Please answer the following:

1. What have you learned about the different sampling techniques?
2. Are there times when one technique is better than another? Please explain.

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Managing tax audits using sampling technique

state and federal tax examiners regularly use sampling and estimation in their tax audits. While sampling in an audit can be a convenient time-saver for both taxpayers and examiners, it is important to know the pitfalls that can cause unduly overstated estimated adjustments when sampling is used in a tax audit. This article explores those potential pitfalls and offers practical advice and best practices.

Sampling is a tool that is generally used whenever there is a list of records, also known as the population, that requires an assessment in order for the taxpayer to categorize the costs in a correct manner. Taxpayers use sampling to estimate the total amount of taxable transactions, meals deductions, expenditures qualifying for the Sec. 41 research credit (R&D credit), and several other applications. 1 The IRS and state taxing authorities typically use sampling to audit taxpayer determinations and estimate adjustments to amounts reported on tax returns. Sampling can produce efficiencies by reducing the volume of work and time required to make the necessary determinations required for tax filings or audits of tax fillings.

The two types of sampling: Statistical and judgmental

The two types of sampling used across tax audits are statistical (random) sampling and judgmental (nonrandom) sampling.

A statistical sample gives each record in the population a known, nonzero chance of selection. This allows for an unbiased sample selection and an unbiased representation of the population. Moreover, the examiner can make mathematically defensible conclusions about the population and the accuracy of the estimates.

A judgmental (nonrandom) sample is based entirely on the examiners judgment. For example, the examiner may pick the sample based on prior research and knowledge of problematic areas. While this can be efficient for finding issues, it causes gross bias when extrapolating sample results to make conclusions about the population. Even when the examiner attempts to select the sample haphazardly in an effort to judgmentally choose a random assortment, there is a human tendency to select a sample that is not representative of the population, and therefore judgmental samples risk a skewed calculation of adjustments, disallowed amounts, or even penalties and fines.

Both methods of sampling have advantages and disadvantages.

Pros and cons

A common fallacy is that statistical samples require larger sample sizes than judgmental ones. The apparent larger sample sizes are due to stricter specifications for confidence levels and accuracy of estimates, not because the sample is statistically selected.

For example, in an IRS field directive on the use of statistical and judgmental sampling in R&D credit examinations, 2 exam teams are instructed to first calculate the sample size required for an estimate of the disallowance to be accurate within plus or minus 10%. If that required sample size is too large, the directive recommends discussing a smaller sample size with the taxpayer using judgmental sampling. However, often, that judgment sample is merely a randomly selected statistical sample just a smaller sample size. While many taxpayers would find a smaller, less intrusive audit more appealing, it is important to consider the potential resulting accuracy of an adjustment from a sample that is too small; it could result in a wildly inaccurate estimate of the disallowance. True, a smaller effort could result in a wildly small or wildly large estimated adjustment. The point is that the small sample size is akin to playing high-stakes adjustment roulette.

As a side note, in this particular example, if the taxpayer agreed to the smaller size under a judgmental sample, they would give up more than just protection from a wildcard on the accuracy whether it is randomly selected or not. IRS guidelines give taxpayers the benefit of the doubt on accuracy when the IRS draws a random sample in an audit. 3 For example, as a result of the sampling, if an unfavorable taxpayer adjustment is estimated to be, say, $2 million plus or minus 30%, then the IRS will reduce the adjustment by 30% due to the inaccuracy of the estimate. (When the estimate is accurate within plus or minus 10%, the Service will use the estimated adjustment as is.) In this example, that means the unfavorable adjustment would be only $1.4 million instead of $2 million. When the IRS asks a taxpayer to accept an estimate without this accuracy adjustment, and the sample is reduced to an arbitrarily negotiated, mutually agreed-upon comfortable sample size, rather than one statistically computed to achieve a targeted level of accuracy, it is essentially asking the taxpayer to accept a less accurate figure with no consideration of the accuracy in the consequences of the audit. 4

It is best to have a statistician looking out for the taxpayers interest, reviewing proposed methods, advising on pros and cons of proposed audit plans, and/or working with the IRS or state taxing authority cooperatively to devise a fair and equitable plan that favors neither the taxing authority nor the taxpayer.

It should also be noted that the IRS does not allow taxpayers to use judgmental sampling when taxpayers use sampling to estimate values for tax returns. Only statistical random-based sample selection is allowed and the accuracy of the estimates must be calculated. Further, if the taxpayer is estimating a benefit with worse (greater) than plus or minus 15% precision, the taxpayer may not claim the full amount of the estimated benefit. Instead, the benefit is subject to a reduction equal to the precision level. For example, if the taxpayer estimated a deduction of $1 million plus or minus 50%, there is a 50% reduction in the deduction, and the taxpayer may only deduct $500,000. There is not an option to call it a judgmental sample and claim the full $1 million.

Below are examples of audit approaches that use judgmental sampling. Although these are basic hypothetical examples, all three approaches are seen in practice in both state and federal tax audits.

Example 1. The auditor chooses the sample: A state auditor is looking for rare instances of taxable transactions and will be estimating the total taxable amount. Suppose the taxpayer has a population of only 10 transactions. The transaction amount is known for the entire listing,

The taxable amount for each transaction is not known prior to reviewing the sample selections, but for the sake of this example, taxable amounts are also shown in the table

The auditor uses his judgment to select five transactions in an area he knows is problematic. He determines the taxable amount on five records. The auditors choices are denoted under the Sample column in the table

The average of the taxable amount, based on the auditors choice, is $3,000, as shown by the equation Average of the Taxable Amount

This average amount extrapolates to an estimated taxable amount of $30,000 ($3,000 10).

Note that the actual taxable amount in the population is $17,000. Thus, the estimate from the auditors examination overestimates the actual taxable amount by a significant amount.

This example may raise the question, can statistical samples be off, too?

Yes, but the accuracy of the estimate can be calculated and therefore incorporated in the interpretation and reliance on the estimate. Furthermore, unbiased estimates can be extrapolated from statistical samples; they favor neither the taxpayer nor the tax authority. A statistician can consider confidence and accuracy specifications to determine a sample size that will extrapolate an estimate with a reasonable level of accuracy.

Example 2. The auditor and taxpayer both choose half of the sample: This second example has been suggested by the IRS in R&D credit audits; it was common in the past but rarely has been seen in recent years. The IRS proposes that it and the taxpayer each select an equal portion of the sample using their own judgment. It sounds fair, but it is problematic. Suppose the taxpayers qualified research expenditures (QREs) as filed are listed in the table Transactions in Example 2, below, along with the likely favorable and unfavorable adjustments, if audited. (Normally, before sampling, the adjustment amounts would not be known. They are shown here for illustrative purposes.)

Note that in this example, the favorable and unfavorable adjustments net to zero. So, the taxpayer filed the correct amount even though projects were a little under- or overstated.

Now suppose the IRS selects two projects, and the taxpayer (TP) selects two projects as denoted under the Sample column in the table

The taxpayer chooses typical projects that they deem would have a favorable adjustment, and the IRS chooses two projects that it thinks would have an unfavorable adjustment.

Based on this method of selection, the extrapolated adjustment is $500,000. This is estimated from the average adjustment ($50,000) in the sample times the number of projects in the population (10). See the equation

Note that the true adjustment is $0. Thus, the taxpayer ends up in an unfavorable position. There is no reduction of the adjustment due to inaccuracies from a smaller size. Typically, the sample size is more than four projects; the small sample size here is for illustrative purposes. With a small or large sample, however, the point is the same: The taxpayer could end up with an inaccurate unfavorable adjustment due to a biased sampling method, even when the taxpayer chooses half of the sample selections.

Example 3. More on small random samples labeled as judgmental samples: As discussed above, when specified criteria for a statistical sample yield a large sample size, the IRS may approach the taxpayer to agree to use an extrapolated adjustment from a smaller judgmental sample. However, the judgmental sample is randomly selected just like a statistical sample. In actuality, if they consent, the taxpayer agrees to an inaccurate sample and allows the IRS to ignore the inaccuracy.

The margin of error (ME) is the plus or minus amount reported around an estimate. For example, an adjustment could be estimated to be $50,000 plus or minus $20,000. Relative precision is an estimates ME divided by the estimate. It describes how much an estimate may vary in relationship to itself. The IRS measures accuracy in terms of relative precision. In this example, the relative precision is $20,000 $50,000 = 40%. The ME creates a confidence interval from $30,000 to $70,000 ($50,000 $20,000 = $30,000 and $50,000 + $20,000 = $70,000).

When there is an adjustment in a statistical sample, the IRS uses the most taxpayer-beneficial confidence bound, which is $30,000 in this example.

If the IRS were to use this approach on data from the prior example, the results could look like those in the table Sample of Transactions in Example 3, below. The Random Sample column in this table represents a randomly selected list of the projects.

The estimated adjustment extrapolated from the random selection becomes as shown in the equation Estimated Adjustment in Example 3, below.

However, since random sampling was applied, the accuracy measures can be calculated, resulting in an ME of $1,745,000, relative precision of 873%, and a confidence interval ranging from $1,945,000 to $1,545,000.

Note that zero is inside the confidence interval which means there is no statistically supported evidence that there even should be any adjustment at all.

The correct statistical decision from this IRS sample is that there is no statistical evidence the taxpayers claim of $30,000,000 was under- or overstated. Even if there were an adjustment, according to IRS guidance, the taxpayerfavorable confidence limit bound should be used, which is $1,545,000. Yes, the IRS would owe the taxpayer in this hypothetical scenario with these facts.

By agreeing to a judgmental sample, this taxpayer pays an unfavorable adjustment when there should not be any and gives up on the reduction of the adjustment due to imprecision resulting from the small sample size.

Avoiding judgmental samples

In summary, it is advisable in general to avoid judgmental samples when quantifying an adjustment to a figure on a tax return. They can be biased and result in wild estimates, and taxpayers lose out on IRS adjustment reductions due to poor precision. However, they can be appealing to a taxpayer especially with the smaller size of the audit. Know what is being given up by agreeing to a judgmental sample approach, though. A statistician can quantify that for your company under hypothetical scenarios.

By contrast, the accuracy of statistical samples can be mathematically determined, which is why they are more defensible in court. Therefore, statistical samples should be used by taxpayers when they conduct samples to estimate values for tax returns. Furthermore, taxpayers would be wise to advocate to be audited under a statistical rather than a judgmental sample plan. This reduces the risk of undue adjustments due to a poor statistical plan. In the case of IRS audits, this also maintains the adjustment reduction from inaccuracies should the IRS choose to use a smaller sample size.