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.
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 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
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.
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.
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.
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.