projected--             2,800       .064
Other                     -44,930      -.270
                        (128,618)      (.751)

(a) Amounts were computed by the authors because these errors
were not projected by the auditors.

(b) Projected amounts could not be computed for ten observations
due to lack of information on population size, primarily for
cutoff tests. Five of the ten are from the Not
Projected--Immaterial category, three are from the Not
Projected--Contained category, and two are from the Not
Projected--Other category.

(c) Sample size is 76 for projected error/planning materiality
due to lack of planning materiality data for two observations.


The first set of columns in table 3 report the value of the variables ignoring the direction of the error, so that all errors are reported as positive amounts. The mean projected error, approximately $51,000, represented 22.4 percent of planning materiality, while the mean nonprojected error was approximately $64,000 and 30.2 percent of planning materiality. The similarity of the nonprojected errors to the projected errors masks significant differences among the various types of nonprojected errors.

Projected amounts could be computed for 13 of the 18 errors deemed immaterial by the auditors. The average error, approximately $28,000, represented 9.1 percent of materiality. Both of these amounts are significantly lower than the mean value for the projected errors. (7) Excluding two large errors, the mean error is 2.9 percent of materiality. Both large errors involved price testing of subcomponents of inventory, such as testing direct labor in inventory. The sample size for each test was quite small, and the auditors' notations indicated that they considered other tests, including analytical procedures, in their evaluation of the significance of the errors.

The lower projected amounts for errors deemed immaterial by the auditor are consistent with the auditor being less likely to project small errors. Although the errors themselves appear to be immaterial, the auditor must aggregate immaterial errors found in other segments of the audit. In one study which looked at passed adjustments, Kreutzfeldt and Wallace (1986) found that the sum of passed adjustments averaged approximately 50 percent of materiality. This suggests that the nonprojected errors may be unlikely to change the auditor's conclusion about the fairness of the financial statements. However, we believe that it is preferable to project the errors, and reach the conclusion that an error is immaterial based on the projected amount.

Materiality--Contained and Other Errors

The mean projected error for contained errors, approximately $130,000, represented 54 percent of materiality. Both amounts are significantly larger than the amounts for projected errors. The auditor likely would not make an effort to contain an error if the projected amount was not expected to be significant. The mean projected amounts for errors not projected and considered neither immaterial or contained was approximately $57,000 and represented 41 percent of materiality. Although these errors are quite large, most of the errors decreased net income.

The last two columns of table 3 present a summary of the errors considering error direction. The mean projected error, approximately $40,000, represented 12.5 percent of planning materiality, while the mean nonprojected error was approximately $1,380 and 0.2 percent of planning materiality. The decrease in the mean value of the nonprojected errors reflects a large decrease in the mean value of the contained and other categories of nonprojected errors. The contained error group included one large understatement error. The other nonprojected errors were mostly understatement errors, resulting in a negative value for the mean projected error. This suggests that auditors consider the direction of the error in their error projection decision.

Kinney and Martin (1994) perform a meta-analysis of audit adjustment studies, and find that, on average, audit adjustments reduce income. They suggest that auditing serves to reduce reporting bias. Icerman and Hillison (1991) examined waived vs. booked audit adjustments, and found that the direction of the error did not appear to affect its disposition. In contrast, our results suggest that the direction of the error may affect the projection decision, one form of error evaluation.

Auditor Consideration of Sampling Risk of Projected Amounts

Audit risk increases when the auditor fails to adequately consider sampling risk. In almost all cases, auditors made a direct projection of the errors, without including an estimate of sampling risk as part of the projection. The auditors most often used some form of probability proportionate to size method to select sample items. However, we did not find a single sampling application in which the sample results were evaluated using statistical methods. Commenting on the results of peer reviews, Sullivan (1992, 57) notes "we do not recall seeing one statistical sampling application."

SAS No. 39 indicates that "total projected misstatement should be compared with the tolerable misstatement for the account balance or class of transactions, and appropriate consideration should be given to sampling risk" (AU [section] 350.26). Documentation from one audit firm indicates that sampling risk is explicitly considered only when the projected error is close to being material. Although this approach appears to comply with professional standards, the failure to adequately consider sampling risk, combined with relatively small sample sizes, may unacceptably increase the risk of incorrectly accepting the financial statements as fairly stated. This suggests that auditors may significantly underestimate sampling risk. In one study, Burgstahler et al. (1996) find that auditors are more likely to recommend an audit adjustment when sampling risk is explicitly considered. Further research is needed into how auditors consider sampling risk when using nonstatistical sample evaluation methods, and the potential effects of sampling risk on common sampling applications.

Containment Procedures

Table 4 contains descriptive information on the 11 contained errors. There is some evidence that containment is more common for certain auditors. Cases 2 and 3 involved the same audit, and Cases 4, 5, 6 and 7 were also from one audit. As previously discussed, the contained errors averaged 54 percent of materiality, because auditors generally would not engage in the effort to contain an error if the amounts involved were immaterial.
TABLE 4
Description of Contained Errors

        Test           Description of Error

1.      Cutoff         Sales cutoff error for
        (sales)        foreign shipments

2.      Accounts       Unrecorded magazine
        Receivable     subscription cancellation

3.      Inventory      Test count error
        test count

4.      Cutoff         Inventory purchase
        (purchase)     cutoff

5.      Inventory      Change in type of
        price test     inventory item

6.      Inventory      Inventory test count
        test count     errors

7.      Cutoff         Cutoff error
        (sales)

8.      Inventory      Unit of measure for
        price test     standard changed

9.      Test count     Errors in one location

10.     Accounts       Bankrupt account
        Receivable     receivable renegotiated

11. (d) Accounts       Failure to record
        Receivable     discounts for one type
                       of customer

        Mean amounts

                                     (000)
                         (000)     Projected
        Test             Error     Error (a)

1.      Cutoff          42.5         180.4
        (sales)

2.      Accounts         2.51        232.5
        Receivable

3.      Inventory      1 unit          8.2
        test count

4.      Cutoff          30.6 (b)    NA (c)
        (purchase)

5.      Inventory       43.0         310.9
        price test

6.      Inventory         NA        NA (c)
        test count

7.      Cutoff           6.4        NA (c)
        (sales)

8.      Inventory       19.2         111.5
        price test

9.      Test count     337 units     13.4

10.     Accounts        54           59.8
        Receivable

11. (d) Accounts         3.2        125.7
        Receivable

        Mean amounts    25.2 (e)    130.3

                                      Projected
                          (000)        Error/
        Test           Materiality   Materiality

1.      Cutoff             147          1.23
        (sales)

2.      Accounts           553          0.42
        Receivable

3.      Inventory          553          0.01
        test count

4.      Cutoff             870           NA
        (purchase)

5.      Inventory          870          0.36
        price test

6.      Inventory          870           NA
        test count

7.      Cutoff             870           NA
        (sales)

8.      Inventory           85          1.31
        price test

9.      Test count         160          0.08

10.     Accounts           170          0.35
        Receivable

11. (d) Accounts           240          0.52
        Receivable

        Mean amounts       489.8        0.54

        Test           Disposition

1.      Cutoff         Tested 100 percent of foreign shipments
        (sales)        during cutoff. Recorded adjustment for
                       actual error.

2.      Accounts       Extended test of magazine cancellations.
        Receivable     Estimated error placed on passed
                       adjustments.

3.      Inventory      Treated error as being confined to one
        test count     type of inventory.

4.      Cutoff         Determined that errors related to one
        (purchase)     plant and were immaterial.

5.      Inventory      Understatement error treated as unique.
        price test     Actual error placed on passed
                       adjustments.

6.      Inventory      Determined errors were at one warehouse;
        test count     client recounted amounts in warehouse.

7.      Cutoff         Tested particular type of sale further.
        (sales)        Projected to contained population and
                       passed adjustment.

8.      Inventory      Extended tests of standards and units of
        price test     measure. Passed adjustment for actual
                       error.

9.      Test count     Client recounted inventory; auditors
                       retested.

10.     Accounts       Significant portion of accounts
        Receivable     receivable tested. Adjustment recorded
                       for actual error.

11. (d) Accounts       Performed additional procedures for class
        Receivable     of customer with errors. Projected errors
                       by type of customer and passed
                       adjustment.

        Mean amounts

(a) Projected amounts computed by researchers. Based on units
for inventory test counts where units are indicated.

(b) Error had no income effect.

(c) NA--Amount not available due to lack of information on one
or more variables.

(d) Table contains 11 observations consistent with table 1.
Projected amounts are available for 8 observations as reported
in table 3.

(e) Mean does not reflect errors based on units.


Containment Procedures--Unique Errors

Three of the 11 errors were treated as unique. One involved a change in a unit of measure for a standard (Case 8). In this case, the auditors performed additional tests to ascertain whether other such errors existed. Not locating additional errors, they passed adjustment for the actual error. A second case involved a renegotiation of a bankrupt accounts receivable (Case 10). In this case, projection of the error would not have made a substantive difference, since over 90 percent of the population was tested by confirmation. The third case (Case 5) involved a change in an inventory item. This was an understatement error, and the auditors did not perform additional tests to verify that there were no similar transactions beyond the existing testing.

Containment of Errors to Sub-Populations

The remaining eight errors were contained to a sub-population. When the actual error is large, the projected error is likely to exceed materiality, and the auditor generally must perform more tests to determine the extent of the actual errors in the population. Rather than an unrestricted increase in testing, the auditor often focuses testing on the sub-population containing the error. Several cases capture some of the issues that auditors face in making these judgments.

In Case 1, a timing error occurred for a foreign shipment. The nature of the timing error is such that it would not occur for a domestic shipment. The auditors performed 100 percent testing of foreign sales within the cutoff period and recorded an adjustment for the actual error. Because the sub-population was completely tested, it was not necessary to project the error. In Case 9, test count errors were substantial in one warehouse, but not in another. Since the accuracy of test counts depends largely on the ability of the individuals taking and controlling the inventory counts, the two populations were not combined for purposes of projecting errors. Because of the number of errors, the client recounted all amounts in the one location. The errors in this case were also fully contained to a sub-population. However, because the population was large, the auditors relied on the client to fix the population.

Case 11, involving a failure to record discounts for one type of customer, is an example of partial containment. The auditors performed additional tests for this type of customer, and the errors were then projected by type of customer. However, in the other cases of partial containment, the errors were not projected to the contained sub-population.

Appropriateness of Containment Procedures

Although based on a limited number of observations, our sample suggests that auditors do contain errors to sub-populations. The use of containment procedures may be justified by the AICPA (1983) Audit Sampling Guide, which notes that audit sampling differs from sampling in other professions. However, the results of the current study also indicate that auditors do not always justify the containment of errors, or the determination that an error is unique. The results also suggest the need for professional guidance related to the use of containment procedures. Auditing standards do not address the use of containment, other than indicating that "auditors can also reduce this risk of material misstatement by modifying the nature, timing, and extent of planned auditing procedures on a continuous basis in performing the audit" (AU [section] 312.32).

Whether to contain an error depends on auditor judgment, including knowledge of the client gained from other tests. One relevant factor is whether the error arises from a characteristic that is unique to the transaction or sub-population. For example, Case 2 in Burgstahler and Jiambalvo (1986) involves an error in the recording of an interest-bearing receivable. The auditors determined through tests of transactions and discussions with the client that no other sales with special sales terms occurred during the year. In such a case, the auditors might conclude that this error should not be projected to receivables arising from recurring transactions. (8) This example is consistent with the treatment of Cases 8 and 10 on table 4. However, of particular concern is the auditor treatment of Case 5 in which auditors concluded that the error was unique, but did not document any procedures to confirm that the error was, in fact, unique.

If it is determined that the error is confined to a small segment of the population, procedures should be designed to rule out similar errors, or to determine the extent of similar errors in that segment of the population. Case 3 in Burgstahler and Jiambalvo (1986) involved a footing error on a credit memo. The auditors examined all the credit memos for the year and determined that no additional footing errors had occurred.

In Dusenbury et al. (1994), error containment was based on well-defined sub-populations in which every transaction had been investigated. However, in practice, auditors may not completely contain an error due to the cost of testing every transaction, unless the sub-population is small. In several cases the containment procedures involved sampling from the sub-population, but the error was not projected to that sub-population. If errors are contained to a sub-population and all transactions in the sub-population are not examined, then the containment procedures are a sampling application and the auditor should consider projecting the error to the sub-population.

Other Nonprojected Errors

Table 5 describes the other nonprojected errors that were neither contained nor explicitly described as immaterial by the auditors. Many of the errors were relatively small, with projected amounts less than 12 percent of materiality. The most interesting characteristic of the larger errors is that almost all of them are understatement errors, suggesting that error direction affects the projection decision.
TABLE 5
Description of Other Nonprojected Errors (Not Contained or
Classified as Immaterial)

        Test           Description of Error

1.      Accounts       Errors in confirmations
        Receivable     and alternative procedures

2.      Sales          Sales cutoff error
        cutoff

3.      Test           Test count error
        counts

4.      Accounts       Errors in confirmations
        Receivable     and alternative procedures

5.      Inventory      Inventory confirmation

6.      Accounts       Errors in confirmations
        Receivable     and alternative procedures

7.      Test           Test count errors
        counts

8.      Test           Test count errors
        counts

9.      Test           Test count errors
        counts

10. (d) Accounts       Errors in confirmations
        Receivable

        Mean amounts

                                    (000)
                        (000)     Projected
        Test            Error      Errors

1.      Accounts        6.2         6.9
        Receivable

2.      Sales          1555 (b)    NA (c)
        cutoff

3.      Test           20 units    23.4
        counts

4.      Accounts         .9        12
        Receivable

5.      Inventory      24.4        37.8

6.      Accounts        2.2         2.2
        Receivable

7.      Test           30 units   360.1
        counts

8.      Test           14 units     3.4
        counts

9.      Test              NA       NA (c)
        counts

10. (d) Accounts        4.8         9.4
        Receivable

        Mean amounts    7.7 (e)    56.9

                                      Projected
                          (000)        Error/
        Test           Materiality   Materiality

1.      Accounts            60          0.12
        Receivable

2.      Sales              908           NA
        cutoff

3.      Test               117          0.20
        counts

4.      Accounts           100          0.12
        Receivable

5.      Inventory          115          0.33

6.      Accounts            25          0.09
        Receivable

7.      Test               175          2.06
        counts

8.      Test                85          0.04
        counts

9.      Test               NA            NA
        counts

10. (d) Accounts            28          0.34
        Receivable

        Mean amounts       179.2        0.41

        Test           Authors' Comment

1.      Accounts       Test had high dollar coverage. Error not
        Receivable     included with passed entries.

2.      Sales          Error was an understatement error.
        cutoff

3.      Test           Projection based on units.
        counts

4.      Accounts       Primarily untested amounts from
        Receivable     alternative procedures. Placed on passed
                       adjustments.

5.      Inventory      Understatement error; not on passed
                       entries.

6.      Accounts       Essentially entire population tested. Not
        Receivable     placed on passed adjustments.

7.      Test           Understatement error. Projection based
        counts         on units.

8.      Test           Projection based on units.
        counts

9.      Test           Amounts not quantified; most differences
        counts         were small.

10. (d) Accounts       Understatement errors. Recorded
        Receivable     adjustment for actual errors.

        Mean amounts

(a) Projected amounts computed by researchers. Based on units
for inventory test counts where units are indicated.

(b) Gross amount of sale. Only the gross profit effect was
placed on passed entries.

(c) NA--Amount not available due to lack of information on one
or more variables.

(d) Table contains 10 observations consistent with table 1.
Projected amounts are available for 8 observations as reported
in table 3.

(e) Mean does not reflect errors based on units, or the sales
cutoff error (error #2).


The most common type of error is a test count error. Auditors may be less likely to project test counts, because the error information is units, and pricing information may not be readily available when the errors are uncovered during the inventory observation. Although unit errors can be converted to dollars, this is time-consuming, since sample sizes tend to be largest for test counts. However, the danger is that what appear to be small error rates in units could result in large estimates of error when projected to the population. (9) Although SAS No. 39 and the Audit Sampling Guide discuss several different methods of error projection, they do not discuss error projection based on measures other than dollars.

Limitations

The reported results are based on a univariate analysis, consistent with the descriptive nature of the study and small sample sizes for some of the explanatory variables. As a result, observed relationships could be attributable to spurious relationships among the variables. We reviewed the correlations among the explanatory variables; the results do not appear to be unduly influenced by collinearity among the explanatory variables. (10)

SUMMARY AND CONCLUSIONS

We examined the decision to project errors for a sample of audits from three large accounting firms. We describe the auditor's error evaluation decision as a two-stage process in which errors are projected to quantify the errors. If the error is potentially material, the auditor must then decide how to resolve the error.

Consistent with previous research, we find that many errors are not projected. Factors associated with the decision to project errors include error materiality and direction, type of test, the presence of containment procedures, and task-specific firm structure. Immateriality was the most common reason for not projecting an error. Although most errors were small and unlikely to result in materially misstated financial statements, such immaterial errors could still be material when aggregated with other errors, especially if sampling risk is considered. As a result, we believe that immateriality should not be used as a justification for not projecting errors.

Auditors often contain errors to sub-populations as part of the resolution of large errors. The use of error containment procedures is consistent with the finding in Dusenbury et al. (1994) that auditors frequently support the isolation decision with additional audit effort. Burgstahler and Jiambalvo (1986) argue that isolating errors is rarely appropriate, since the errors proxy for unknown errors. However, error containment appears to be accepted in practice. We believe that the use of error containment is consistent with the nature of audit sampling and the guidance in the AICPA (1983) Audit Sampling Guide, and is an efficient approach to resolving certain types of errors. However, we believe that auditors should document why an error is not representative of the population being sampled. When an error is contained to a sub-population, this represents a sampling procedure, and the error should be projected to the sub-population. Future research could examine auditor perceptions of what constitutes appropriate and inappropriate containment procedures as a basis for developing further guidance on the use of error containment.

We find that auditors frequently use random-based methods to select samples. However, they use nonstatistical methods in evaluating sample items. Sampling error is objectively determinable when statistical evaluation methods are used. However, little is known about how auditors consider sampling risk when using nonstatistical methods. SAS No. 39 indicates that the auditor should consider sampling risk when the projected misstatement is close to tolerable misstatement. Research is necessary to address how auditors interpret this requirement. Additional guidance would be helpful to specifically describe what would be considered an adequate allowance for sampling risk, given a range of sample sizes and materiality levels. Given the relatively small sample sizes observed in some sampling applications, we believe it would be beneficial to require auditors to document in the working papers an assessment of the adequacy of sampling risk for all sampling applications.

We would like to thank Barry Cushing, Bill Felix, Jim Frederickson, Jim Loebbecke, the anonymous reviewers, workshop participants at Syracuse University, and the University of Utah for helpful comments on earlier versions of this paper. Access to workpapers was generously provided by three accounting firms.

The nonalphabetical order of the authors' names reflects a rotation across multiple projects. Both authors made equal contributions to this project.

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(1) Error containment procedures are additional procedures performed by the auditor after an error is detected in an audit sample. These procedures are designed to help the auditor determine the extent of errors in a sub-population or to determine that an error is unique and nonrecurring (Dusenbury et al. 1994).

(2) It would appear that the materiality of an error cannot be determined until it has been projected. However, the auditor can likely make a rough mental determination of the projected materiality based on the magnitude of the error and the size of the population.

(3) DeFond and Jiambalvo (1991) indicate that the greater frequency of error corrections involving overstatement errors is consistent with management incentives to increase income. The infrequency of error corrections involving understatement errors may also partially reflect auditor incentives if auditors are less likely to require correction of understatement errors.

(4) Some have suggested that cutoff is not a sampling application. For the audits we examined, the auditors examined only a small number of transactions in the defined cutoff period. The AICPA (1983, 9) Audit Sampling Guide defines audit sampling as "the application of an audit procedure to less than 100 percent of items within an account balance or class of transactions."

(5) There are several possible explanations for the higher projection rate in this study compared with the results in Burgstahler and Jiambalvo (1986), including differences in error size and type, differing incentives in laboratory experiments, and changes in auditor behavior over time. The cases in Burgstahler and Jiambalvo (1986) were all material errors. We find that auditors are more likely to not project and contain an error when it is material. Also, while the errors in Burgstahler and Jiambalvo (1986) are realistic, they may not be representative of the errors which auditors encounter in practice. Projection rates may also have been affected by incentives; Cushing and Ahlawat (1996) indicate that auditors are more involved in decisions in real-world settings. Error projection rates may also have improved as auditors gained experience with error projection.

(6) When a sample contained both overstatement and understatement errors, the auditors netted the errors prior to projection. The projections were point estimates of the total error and did not include an allowance for sampling risk. The projected error was computed by the authors when the auditors did not compute a projected error. Projected amount for test count errors were based on unit, rather than dollar, error rates. We were unable to compute projected errors in ten cases due to lack of information on population size, primarily for cutoff errors. Five of the ten are from the Not Projected--Immaterial category, three are from the Not Projected--Contained category, and two are from the Not Projected--Other category.

(7) Firm C projected almost all errors, including very small errors. When this firm is excluded from the analysis, the difference between nonprojected immaterial errors and projected errors increases in significance.

(8) For instance, an auditor might argue that the interest-bearing receivable has been improperly included in the population of trade accounts receivable. In such a case, the auditor is not arguing that the error is not representative, but that the sample item was improperly included in the population of interest.

(9) We project test count errors as (errors in units/units counted) x (book value of inventory). This method may overstate the projected error, because auditors often take additional test counts of the inventory without recording them. If the additional tests were included in the sample, the projected error would be lower. Also, auditors will usually recognize whether the error occurred with a high dollar-value item, and may be more likely to project an error if it occurred with a high value product.

(10) The use of containment procedures was positively related to the materiality of the error, and negatively related to the error rate for that test, as predicted. Containment is less likely for common errors, and is not used if the error is immaterial. Auditors are also less likely to indicate that an error is immaterial if that type of test has a high error rate.

Randal J. Elder is an Associate Professor at Syracuse University and Robert D. Allen is an Assistant Professor at the University of Utah.
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Date:Sep 22, 1998
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