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Sampling for Sales and Use Tax Audits, Winner of the IPT Sales Tax Literary Award Competition, by Dr. William F. Yancey

Press Release Jun 15, 1999

Sampling is growing as an important issue in sales and use tax audits. Auditors from some state tax departments are implementing more advanced sampling methods than block sampling that has been used so heavily in the past. Taxpayers are more carefully analyzing audit sampling plans to verify the accuracy and efficiency of those plans.

The purpose of this essay is to describe some fundamental concepts of sampling in sales and use tax audits. First, the essay answers the question, "Why sample instead of detail examination of each transaction?" Answering this question leads to the second topic, the definitions of sampling risk, nonsampling risk, and sampling cost. Third, nonstatistical and statistical sampling methods are compared. Fourth, differences between financial statement audits and transaction tax audits are explained. The final section provides a summary and call for more education on sampling for sales and use tax professionals.

Why Sample?
Sampling is necessary when the taxpayer has so many records that a detailed examination of each record is not possible. Virtually all state sales and use tax auditors use some form of sampling on large corporate taxpayers. Without sampling the auditors would be unable to complete audits in a reasonable amount of time.

Sales and use tax audit samples consist of a subset of records drawn from a large population of transaction records. These sample transactions are examined for errors, including tax underpayments and overpayments. Projections are made from the errors observed in the sample to an estimate of the errors in the population. Usually positive and negative errors from the sample transactions are netted against each other to yield a total net error. Some audits consist of detail examination of all transactions above some dollar threshold, and sampling for transactions below that threshold.

Taxpayers benefit from efficient and effective sampling in sales and use tax audits. Proper sampling improves efficiency by testing a much smaller number of records than a complete detail examination of the population. The sampling plan is effective when it provides an accurate estimate of the true amount of error in the population. Effectiveness is not directly measurable, since the true amount of error would be known only if every record were examined in detail.

Sampling Risk, Nonsampling Risk, and Sampling Cost
Researchers in many scientific disciplines have evolved sophisticated sampling methods over the past century. Some concepts relevant to sales and use tax audits are sampling risk, nonsampling risk, and sampling costs.

Sampling risk is the chance that the estimate projected from the sample is significantly different from the amount that would be determined if every item in the population were tested. Sampling risk is inevitable whenever a sample is tested rather than the complete population. Good sampling procedures are designed to reduce sampling risk, but this risk cannot be eliminated without testing every item in the population. Unless we test every item in the population, we do not know the difference between the amount projected from the sample and the true amount in the population.

Sampling risk is increased when small samples are taken. For example, suppose we know that in a population of 1,000,000 records approximately two percent of those records contain tax errors. Taking a sample of only 50 records from this population has a high sampling risk, because there is a high chance that this sample will show zero errors. It is remotely possible that a sample of 50 will include exactly one error and that the projection from that one error will be close to the true amount of underpaid or overpaid tax in the population. Taking a sample of 500 items increases the chances of accurately estimating the error rate (10 errors in a sample of 500 gives a two percent error rate).

Sampling risk should not be confused with sampling bias. Sampling risk is the probability that the sample projection differs from the population without specifying a direction. Sampling bias is the probable direction of the difference between the estimate and the population. The government will probably collect more revenue than it should when the sample is biased towards over assessment. The taxpayer probably pays less than it should when the sample bias is towards under assessment. People experienced with sampling in the sales and use tax environment can evaluate an audit sampling plan for both risk and bias.

Nonsampling risk is the risk that an incorrect determination of total error would be made even if the testing procedures were applied to every item in the population. An example of nonsampling risk is where the auditor incorrectly applies the law to determine the taxability of items in the sample. Another example of nonsampling risk is when reversing entries are omitted from the sample, but the projection is made over a population that includes reversing entries.

Sampling cost in a sales and use tax audit is the total cost of planning, selecting, testing, and reviewing the sample. The most obvious costs are the time for clerical staff to find and copy documents, and for the auditor to examine those documents. Sampling costs also include the time and expense for the taxpayer and its representatives to review the auditor’s work and to resolve difficult items in the sample.

Proper sample planning must consider the trade-offs between sampling risk, nonsampling risk, and sampling cost. Decreasing sampling risk often requires increasing sample size and sampling cost. Decreasing nonsampling risk may require more extensive training and review that increases sampling cost. However, sampling risk and nonsampling risk are also costly in the sense that incorrect assessments or refunds. The taxpayer and the auditor should become aware of the risks and costs, and reach some agreement on how to trade-off those risks and costs.

Nonstatistical Versus Statistical Sampling
In nonstatistical sampling, the auditors estimate sampling risk by relying on professional judgment. The severe limitation of nonstatistical sampling is that it does not allow the auditor to make a quantitative estimate of sampling risk. An example of nonstatistical sampling is block sampling where auditors select a few days, weeks, or months from the population. The auditor assumes the sample time periods are representative of the entire population. By not taking sample transactions over the entire audit period, block samples increase sampling risk. If the tax error rate in the sample time periods differs significantly from the time periods not sampled, the block sampling method will produce results that are not valid.

Statistical sampling methods do provide quantitative estimates of sampling risk. Statistical sampling requires that the person selecting the sample relies on a random sample selection process rather than his or her judgment about the extent to which the sample represents the population. The projected error from a statistical sample may differ significantly from the true error in the population, but this sampling risk can be quantified using statistical formulas derived from the theory of probability. Sampling risk is usually expressed as a confidence interval, such as a 95 percent chance that the total error is between $400,000 and $480,000.

A statistical sampling plan begins with (1) a goal for accuracy, such as a 95 percent confidence interval, (2) a tolerable error, such as $25,000, and (3) an estimate of the error rate in the population, such as one percent. Statistical formulas are used to compute the sample size that is likely to achieve these goals. The population is divided into two or more strata, and a specified number of items are randomly selected from each stratum. After the sample results are collected, the sample is evaluated to determine if the sampling goals are achieved. If those goals are not achieved, the sample could be expanded or the goals could be modified.

One nonstatistical method of sample evaluation used by some auditors is to compare the distribution of invoice dollars in the sample to the distribution of invoice dollars in the population from which the sample is drawn. If the sample’s mean dollars per transaction is close to the population’s mean, the auditor concludes the sample is representative of the population. The auditor assumes that if the invoice dollars are representative, then the projected error from the sample will also be representative of the population. This method relies on the auditor’s judgment rather than a quantified estimate of sampling risk.

Financial Statement Versus Transaction Tax Audits
The primary purpose of a financial statement audit is to determine whether the financial statements taken as whole are materially correct. Financial auditors explicitly consider materiality. For example, the materiality threshold for a corporation with $10 billion in assets might be $50 million. The financial auditors’ null hypothesis is that the financial statements are materially correct. Sample data is gathered to determine whether there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis that the financial statements are materially incorrect. Similarly, financial auditors also test a corporation’s system of internal controls to determine whether they are or are not functioning properly. Thus, the primary purpose of financial statement auditors is reach a conclusion about whether to accept or reject a null hypothesis. A secondary purpose of financial audits is to estimate the amount of adjustment that would materially correct the financial statements.

In contrast, the primary purpose of a tax audit is to estimate the amount of overpaid or underpaid tax. The tax auditor may have no specific policy on the materiality threshold for a sales and use tax audit. If the threshold is zero, then any adjustment including one single dollar is material. When a materiality threshold is specified for tax audits, it is far less than the level chosen for the audit of taxpayer’s consolidated financial statements. A possible secondary purpose of a tax audit is to accept or reject the hypothesis that the taxpayer’s tax accrual system is functioning with an acceptably low error rate.

Financial statement auditors have the advantage of well-developed set of professional standards on audit sampling. The best-known financial statement audit standard is the American Institute of Certified Public Accountants’ Statement on Auditing Standards Number 39 ("SAS 39") that describes both statistical and nonstatistical sampling. SAS 39 provides general guidance for auditors to consider in planning an financial statement audit. Professional standards for sales and use tax audits do not exist at this time.

Summary And Call For Education
The preceding sections of this essay describe some general concepts for sampling in sales and use tax audits. Sampling is needed when the taxpayer’s records are too voluminous to examine in detail. Sample planning requires trade-offs between sampling risk, nonsampling risk, and sampling cost. Statistical sampling methods provide a quantified estimate of sampling risk, and nonstatistical methods do not. Financial statement audits have a higher materiality threshold and more emphasis on hypothesis testing than sales and use tax audits.

The reluctance of auditors, taxpayers, and consultants to discuss sampling issues is due to a lack of understanding of the fundamental concepts. Better education and training guides specifically applying sampling to practical problems in sales and use tax audits will improve understanding. Cooperation between government agencies and professional associations will improve the implementation and training for sales and use tax audit sampling. As all parties become better educated, they will become more confident in the use of sampling. Better cooperation might decrease sampling costs and audit dispute resolution time.

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