One thing not covered by SAS No. 56 is how several individual analytical procedures used as substantive tests should be combined. Researchers have observed that auditors seek a large and varied amount of information when applying analytical procedures. Several ratios are computed and trends analyzed.

However, it is not clear how these individual elements are combined in reaching a final decision, and how the individual elements are weighted.

A possible approach to combining audit assurances from several individual analytical procedures and integrating the results into the overall audit risk model is based upon the following:

* Consideration of the effectiveness of analytical procedures as substantive tests; and

* A categorization of analytical procedures and an approach to valuing the effectiveness of each.

Measuring the Effectiveness of Analytical Procedures

There is substantial empirical evidence concerning the effectiveness of analytical procedures. Several studies have shown that formal analytical procedures, discussion with clients, and expectations derived from prior years' error experience together accounted for 40% to 50% of errors detected. These studies also suggest that more errors are found by detailed tests than by analytical procedures, thereby confirming the intuitive belief of many auditors that detailed tests are often the most effective form of audit evidence. However, considering how time- consuming and costly many detailed tests can be, many practitioners believe analytical procedures an a more efficient source of audit evidence.

Nevertheless, analytical procedures are not a panacea. How can an auditor decide whether a particular procedure is more effective than an alternative form of evidence? The factors suggested by SAS No. 56 are--

* the existence of a plausible and predictable relationship,

* the nature of the assertion being addressed,

* the reliability of the data used to develop the expectation, and

* the precision of the expectation.

Plausible and Predictable Relationship. To begin with, the analytical procedure must be applied to a plausible, predictable relationship. This is often a function of the particular accounting variable being audited. Generally, income statement accounts tend to be more easily predictable than balance sheet accounts. The difference in predictive power seems to be attributable to the fact that income statement accounts often represent a single economic event, whereas balance sheet accounts are dependent on multiple economic events, each of which may be subject to unique influences.

Nature of Assertion. A second consideration when assessing the effectiveness of an analytical procedure is the particular audit assertion under consideration. Analytical procedures are particularly useful evidence with respect to assertions for which potential misstatements would not necessarily be apparent from examining detailed evidence, or for which detailed evidence is not available. This is particularly applicable to the completeness assertion. Consider, for example, the assertion that a brewing company has completely recorded its revenue. Doing a detailed test of the recorded beer sales will tell the auditor nothing about the risk that other sales may not have been recorded. However, an analytical procedure that relates recorded beer sales to barrels shipped as verified by a government excise tax agent may be very powerful audit evidence.

Reliability of Data Used. A third consideration is the reliability of the data being used to predict the dependent variable. The following considerations (most of which are drawn from SAS No. 31, Evidential Matter) are pertinent:

* Data derived from sources external to the client are usually more reliable than data from internal sources.

* Independently, internally generated data are generally more reliable than data generated by the accounting system. However, the auditor must consider whether there is any need to evaluate the controls over the preparation of operational data.

* If the data is generated from the accounting system, reliability is affected by whether the system is well controlled or poorly controlled and whether the data has been subjected to substantiation by other procedures. Some analytical procedures may only be reliable if the auditor also selects audit procedures that provide evidence concerning the accurate processing of transaction data.

* Apart from the quality of the data, the greater the number of sources of data, the more effective the test is likely to be.

Precision of Expectation. Finally, the effectiveness of analytical procedures is affected by their precision. The precision, in turn, will be dependent on whether reliable, relevant data are used, as discussed previously, and also, the level of data disaggregation at which they are employed. The greater the disaggregation of the data, the more effective these procedures will be at detecting error because there is less chance of the error being masked by bona fide offsetting changes in the business. Accordingly, analysis at the business unit level is more effective than analysis at the consolidated level, and analysis at the product-line level is more effective than analysis at the business-unit level. Similarly, analysis of data on a monthly basis is much more likely to detect errors than analysis of annual data.

Evaluating Specific Analytical Procedures

The evaluation of an individual analytical procedure should logically be related to the preceding effectiveness factors.

The first two factors affecting the procedure's effectiveness are closely associated with the financial statement item and particular assertion under consideration. Based on the consensus judgment of a group of experienced auditors, the linkage between each analytical procedure and each assertion it addresses can be evaluated as either strong or weak.

The third effectiveness factor pertains to the quality of the data. This seems to be strongly related to the type of analytical procedure.

CONFIDENCELEVELSFORCATEGORIESOFANALYTICALPROCEDURES

AggregatedataDetaileddata

LinktoassertionLinktoassertion

CategoryofProcedureStrongWeakStrongWeak

Single-variabletest:

Comparisontobudget10%10%30%10%

Trendanalysis10%10%30%10%

Scanning10%N/AN/A30%

Ratioanalysis20%10%40%10%

Testofreasonableness(*)(*)50%20%

Regressionanalysis(*)(*)70%40%

*Testconsideredunlikelytobeappropriatewhenappliedtoaggregatedata.

Analytical procedures can be categorized into the following groupings:

1. Single-variable analytical procedures, including--

* comparison of recorded amounts against current-period budget amounts;

* trend analysis comparing recorded amounts against corresponding amounts from prior periods: and

* scanning items in transaction listings, subsidiary ledgers, general ledger control accounts, adjusting entries, suspense accounts, and reconciliations.

2. Financial ratio analysis, which tends to be more effective than single-component procedures because it explicitly considers interrelationships among financial variables. By developing an expectation of the normal relationship between two or more variables, we can often detect errors in one of those variables. Multiple ratios can be considered together to identify the type of error likely to arise. For example, a decrease in accounts receivable turnover accompanied by an increased inventory turnover could suggest the possibility of omitted credit purchases.

3. Tests of reasonableness, which have been defined as non-statistical models using operating or external data as well as financial data to predict an amount under examination. Two examples are the use of a client's average borrowings and market interest rates to predict interest expense, and the use of employee head counts and average remuneration statistics to predict payroll expense. The inclusion of non-accounting as well as accounting variables in the predictive model will enhance the reliability of a test of reasonableness compared to single variable and financial ratio analysis.

4. Regression analysis, which is similar to a test of reasonableness in that it involves the creation of a model using operating and external data as well as financial data. However, the added objectivity and precision of the procedure make it a more reliable form of audit evidence.

The fourth effectiveness factor, precision, is closely related to the degree of disaggregation of the data. Most, although not all, analytical procedures can be applied at distinctly different levels of detail. The more detailed the data, the more powerful the procedure.

Based upon the preceding evaluation structure, confidence levels may be assigned judgmentally to the categories of analytical procedures as shown in the accompanying table. The confidence levels in the table give guidance as to how much weight to give to the category in reaching an overall conclusion about the assertion being evaluated. Because the procedures "comparison to budget" and "trend analysis" when applied to aggregate data are less effective than other categories, whether the link to the assertion is considered strong or weak, the confidence level is considered 10%. When detailed data are used, the more effective the category of procedure and the greater the link to the assertion, the more weight (or greater confidence) can be given to the result of the analytical procedure.

David A. Scott, CA, is a partner of Price Waterhouse in Canada. Wanda A. Wallace, PhD, CPA, CMA, CIA, is John N. Dalton Professor of Business Administration of the College of William and Mary.