Rp 2007-35

come so that the § 199 deduction is not limited by § 199(a)(1)(B), and that the partnership and each of its partners (whether
individual or corporate) are calendar year
taxpayers.
Example.
Small business simplified overall
method. A, an individual, and X, a corporation,
are partners in PRS. PRS engages in manufacturing
activities that generate both DPGR and non-DPGR.
X, but not A, has other manufacturing activities that
generate DPGR and W–2 wages. A and X share all
items of income, gain, loss, deduction, and credit
equally. For the 2010 taxable year, PRS has total
costs of no more than $5 million, and it qualifies
and chooses to calculate QPAI and W–2 wages at
the entity level under section 3.03(c) of this revenue
procedure for the 2010 taxable year. For 2010, PRS
has total gross receipts of $2,000x ($1,000x of which
is DPGR), CGS of $900x (including $400x of wage
expenses), and deductions of $700x (including $50x
of R&E expenditures under § 174(a) and $100x
of § 179 expenses). In this example, the paragraph
(e)(1) wages are equal to the $400x of wage expenses.
PRS uses the safe harbor under § 1.199–2T(e)(2)(iii)
to calculate W–2 wages. Accordingly, PRS’s W–2
wages equal $200x ($400x of wages described in
§ 1.199–2(e)(1) multiplied by ($1,000x DPGR divided by $2,000x total gross receipts)). Pursuant to
section 3.05(f) of this revenue procedure, PRS disregards A’s election under § 59(e) to write off A’s share
of R&E expenditures over 10 years. In addition,
pursuant to section 3.05(e) of this revenue procedure,
PRS disregards any limitation under § 179(b) on A’s
ability to deduct A’s share of the § 179 expenses.
Under the small business simplified overall method,
PRS’s CGS and deductions apportioned to DPGR
equal $800x (($900x CGS plus $700x of other deductions) multiplied by ($1,000x DPGR divided by
$2,000x total gross receipts)). Accordingly, PRS’s
QPAI is $200x ($1,000x DPGR minus $800x CGS
and other deductions). Under section 3.06(a) of this
revenue procedure, PRS’s QPAI is allocated $100x
to A and $100x to X. Under section 3.06(b) of this
revenue procedure, PRS’s W–2 wages are allocated
$100x to A and $100x to X. Because A engages in
no other activities generating DPGR, A’s tentative
deduction is $9x (its $100x share of QPAI from PRS
multiplied by .09), subject to the § 199(b)(1) wage
limitation (50% of A’s $100x share of W–2 wages
from PRS, as defined by § 1.199–2T(e)(2)). Because
X does engage in other production activities generating DPGR, X must combine its $100x share of QPAI
and its $100x share of W–2 wages from PRS with its
QPAI and W–2 wages from all other sources, and X
is not permitted to recompute its share of QPAI from
PRS using another cost allocation method.

SECTION 7. EFFECTIVE DATE
This revenue procedure is effective for
taxable years beginning on or after May 11,
2007. However, taxpayers may apply this
revenue procedure to taxable years beginning after May 17, 2006.

2007–23 I.R.B.

SECTION 8. REQUEST FOR
COMMENTS
Comments on all aspects of this revenue procedure are welcome. The IRS
specifically requests comments on the
clarity of these rules and how they can
be made easier to understand and to implement. All comments will be available
for public inspection and copying. Send
comments to: CC:PA:LPD:PR (Rev. Proc.
2007–34), room 5203, Internal Revenue
Service, PO Box 7604, Ben Franklin Station, Washington, DC 20044. Submissions
may be hand-delivered Monday through
Friday between the hours of 8 a.m. and
4 p.m. to CC:PA:LPD:PR (Rev. Proc.
2007–34), Courier’s Desk, Internal Revenue Service, 1111 Constitution Avenue,
NW, Washington, DC. Submissions may
also be sent electronically via the Internet to the following e-mail address:
[email protected].
Include the revenue procedure number
(Rev. Proc. 2007–34) in the subject line.
Comments must be received on or before
August 9, 2007.
DRAFTING INFORMATION
The principal author of this revenue
procedure is Martin Schäffer, formerly
of the Office of Associate Chief Counsel
(Passthroughs and Special Industries). For
further information regarding this revenue procedure, contact William Kostak
at (202) 622–3060 (not a toll-free call).
26 CFR 601.105: Examination of returns and claims
for refund, credit or abatement; determination of
correct tax liability.
(Also Part I, §§ 199; 1.199–1 through 1.199–9,
1.199–3T, 1.199–5T, 1.199–7T, 1.199–8T.)

Rev. Proc. 2007–35
SECTION 1. PURPOSE
This revenue procedure provides guidance for determining when statistical sampling may be used for purposes of § 199 of
the Internal Revenue Code and establishes
acceptable statistical sampling methodologies.

1349

SECTION 2. BACKGROUND
.01 Section 199(a)(1) allows a deduction equal to 9 percent (3 percent in the
case of taxable years beginning in 2005 or
2006, and 6 percent in the case of taxable
years beginning in 2007, 2008, or 2009) of
the lesser of (A) the qualified production
activities income (QPAI) of the taxpayer
for the taxable year, or (B) taxable income
(determined without regard to § 199) for
the taxable year (or, in the case of an individual, adjusted gross income (AGI)).
Section 199(b)(1) limits the deduction for
a taxable year to 50 percent of the W–2
wages paid by the taxpayer during the calendar year that ends in such taxable year.
.02 Section 199(c)(1) defines QPAI for
any taxable year as an amount equal to the
excess (if any) of (A) the taxpayer’s domestic production gross receipts (DPGR)
for such taxable year, over (B) the sum of
(i) the cost of goods sold (CGS) that are allocable to such receipts; and (ii) other expenses, losses, or deductions (other than
the deduction under § 199) that are properly allocable to such receipts.
.03 Section 199(c)(2) provides that
the Secretary shall prescribe rules for the
proper allocation of items described in
§ 199(c)(1) for purposes of determining
QPAI. Such rules shall provide for the
proper allocation of items whether or not
such items are directly allocable to DPGR.
.04 Section 199(c)(4)(A) defines DPGR
to mean the taxpayer’s gross receipts that
are derived from: (i) any lease, rental, license, sale, exchange, or other disposition of (I) qualifying production property
(QPP) that was manufactured, produced,
grown, or extracted (MPGE) by the taxpayer in whole or in significant part within
the United States; (II) any qualified film
produced by the taxpayer; or (III) electricity, natural gas, or potable water (collectively, utilities) produced by the taxpayer
in the United States; (ii) in the case of
a taxpayer engaged in the active conduct
of a construction trade or business, construction of real property performed in the
United States by the taxpayer in the ordinary course of such trade or business;
or (iii) in the case of a taxpayer engaged
in the active conduct of an engineering
or architectural services trade or business,
engineering or architectural services performed in the United States by the taxpayer
in the ordinary course of such trade or busi-

June 4, 2007

ness with respect to the construction of real
property in the United States.
.05 Section 199(c)(4)(B) excepts from
DPGR gross receipts of the taxpayer that
are derived from: (i) the sale of food and
beverages prepared by the taxpayer at a retail establishment; (ii) the transmission or
distribution of utilities; or (iii) the lease,
rental, license, sale, exchange, or other disposition of land.
.06 Section 199(c)(5) defines QPP to
mean: (A) tangible personal property; (B)
any computer software; and (C) any property described in § 168(f)(4) (certain sound
recordings).
.07 Section 199(c)(6) defines a qualified film to mean any property described
in § 168(f)(3) if not less than 50 percent
of the total compensation relating to production of the property is compensation
for services performed in the United States
by actors, production personnel, directors,
and producers. The term does not include
property with respect to which records are
required to be maintained under 18 U.S.C.
§ 2257 (generally, films, videotapes, or
other matter that depict actual sexually explicit conduct and are produced in whole
or in part with materials that have been
mailed or shipped in interstate or foreign
commerce, or are shipped or transported or
are intended for shipment or transportation
in interstate or foreign commerce).
.08 Section 199 was added to the Code
by section 102 of the American Jobs
Creation Act of 2004 (Act) (Public Law
108–357), and amended by section 403(a)
of the Gulf Opportunity Zone Act of 2005
(GOZA) (Public Law 109–135), section
514 of the Tax Increase Prevention and
Reconciliation Act of 2005 (Public Law
109–222), and section 401 of the Tax Relief and Health Care Act of 2006 (Public
Law 109–432). Section 102(e)(1) of the
Act, as amended by section 403(a)(19)
of GOZA, provides that section 199 shall
apply to taxable years beginning after December 31, 2004. Section 102(e)(2) of the
Act, as amended by section 403(a)(19) of
GOZA, provides that, in determining the
deduction under § 199, items arising from
a taxable year of a partnership, S corporation, estate, or trust beginning before
January 1, 2005, shall not be taken into
account for purposes of § 199(d)(1).

June 4, 2007

SECTION 3. SCOPE
This revenue procedure applies to a taxpayer filing an original return, under examination, in litigation, or making a refund
claim with respect to § 199.
SECTION 4. APPLICATION
.01 In general. For purposes of § 199,
the use of statistical sampling will be considered a reasonable method that is satisfactory to the Secretary to the extent the
sampling methodology used meets the requirements of section 4.02 of this revenue
procedure and follows the procedures provided in Appendix A (Sampling Plan Standards), Appendix B (Sampling Documentation Standards), and Appendix C (Technical Formulas). For example, pursuant
to this revenue procedure, statistical sampling may be used to:
(1) allocate gross receipts between DPGR and non-DPGR under
§ 1.199–1(d)(1) of the Income Tax Regulations;
(2) determine whether gross receipts
qualify as DPGR on an item-by-item basis
under § 1.199–3(d)(1);
(3) allocate CGS between DPGR and
non-DPGR under § 1.199–4(b)(2)(i); and
(4) allocate deductions that are properly
allocable to DPGR or gross income attributable to DPGR under § 1.199–4(c)(1).
.02 When statistical sampling is appropriate. The appropriateness of using a statistical sample for purposes of § 199 is
a facts and circumstances determination.
Factors used in determining whether a statistical sample is appropriate include, but
are not limited to, the time required to
analyze large volumes of data, the cost
of analyzing data, the existence of verifiable information relevant to the taxpayer’s
§ 199 calculation, and the availability of
more accurate information. For purposes
of § 199, statistical sampling will generally
be considered appropriate if the taxpayer
can demonstrate a compelling reason for
its use.
.03 Examples.
Example 1. X manufactures domestically and
sells a variety of mechanical fasteners, including
bolts, nuts, and screws. Some of these products are
not manufactured by X but instead are purchased
from non-related entities. In many cases, products
that are purchased by X are the same type of products
manufactured by X. In addition, X manufactures the
same products in Mexico. Because these products

1350

come in many different sizes, compounds, and packages, X sells over five thousand products, each of
which may constitute an item within the meaning of
§ 1.199–3(d)(1).
X has a separate stock keeping unit (SKU) for
each of its products. X’s computerized sales journal
does not identify whether a product sold was manufactured by X in the United States, manufactured by
X in Mexico, or manufactured by a non-related entity.
However, X’s sales journal does maintain the SKU
number for each product and is capable of determining the gross receipts derived from the sale of each
product. X has devised a methodology to determine
what portion, if any, of the gross receipts derived from
the sale of each SKU qualifies as DPGR. X estimates
it needs one staff-day to make this determination for
each SKU. Therefore, X would have to spend over
five thousand staff-days to make a determination regarding DPGR with respect to all of its sales.
In this case, it would be appropriate for X to use
statistical sampling to determine DPGR derived from
the sale of each product.
Example 2. Y domestically manufactures fertilizer. When Y sells its fertilizer to a customer, it does
so by entering into a contract wherein Y agrees to apply its fertilizer to the customer’s lawn. The application services provided by Y are not an MPGE activity.
Each contract contains variables such as the amount
of fertilizer to apply, the frequency of the service, the
size of lawn, and specific customer discounts. Each
of these variables affects the total contract price.
Y’s computerized accounting system does not
track what portion of its gross receipts is derived
from the sale of fertilizer and what portion is derived from services. In 2005, Y had 20,000 separate
contracts. Y has determined that there is sufficient
information in each contract to separate the fertilizer
application services from the sale of fertilizer. However, the time and expense involved in the manual
review of 20,000 contracts make this determination
impractical. In this case, it would be reasonable for
Y to use statistical sampling to determine the DPGR
derived from the sale of fertilizer.
Example 3. PRS provides a broad range of consulting services for dental practices. In addition to
its consulting services, PRS develops and licenses
specialized software for managing dental records.
PRS’ consulting services are not an MPGE activity,
while its development and licensing of software is. In
2005 PRS had 50 customers. PRS can determine the
amount of DPGR generated in a particular tax year
through a simple review of its contracts. Given the
limited number of contracts to be reviewed, pursuant
to section 4.02 of this section, there is no compelling
reason for PRS’s use of statistical sampling to determine its DPGR.
Example 4. Z produces, distributes, and licenses
motion pictures and has been doing so since 1930. Z
has a collection of over 5,000 films some of which
Z produced within the United States and some of
which it produced abroad. Z believes that historical
records exist with respect to each film in its collection and that by reviewing these records it is possible to determine whether a particular film represents
a “qualified film” produced by Z within the meaning of § 199(c)(4)(A)(i)(II) and (c)(6). However, the
time and costs involved in obtaining and reviewing
such records on an individual film basis are significant. In this case, Z could use statistical sampling to

2007–23 I.R.B.

determine the DPGR derived from the license of its
film collection.
Example 5. Assume the same facts as in Example 4 except that Z develops and executes a proper
sampling plan as described in Appendix A. In the
process, Z discovers that for some of the sampled
films it has no historical records and no reliable
data can be obtained from other sources that would
help determine whether or not each film represents a
“qualified film” produced by Z within the meaning of
§ 199(c)(4)(A)(i)(II) and (c)(6). In accordance with
Paragraph 5 of Appendix A, Z must give a value to
any film selected as part of its sample. Therefore, if
a film is selected for which no historical records and
no reliable data can be obtained, Z will be required
to treat the selected film as failing the requirements
to be a “qualified film” produced by Z for purposes
of § 199(c)(4)(A)(i)(II) and (c)(6).
Example 6. X manufactures and sells a variety
of tools. Some tools sold by X are manufactured entirely by X in the United States. Other tools sold by X
are purchased for resale from F, an unrelated foreign
corporation. X maintains a computerized sales journal which tracks whether a tool sold by X was manufactured by X or F. Assuming the gross receipts derived from the sale of tools manufactured by X qualify
as DPGR and gross receipts derived from the sale of
tools purchased from F for resale do not qualify as
DPGR, the use of statistical sampling by X to compute its DPGR from the sale of tools would not be appropriate because evidence is readily available from
another source that can be demonstrated to be a more
accurate determination of DPGR.

.04 Limitations.
(1) This revenue procedure applies only
to § 199.
(2) This revenue procedure does not establish the correctness of a taxpayer’s interpretation of § 199.
(3) This revenue procedure does not
preclude the Internal Revenue Service
from raising or pursuing any income, employment, or other tax issues identified in
the review of a statistical sample.
SECTION 5. EFFECTIVE DATE
This revenue procedure is generally effective for taxable years beginning on or
after May 11, 2007. However, taxpayers
may apply this revenue procedure to taxable years beginning after December 31,
2004, and before May 11, 2007.

An agency may not conduct or sponsor,
and a person is not required to respond
to, a collection of information unless the
collection of information displays a valid
OMB control number.
The collection of information in this
revenue procedure is in Appendix B. This
information is required to ensure compliance with the statistical sampling methodology contained in this revenue procedure.
The information will be used to evaluate
compliance with the procedures described
in this revenue procedure. The collection
of information is mandatory. The likely
recordkeepers are businesses or other forprofit institutions.
The estimated total annual recordkeeping burden is 2,400 hours. The estimated
annual burden per recordkeeper varies
from 6 to 10 hours, depending on individual circumstances, with an estimated
average of 8 hours. The estimated number
of recordkeepers is 300.
Books or records relating to a collection
of information must be retained as long
as their contents may become material in
the administration of any internal revenue
law. Generally tax returns and tax return
information are confidential, as required
by 26 U.S.C. 6103.
DRAFTING INFORMATION
The authors of this revenue procedure are David McDonnell and
Lauren Ross Taylor of the Office of Associate Chief Counsel (Passthroughs and
Special Industries). For further information regarding this revenue procedure,
contact Mr. McDonnell or Ms. Taylor at
(202) 622–3040 (not a toll-free call). For
further information regarding Appendices
A, B, and C, contact Michael Curley of
the Large and Mid-Size Business Division
at (630) 699–6020 (not a toll-free call).
APPENDIX A
SAMPLING PLAN STANDARDS

SECTION 6. PAPERWORK
REDUCTION ACT
The collection of information contained in this revenue procedure has been
reviewed and approved by the Office
of Management and Budget in accordance with the Paperwork Reduction Act
(44 U.S.C. 3507) under control number
1545–2072.

2007–23 I.R.B.

The statistical sampling must be conducted in accordance with the following
methodology.
1. The statistical sample must be conducted in an unbiased scientific manner
with the goal of achieving the correct
answer. Any attempt to manipulate the
process to achieve a desired result will
invalidate the sample. However, steps

1351

designed to improve the precision of the
estimate, such as stratification techniques,
are acceptable and often preferred.
2. Statistical sampling methodology
may not include the use of judgment sampling.
3. Taxpayers may apply the results of a
statistical sample only to transactions that
both (a) occurred in the taxable year in
which the § 199 deduction is recognized
and (b) involve items included in the population from which the statistical sample
was taken.
4. Any estimated amount must be based
on a statistical sample, in which each sampling unit has a known (non-zero) chance
of selection, using either a simple random sampling method or stratified random
sampling method.
5. A conclusion must be reached as
to the treatment of each selected sampling
unit. It is never valid to replace a sampling
unit that was selected in the random selection process with another sampling unit,
merely because documentation is unavailable or difficult to obtain. In evaluating a
sampling unit, the decision reached as to
the treatment of the sampling unit must be
the same as the conclusion which would
be reached if that sampling unit was encountered in a 100% analysis. Therefore,
a sampling unit with documentation that is
unavailable or difficult to obtain must be
treated as failing the § 199 requirement(s)
being tested.
6. In general, the computation of any
estimated amount must be at the least
advantageous 95% one-sided confidence
limit. The “least advantageous” confidence limit is either the upper or lower
limit that results in the least benefit to the
taxpayer. However, if the precision of
estimated difference divided by the estimated difference does not exceed 10%,
the point estimate may be used in place of
the least advantageous confidence limit.
All strata for which “substantially all” of
the population sampling units are sampled
will be treated as 100% strata. That is, the
overall point estimate and its precision will
be estimated by treating all 100% strata
appropriately for the sample design used.
Also, the calculation of the denominator
for the relative precision will exclude all
100% strata. For this revenue procedure,
“substantially all” is defined as 80% or
more.

June 4, 2007

7. Recognizing that many methods exist to estimate population values from the
sample data, only the following estimators will be considered acceptable by the
Service. Variable estimators permitted include the mean (also known as the direct projection method), difference (using
“paired variables”), (combined) ratio (using a variable of interest and a “correlated”
variable), and (combined) regression (using a variable of interest and a “correlated”
variable). The first variable used for the
difference, ratio and regression estimators
must be the variable used in the mean estimator. The second variable used for the
difference, ratio and regression estimators
must be a variable that can be paired with
the first variable and should be related to
the first variable. For example, in a typical
audit-sampling situation, the first variable
would be the audited value of a transaction
and the second variable would be the originally reported value of the same transaction. Because the latter two variable methods are statistically biased, there must be
a demonstration that the bias is negligible
before the Service will accept the method.
8. Variable sampling plans must use the
qualifying final estimate with the smallest
overall standard error as an absolute value
(for example, the size of the estimate is
irrelevant in the determination of the reported value).
9. Variable sampling plans must calculate confidence limits by addition and
subtraction of the precision of the estimate from the point estimate in which the
determination of precision proceeds by
multiplication of the standard error by (i)
the 95% one-sided confidence coefficient
based on the Student’s t-distribution with
the appropriate degrees of freedom, or (ii)
1.645 (the normal distribution), assuming
the sample size is at least 100 in each
non-100% stratum.
10. To demonstrate that little statistical bias exists for either the (combined)
ratio or regression method, the following
applies after excluding all strata tested on
100% basis (the entire population of a stratum is selected for evaluation).
a. The total sample size of all strata
must be at least 100 units.
b. Each stratum for a population estimate should contain at least 30 sample
units.

June 4, 2007

c. The coefficient of variation of the
paired variable must be 15% or less. The
coefficient of variation of the paired variable (y) is defined as the standard error of
the total “y” variables divided by point estimate of the total “y” variables when the
“y” variables are commonly the reported
values in accounting situations.
d. The coefficient of variation of the
primary variable of interest, represented by
either the corrected value or the difference
between the reported and corrected values
in common accounting situations, must be
15% or less. The coefficient of variation
for the corrected value (x) is defined as
the standard error of the total “x” variables divided by point estimate of the total “x” variables when the “x” variables are
commonly the corrected values in accounting situations. The coefficient of variation
for the difference (d) between the reported
and corrected values (x-y) is defined as
the smaller of the standard error of the total “x-y” or total “d” variables divided by
the amount equaling total population value
represented by “Y” plus point estimate of
the total “x-y” or total “d” variables or the
standard error of the total “x-y” or total “d”
variables divided by the total “x-y” or total “d” variables when the “x-y” variables
are commonly the difference (d) between
the reported (y) and corrected (x) values in
accounting situations.
e.
For only the (combined) ratio
method, the reported values of units must
be of the same sign.
11. A written sampling plan is required
prior to the execution of a sample. A plan
must include the following:
a. The objective of the plan including a
description of the value for estimation and
the applicable taxable year;
b. Population definition and reconciliation of the population to the tax return;
c. Definition of the sampling frame;
d. Definition of the sampling unit;
e. Source of the random numbers, the
starting point or seed, and the method of
selection;
f. Sample size, along with supporting
factors in the determination;
g. Method to associate random numbers to the frame;
h. Steps to ensure that the serialization
of the frame is independent of the drawing
of random numbers;

1352

i. Steps for evaluating the sampling
unit; and
j. The estimator that was used for appraising the sample.
APPENDIX B
SAMPLING DOCUMENTATION
STANDARDS
The taxpayer must retain adequate
documentation to support the statistical
application, sample unit findings, and all
aspects of the sample plan and execution.
The execution of the sample must include
information for each of the following
items:
1. The seed or starting point of the
random numbers;
2. The pairing of random numbers to
the frame along with supporting information to retrace the process;
3. List of sampling units selected and
the results of the evaluation of each unit;
4. Supporting documentation such
as notes, invoices, purchase orders, and
project descriptions that support the conclusion reached about each sample item;
5. The calculation of the projected estimate(s) to the population, including computation of the standard error of the estimate(s);
6. A statement describing any slips or
blemishes in the execution of the sampling
procedure and any pertinent decision rules;
and
7. Computation of all associated adjustments.
APPENDIX C
TECHNICAL FORMULAS
The formulas below are included to
clarify the statistical sampling terms used
and to ensure consistent application of
the procedures described in the revenue
procedure.

2007–23 I.R.B.

UNSTRATIFIED (SIMPLE RANDOM SAMPLE)
MEAN ESTIMATOR

STRATIFIED
MEAN ESTIMATOR

Sample Mean of Audited Amounts

Estimate of Total Audited Amount

Estimated Standard Deviation of the Audited Amount

Estimated Standard Error of the Total Audited Amount

Achieved Precision of the Total Audited Amount

UNSTRATIFIED (SIMPLE RANDOM SAMPLE)
DIFFERENCE ESTIMATOR

STRATIFIED
DIFFERENCE ESTIMATOR

Estimate of Total Difference

Estimate of Total Audited Amount

Estimated Standard Deviation of the Difference Amount

2007–23 I.R.B.

1353

June 4, 2007

UNSTRATIFIED (SIMPLE RANDOM SAMPLE)
DIFFERENCE ESTIMATOR

STRATIFIED
DIFFERENCE ESTIMATOR

Estimated Standard Error of the Difference Amount

Achieved Precision of the Difference Amount

UNSTRATIFIED (SIMPLE RANDOM SAMPLE)
RATIO ESTIMATOR

STRATIFIED
COMBINED RATIO ESTIMATOR

Estimated Ratio of Audited Amount to Recorded Amount

Estimate of Total Audited Amount

Estimated Standard Deviation of the Ratio

th
Estimated Standard Deviation of the Ratio in i Stratum

Estimated Standard Error of the Ratio Amounts

Achieved Precision of the Ratio Amounts

June 4, 2007

1354

2007–23 I.R.B.

UNSTRATIFIED (SIMPLE RANDOM SAMPLE)
REGRESSION ESTIMATOR

STRATIFIED
COMBINED REGRESSION ESTIMATOR

Estimated Regression Coefficient

Estimate of Total Audited Amount

Estimated Standard Deviation of the Regression Amounts

Estimated Covariance between the Audited and Recorded Amounts in i

th

Stratum

Estimated Standard Deviation between the Audited and Recorded Amounts in i

th

Stratum

Estimated Standard Error of the Audited and Recorded Amounts

Achieved Precision of the Audited and Recorded Amounts

2007–23 I.R.B.

1355

June 4, 2007

Definition of Symbols

TERM

DEFINITION

n

Sample Size

N

Population Size

x

The value of the sampling unit that is being used as the primary variable of interest. In audit sampling,
this would be the audited (or revised) value of the transaction.

y

The value of the sampling unit that is being used as the “paired” variable that is related to the variable
of interest. In audit sampling, this would be the reported (or original) value of the transaction.

d

The value of the sampling unit that is the difference between “paired” variable (y) and the variable
of interest (x). That is, d = x – y. In audit sampling, this would be the difference (or the change)
of each transaction’s value.

X

The total value of the primary variable of interest. In audit sampling, this would be the estimated total
audited value of the population. Typically, this value is not known for the entire population and is
estimated based on the statistical sample selected.

Y

The total value of the variable that is paired with variable of interest. In audit sampling, this would be
the total reported value of the population. Typically, this value is known for the entire population and
may be estimated based on the statistical sample selected.

D

The total value of the difference between the “paired” variable and the variable of interest. In audit
sampling, this would be the estimated total difference of the population. Typically, this value is not
known for the entire population and is estimated based on the statistical sample selected.

UR

The confidence coefficient which is based on either the Student’s t-distribution or the normal
distribution. For example, a 95% one-sided confidence coefficient based on the normal distribution is
1.645. This term is often referred to as the t-value and the z-value.

June 4, 2007

1356

2007–23 I.R.B.