- For more information contact Dr. Will Yancey at 734.744.4400 or email to wyancey@aclrsbs.com
- For an extensive bibliography on sampling for sales and use tax, see www.willyancey.com/sampling.htm

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.

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.

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 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.

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.

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.

- For more information contact Dr. Will Yancey at 734.744.4400 or email to wyancey@aclrsbs.com
- For an extensive bibliography on sampling for sales and use tax, see www.willyancey.com/sampling.htm