Statistical Sampling: Weighing Costs versus Precision in Providing Taxpayer Guidance

I.                   Introduction

In the months preceding elections in the United States it is difficult to avoid statistical sampling, as polling projections are everywhere.  Only a sample is used to make these projections because it would take too much time and be too expensive to determine how every voter will vote.  [1]  Statistical sampling has many others uses as well, including being used as evidence in a trial [2] or being used to estimate how much a taxpayer owes the government on their tax return.  [3]  As with elections, to determine the exact result for a tax return, every item in the population would need to be investigated.   As a population gets larger, this gets more time consuming and more expensive, especially when the information is collected by experts, lawyers, and accountants. Furthermore, each additional item of the population collected will not result in a proportionate change in the precision of the estimate, because the precision of an estimate varies inversely with the square root of the sample size.  [4]

II.                Statistical Sampling in Trials and Usage by the IRS

Statistical sampling has not always been used as evidence in trials or in preparing tax returns.  Early courts were skeptical of statistical sampling estimates and did not admit these estimates.  [5]  However, modern courts have begun to accept sampled evidence in a wide variety of contexts, including mass torts cases.  [6]  Similarly, the Internal Revenue Service (“IRS”) utilized statistical sampling in performing tax audits as early as 1964 [7], but it has taken the IRS more time to provide taxpayers guidance for using statistical sampling in preparing tax returns.  [8]  Some evidence that the IRS is allowing increased use of statistical sampling for taxpayers, is that the IRS provided guidance on using statistical sampling for substantiating meal and entertainment expenses that are excepted from the 50% disallowance rule under Code section 274(n) in 2004 [9], and provided guidance for calculating qualified production activities for the Domestic Manufacturing Deduction in 2007.  [10]  

The IRS has yet to provide similar guidance for calculating the Research and Development Tax Credit (“R&D Tax Credit”) [11], however recent court decisions have allowed taxpayers to use estimates in calculating their R&D Tax Credits.  In Union Carbide and Subsidiaries v. Commissioner, the United States Tax Court accepted estimates based on extrapolations “as a close approximation of all of the qualified research activities.”  [12]  Similarly, the Fifth Circuit in U.S. v. McFerrin held that employee testimony and estimates may be used to substantiate qualified research expenditures, against arguments by the IRS.  [13]  As the IRS has not yet provided guidance to taxpayers for using statistical sampling in calculating the R&D Tax Credit [14], and they may in the future [15], the R&D Tax Credit provides a good context for examples that follow.

A major benefit for a taxpayer or for a party in a trial who uses statistical sampling, is the costs that can be saved by using a sample rather than using the entire population.  [16]  This is especially true when there is a large sample and when amounts are being calculated by expert witnesses, lawyers, or accountants.  There are additional benefits as well.  For example, additional valuable information can be gained by using the resources available to determine a carefully drawn smaller sample or to collect more information on each item in the sample.  [17]  Also, there may be drawbacks from using an entire large population, as one recording the entire sample results may get tired or bored enough to start recording information incorrectly.  [18]

Even if the costs to calculate a tax deduction or a credit equaled the cost to calculate that deduction or credit, benefits are induced by the presence of the deductions and credits.  [19]  For example, as the name suggests, the R&D Tax Credit was added to encourage research and development in the United States and as part of the American Jobs Creation Act of 2004, the Domestic Manufacturing Deduction was added to encourage increasing the quality of manufacturing and jobs in the United States.  [20]  A study of the effectiveness of the R&D Credit has shown a positive impact on R&D activity and “[t]here is significant evidence that nations and states that adopt an R&D tax credit will experience an increase in R&D investments.”  [21]  If the incentive to participate in these activities was cheaper and easier to calculate, it follows that more people would consider using them.

III.             Precision vs. Costs to Increase Precision

The R&D Tax Credit is a difficult credit to calculate because it requires intrusive examinations to determine how many of the costs of a particular research project qualifies as a research expense for the credit.  [22]  For example, qualified research expenses include qualified wages paid to engineers.  [23]  It may not be difficult to determine how much a company paid its engineers by looking at payroll detail, but it is more difficult to determine how much of an engineer’s wages qualify as a research expense.  This is the case because qualified research expenses, as defined within I.R.C. § 41, which outlines how the R&D Tax Credit is calculated, do not include all wages.  [24]  Even a twenty minute phone conversations with each engineer, to determine wages that qualify, will add up quickly when you take into account that the engineer could be continuing to conduct research instead, and the costs paid those conducting the interviews.  When a company does extensive research and development and has multiple locations with multiple engineers, it adds up even faster. 

The precision of an estimate calculated from a sample varies inversely with the square root of the sample size.  [25]  Therefore, in the example above, if ten engineers were originally interviewed, in order to double the precision the taxpayer would be required to interview forty engineers. [26] Similarly, to increase the precision of a sample by a factor of ten, it would require interviewing one hundred engineers.  [27]  Adding more numbers to this example, if a sample of ten determines that the mean percentage of time engineers spend doing qualified research is 60%, and you can be 95% sure that the mean of the population falls between 40% and 80%, to be 95% sure that this amount is between 50% and 70%, one would have to have to sample forty engineers.  [28] To further increase precision so that you can be 95% sure that the percentage was between 59% and 61% would require interviewing four hundred engineers.  [29]

Although the “longstanding” [30] rule developed in Cohan v. Commissioner is that absolute certainty is not required and that close approximations are acceptable when calculating deductions [31], it would be difficult to argue that such a wide range would be acceptable.  This would be especially true when it is possible to calculate a more precise number.  Using a sample to claim a deduction or credit of $60, that a taxpayer is 95% sure that is between $40 and $80, does not appear to be a close approximation.  However, it would be easier to argue that if it was determined that the deduction or credit was $60 with 95% certainty that that the deduction or credit was between $59 and $61, that $60 is a close approximation.  However, if it costs the taxpayer $1 to determine that they are 95% sure the deduction or credit is between $40 and $80, and $400 to determine that they are 95% sure the deduction or credit is between $59 and $61; it is not worth it for the tax payer to calculate the deduction or credit at all if such a high degree of precision is required.    

IV.             A Compromise is Needed to Make Statistical Sampling Effective

When you have a range of how much tax liability exists, the IRS will always want the taxpayer to pay more and the taxpayer will always want to pay less.  When precision is not very high, this difference may be large.  Consider if instead of the example above that used tens of dollars, a credit of tens of millions was being calculated.  In continuing to provide guidance to what extent statistical sampling is acceptable, the IRS should take into account how much can be saved by using statistical sampling.  While they have a legitimate concern over requiring tax returns that are precise, the IRS should realize that the money saved could go elsewhere.  Even if a deduction or credit fails to net as much revenue for the government, the presence of the deductions and credits encourage other activities for the benefit of the United States.  [32]  If it costs the taxpayer more to collect the information needed to calculate a potential benefit, the taxpayer may not participate in the potentially beneficial activity at all.  [33]

V.                Conclusion

Statistical sampling allows for substantial savings when making conclusions about populations.    At the same time, there comes a point when asking for increased precision may cost more than it is worth to have this precision.  Tax deductions and credits may be difficult to calculate, but rather than render them worthless to taxpayers or get rid of them completely, statistical sampling should be encouraged when calculations would otherwise be too difficult to calculate.

[1] Robert M. Lawless, Jennifer K. Robbenault, & Thomas S. Ulen, Empirical Methods in Law (forthcoming 2010) (manuscript at 188, released to students).

[2] Id at 208.

[3] Rev. Proc. 2004-29, 2004-20 I.R.B. 918.

[4] Hans Zeisel & David H. Kaye, Sampling, in Prove it with Figures 108-109 (1997). 

[5] Lawless, Robbenault, & Ulen, supra note 1, at 208.

[6] Id.

[7] Rev. Proc. 64-4, 1964-1 C.B. 644.

[8] Will Yancey, Sampling for Income Tax and Customs, (last visited Oct. 11, 2009).   

[9] Rev. Proc. 2004-29, 2004-20 I.R.B. 918.

[10] Rev. Proc. 2007-35, 2007-23 I.R.B. 1349.

[11] Yancey, supra note 8.

[12] Union Carbide Corp. and Subsidiaries v. Comm'r., 97 T.C.M. (CCH) 1207, 110 (2009).

[13] U.S. v. McFerrin, 570 F.3d 672, 679 (5th Cir. 2009).

[14] Yancey, supra note 8.

[15] Mary Batcher, Statistical Sampling in Tax Filings:  New Confirmation from the IRS, Tax Executive (2004), available at

[16] Lawless, Robbenault, & Ulen, supra note 1, at 208.

[17] Id at 191-192.

[18] Mary Batcher, Statistical Sampling:  A Potential Win for Business Taxpayers, Tax Executive (2001),

[19] Ross Gitell & Edinaldo Tebaldi, Are Research and Development Tax Credits Effective?  The Economic Impacts of a R&D Tax Credit in New Hampshire, Public Finance and Management (2008),

[20] American Jobs Creation Act of 2004, Pub. L. No. 108-357, 118 Stat. 1418.

[21] Gitell & Tebaldi, supra note 19.

[22] Batcher, supra note 15.

[23] I.R.C. § 41(b)(2)(A)(i) (2008).

[24] Id.

[25] Zeisel & Kaye, supra note 4. 

[26] Id.

[27] Id.

[28] Id.

[29] Id.

[30] U.S. v. McFerrin, 570 F.3d at 679.

[31] Cohan v. Comm'r, 39 F.2d 540, 544 (2d Cir. 1930).

[32] Gitell & Tebaldi, supra note 19.

[33] Mary Batcher, supra note 18.