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Monthly Retail Trade and Food Services

Technical Documentation

SAMPLE DESIGN AND ESTIMATION PROCEDURES

The U.S. Census Bureau introduced new samples with the 2005 Annual Retail Trade Survey 

(ARTS) and the September 2006 Monthly Retail Trade Survey (MRTS). The new samples are 

designed to produce estimates based on the 2002 North American Industry Classification System 

(NAICS). This section describes the design, selection, and estimation procedures for the new 

samples. For descriptions of the prior samples see the Annual Revision of Monthly Retail and Food 

Services (formerly called the Annual Benchmark Report for Retail Trade), or prior benchmark 

reports.

Sampling Frame

The sampling frame used for the MRTS and the ARTS (ARTS) has two types of sampling units 

represented—Employer Identification Numbers (EINs) and large, multiple-establishment firms. 

Both sampling units represent clusters of one or more establishments owned or controlled by the 

same firm. The information used to create these sampling units was extracted from data collected as 

part of the 2002 Economic Census and from establishment records contained on the Census 

Bureau’s Business Register as updated to December 2004. The next few paragraphs give details 

about the Business Register; the distinction between firms, EINs, and establishments; and the 

construction of the sampling units. Though important, they are not essential to understanding the 

basic sample design and readers may continue to the Stratification, Sampling Rates, and 

Allocation section.

The Business Register is a multirelational database that contains a record for each known 

establishment that is located in the United States or one of its territories and has employees. An 

establishment is a single physical location where business transactions take place and for which 

payroll and employment records are kept. Groups of one or more establishments under common 

ownership or control are firms. A single-unit firm owns or operates only one establishment. A 

multiunit firm owns or operates two or more establishments. The treatment of establishments on the 

Business Register differs according to whether the establishment is part of a single-unit or multiunit

firm. In particular, the structure of an establishment’s primary identifier on the Business Register 

differs depending on whether it is owned by a single-unit firm or by a multiunit firm.

A single-unit firm’s primary identifier is its EIN. The Internal Revenue Service (IRS) issues the 

EIN and the firm uses it as an identifier to report social security payments for its employees under 

the Federal Insurance Contributions Act (FICA). The same act requires all employer firms to use 

EINs. Each employer firm is associated with at least one EIN and only one firm can use a given 
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EIN. Because a single-unit firm has only one establishment, there is a one-to-one relationship 

between the firm and the EIN. Thus the firm, the EIN, and the establishment all reference the same 

physical location and all three terms can be used interchangeably and unambiguously when 

referring to a single-unit firm.

For multiunit firms, however, a different structure connects the firm with its establishments via the 

EIN. Essentially, a multiunit firm is associated with a cluster of one or more EINs and EINs are 

associated with one or more establishments. A multiunit firm consists of at least two 

establishments. Each firm is associated with at least one EIN and only one firm can use a given 

EIN. However, one multiunit firm may have several EINs. Similarly, there is a one-to-many 

relationship between EINs and establishments. Each EIN can be associated with many 

establishments, but each establishment is associated with only one EIN. Because of the possibility 

of one-to-many relationships, we must distinguish between the firm, its EINs, and its 

establishments. The multiunit firm that owns or controls a particular establishment is identified on 

the Business Register by way of the establishment’s primary identifier.

The primary identifier of an establishment owned by a multiunit firm consists of a unique 

combination of an alpha number and a plant number. The alpha number identifies the multiunit 

firm, and the plant number identifies a particular establishment within that firm. All establishments 

owned or controlled by the same multiunit firm have the same alpha number. Different multiunit 

firms have different alpha numbers, and different establishments within the same multiunit firm 

have different plant numbers. The Census Bureau assigns both the alpha number to the multiunit 

firm and plant numbers to the corresponding establishments based on the results of the 

quinquennial economic census and the annual Company Organization Survey.

To create the sampling frame, we extract the records for all employer establishments located in the 

United States and classified in the Retail Trade and Accommodation and Food Services sectors as 

defined by the 2002 NAICS. For these establishments, we extract sales, payroll, employment, name 

and address information, as well as primary identifiers and, for establishments owned by multiunit 

firms, associated EINs. 

To create the sampling units for multiunit firms, we aggregate the economic data of the 

establishments owned by these firms to an EIN level by tabulating the establishment data for all 

inscope establishments associated with the same EIN. Similarly, we aggregate the data to a 

multiunit firm level by tabulating the establishment data for all inscope establishments associated 

with the same alpha number. No aggregation is necessary to put single-unit establishment 

information on an EIN basis or a firm basis. Thus, the sampling units created for single-unit firms 

simultaneously represent establishment, EIN, and firm information. In summary, the sampling 

frame is a complex amalgam of establishments, EINs, and firms.

Stratification, Sampling Rates, and Allocation 

The primary stratification of the sampling frame is by industry group based on the detail required 

for publication. We further stratify the sampling units within industry group by a measure of size 

(substratify) related to their annual revenue. Sampling units expected to have a large effect on the 

precision of the estimates are selected ‘‘with certainty.’’ This means they are sure to be selected 
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and will represent only themselves (i.e., have a selection probability of 1 and a sampling weight of 

1). Within each industry stratum, we determine a substratum boundary (or cutoff) that divides the 

certainty units from the noncertainty units. We base these cutoffs on a statistical analysis of data 

from the 2002 Economic Census. Accordingly, these values are on a 2002 sales basis. We also use 

this analysis to determine the number of size substrata for each industry stratum and to set 

preliminary sampling rates needed to achieve specified sampling variability constraints on revenue 

estimates for different industry groups. The size substrata and sampling rates are later updated 

through analysis of the sampling frame.

Sample Selection

The first step in the sample selection identified firms selected with certainty. If a firm’s annual 

sales or end-of-year inventories were greater than the corresponding certainty cutoff, that firm was 

selected into the sample with certainty. The MRTS and ARTS samples use the same certainty 

firms.

All firms not selected with certainty were subjected to sampling on an EIN basis. If a firm had 

more than one EIN, we treated each of its EINs as a separate sampling unit. To be eligible for the 

initial sampling, an EIN had to have nonzero payroll in 2003. The EINs were stratified according to 

their major industry and their estimated revenue (on a 2002 basis). Within each noncertainty 

stratum, a simple random sample of EINs was selected without replacement. The selected 

noncertainty EINs are divided into two equal groups. One group is canvassed for both the monthly 

and the annual survey, the other group is canvassed for only the annual survey. Therefore, the 

noncertainty sample for the annual survey is twice the size of the noncertainty sample for the 

monthly sample.

Quarterly Birth Sampling 

Periodically, we update the samples to represent new EINs appearing on the Business Register 

since the initial sample was selected. These new EINs, called births, are EINs recently assigned by 

the IRS on the latest available IRS mailing list for FICA taxpayers and assigned an industry 

classification (if possible) by the Social Security Administration (SSA). 

EIN births are sampled on a quarterly basis using a two-phase selection procedure. To be eligible 

for selection, a birth must either have no industry classification or be classified in an industry 

within the scope of the ARTS, the Annual Wholesale Trade Survey (AWTS), or the Service Annual 

Survey (SAS), and it must meet certain criteria regarding its number of paid employees or quarterly 

payroll. In the first phase, births are stratified by broad industry groups and a measure of size based 

on quarterly payroll. A relatively large sample is selected using equal probability systematic 

sampling. The selected births are canvassed to obtain a more reliable measure of size, consisting of 

sales in 2 recent months, company affiliation information, and a new or more detailed industry 

classification code. Births that have not returned their questionnaire after 30 days are contacted by 

telephone. 

Using this more reliable information, the selected births from the first phase are subjected to 

probability proportional-to-size sampling with overall probabilities equivalent to those used in 
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drawing the initial MRTS and ARTS samples from the December 2004 Business Register. Because 

of the time it takes for a new employer firm to acquire an EIN from the IRS, and because of the 

time needed to accomplish the two-phase birth-selection procedure, births are added to the samples 

approximately 9 months after they begin operation. The births selected for the MRTS sample are a 

subset of the births selected for the ARTS sample.

If a firm was selected with certainty and had more than one establishment at the time of sampling, 

any new establishments that the firm acquires, even if under new or different EINs, are included in 

the sample with certainty. However, if a single-unit firm was selected with certainty, only future 

establishments associated with that firm’s originally-selected EIN are included in the sample with 

certainty; any new EINs that might later be associated with that firm are subjected to sampling 

through the quarterly birth-selection procedure. 

Single-unit EINs selected into the sample with certainty are not dropped from canvass and 

tabulation if they are no longer on the IRS mailing list. Rather, the firm that used the EIN is 

contacted, and if a successor EIN is found, it is added to the survey. For both inactive and 

reactivated EINs, data are tabulated for only the portion of the reference year that these EINs 

reported payroll to the IRS.

Sample Maintenance Procedures for the Annual Survey

Births that are selected in the quarterly birth-selection operation in November of the annual survey 

reference year are included in the initial mailing of the annual survey questionnaires in January of 

the following year. To better represent all EIN births in the reference year, and specifically to 

account for the lag between the time a business starts operation and the time it takes to acquire an 

EIN and identify and select the EIN into one of our surveys, we add births to the annual survey 

sample that are selected in February, May, and August of the year following the annual survey 

reference year. We mail annual survey forms to these births in June and August to supplement the 

initial annual survey mailings.

Sample Maintenance Procedures for the Monthly Survey

Because births are not represented in the monthly survey until they go through the two-phase 

selection procedure, an interim procedure is used to account for births during the period between 

the onset of activity and the time of birth selection. This interim procedure consists of imputing 

data for all EINs currently in the monthly survey that go out of business but are still on the IRS 

mailing list.

Births are added to the monthly survey in February, May, August, and November of each year. At 

the same time, deaths are removed from the survey. To minimize the effect of births and deaths on 

the month-to-month change estimates, we phase-in these changes by incrementally increasing the 

sampling weights of the births and decreasing the sampling weights of the deaths in a similar 

fashion. In the first month, we tabulate the births at one-third their sampling weight and tabulate the 

deaths at two-thirds their sampling weight. In the second month, we tabulate the births at two-thirds 

their sampling weight and tabulate the deaths at one-third their sampling weight. In the third month, 
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we tabulate the births at their full sampling weight and the deaths are dropped (sampling weight 

equal zero). 

Procedures for Producing Annual Estimates

Estimates of annual sales and end-of-year inventories are derived from data collected in the ARTS. 

Firms in the ARTS sample are asked to report their sales and inventory data for the year just 

ending. Two years of data are requested in the year in which a new sample is introduced. Annual

totals are computed as the sum of weighted data (reported and imputed) for all selected sampling 

units that meet the sample canvass and tabulation criteria given above. The weight for a given 

sampling unit is the reciprocal of its probability of selection into the ARTS sample. The annual

estimates are adjusted using results of the 2007 Economic Census. 

See <http://www.census.gov/retail/arts/summary.html> for a description of the adjustment 

procedures. Annual total estimates for broad industry groups (e.g., two-, three-, and four-digit 

NAICS levels) are computed by summing the census-adjusted annual totals for the appropriate 

detailed industries comprising the broader industry group.

Variances are estimated using the method of random groups.

Procedures for Producing Monthly Estimates

Estimates of monthly sales and end-of-month inventories are derived from data collected in the 

MRTS. Each month, firms in the MRTS sample are asked to report their sales and inventory data 

for the month just ending. Monthly totals are computed as the sum of weighted data (reported and 

imputed) for all selected sampling units that meet the sample canvass and tabulation criteria given 

below. The weight for a given sampling unit is the reciprocal of its probability of selection into the 

sample. The monthly totals are then benchmarked to the latest available annual survey totals. See 

the Revisions to Previously Published Estimates section for a description of the benchmarking 

procedures.

To be eligible for the sample canvass and tabulation, an EIN selected in the noncertainty sampling 

operations must meet both of the following requirements:

• It must be on the latest available IRS mailing list for FICA taxpayers from the previous quarter.

• It must have been selected from the Business Register in either the initial sampling or during the 

quarterly birth-selection procedure.

Monthly total estimates for broad industry groups (e.g., two-, three-, and four-digit NAICS levels) 

are computed by summing the benchmarked monthly totals for the appropriate detailed industries 

comprising the broader industry group.

Variances are estimated using the method of random groups.

Reliability of Estimates
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The published estimates may differ from the actual, but unknown, population values. For a 

particular estimate, statisticians define this difference as the total error of the estimate. When 

describing the accuracy of survey results, it is convenient to discuss total error as the sum of 

sampling error and nonsampling error. Sampling error is the error arising from the use of a sample, 

rather than a census, to estimate population values. Nonsampling error encompasses all other 

factors that contribute to the total error of a sample survey estimate. The sampling error of an 

estimate can usually be estimated from the sample, whereas the nonsampling error of an estimate is 

difficult to measure and can rarely be estimated. Consequently, the actual error in an estimate 

exceeds the error that can be estimated. Further descriptions of sampling error and nonsampling 

error are provided in the following sections. Data users should take into account the estimates of 

sampling error and the potential effects of nonsampling error when using the published estimates.

Sampling Error

Because the estimates are based on a sample, exact agreement with results that would be obtained 

from a complete enumeration of firms on the sampling frame using the same enumeration 

procedures is not expected. However, because each firm on the sampling frame has a known 

probability of being selected into the sample, it is possible to estimate the sampling variability of 

the survey estimates.

The particular sample used in this survey is one of a large number of samples of the same size that 

could have been selected using the same design. If all possible samples had been surveyed under 

the same conditions, an estimate of a population parameter of interest could have been obtained 

from each sample. For the parameter of interest, estimates derived from the different samples 

would, in general, differ from each other. Common measures of the variability among these 

estimates are the sampling variance, the standard error, and the coefficient of variation (CV). The 

sampling variance is defined as the squared difference, averaged over all possible samples of the 

same size and design, between the estimator and its average value. The standard error is the square 

root of the sampling variance. The CV expresses the standard error as a percentage of the estimate 

to which it refers. For example, an estimate of 200 units that has an estimated standard error of 10 

units has an estimated CV of 5 percent. The sampling variance, standard error, and CV of an 

estimate can be estimated from the selected sample because the sample was selected using 

probability sampling. Note that measures of sampling variability, such as the standard error and 

CV, are estimated from the sample and are also subject to sampling variability. (Technically, we 

should refer to the estimated standard error or the estimated CV of an estimator. However, for the 

sake of brevity we have omitted this detail). It is important to note that the standard error and CV 

only measure sampling variability. They do not measure any systematic biases in the estimates.

We estimate variances for published statistics (totals, ratios, and percent changes) using the 

method of random groups. To implement the random group method of variance estimation, we 

assign a random group number to each sampling unit at the time of sample selection. Then, for 

each tabulation level at which estimates are produced, we compute variance estimates using the 

assigned random group numbers. We use 16 random groups (G=16) to estimate variances for the 

Service Annual Survey. For more information on the random group method of variance estimation, 

click here. 
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The Census Bureau recommends that individuals using published estimates incorporate this 

information into their analyses, as sampling error could affect the conclusions drawn from these 

estimates.

The estimate from a particular sample and its associated standard error can be used to construct a 

confidence interval. A confidence interval is a range about a given estimator that has a specified 

probability of containing the average of the estimates for the parameter derived from all possible 

samples of the same size and design. Associated with each interval is a percentage of confidence, 

which is interpreted as follows. If, for each possible sample, an estimate of a population parameter 

and its approximate standard error were obtained, then:

• For approximately 90 percent of the possible samples, the interval from 1.753 standard errors 

below to 1.753 standard errors above the estimate would include the average of the estimates 

derived from all possible samples of the same size and design.

To illustrate the computation of a confidence interval for an estimate of total revenue, assume that 

an estimate of total revenue is $10,750 million and the CV for this estimate is 1.8 percent, or 0.018. 

First, obtain the standard error of the estimate by multiplying the total revenue estimate by its CV. 

For this example, multiply $10,750 million by 0.018. This yields a standard error of $193.5 million. 

The upper and lower bounds of the 90-percent confidence interval are computed as $10,750 million 

± 1.753 x $193.5 million. Consequently, the 90-percent confidence interval is $10,411 million to 

$11,089 million. If corresponding confidence intervals were constructed for all possible samples of 

the same size and design, approximately 9 out of 10 (90 percent) of these intervals would contain 

the average of the estimates derived from all possible samples.

Nonsampling Error 

Nonsampling error encompasses all other factors, other than sampling error, that contribute to the 

total error of a sample survey estimate and may also occur in censuses. It is often helpful to think of 

nonsampling error as arising from deficiencies or mistakes in the survey process. Nonsampling 

errors are difficult to measure and can be attributed to many sources: the inclusion of erroneous 

units in the survey (overcoverage), the exclusion of eligible units from the survey (undercoverage), 

nonresponse, misreporting, mistakes in recording and coding responses, misinterpretation of 

questions, and other errors of collection, response, coverage, or processing. Although nonsampling 

error is not measured directly, the Census Bureau employs quality control procedures throughout 

the process to minimize this type of error.

A potential source of bias in the estimates is nonresponse. Nonresponse is defined as the inability to 

obtain all the intended measurements or responses about all selected units. Two types of 

nonresponse are often distinguished. Unit nonresponse is used to describe the inability to obtain 

any of the substantive data for a sampled unit. In most cases of unit nonresponse, the questionnaire 

was never returned to the Census Bureau after several attempts to elicit a response. Item 

nonresponse occurs either when a question is unanswered or the response to the question fails 

computer or analyst edits.
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For both unit and item nonresponse, a missing value is replaced by a predicted value obtained from 

an appropriate model for nonresponse. This procedure is called imputation and uses survey data 

and administrative data as input. In any given month, imputed data amount to about 25 percent of 

the total monthly retail and food services sales estimate and about 29 percent of the total retail endof-month inventory estimate. For the annual survey, imputed data amount to about 8 percent of the 

total retail sales and food services estimate and about 7 percent of the total retail end-of-year 

inventory estimate.

Estimates with a coefficient of variation greater than 30% or with a total quantity response rate 

less than 50% have been suppressed from publication. These estimates have been replaced with an 

“S” in the published table. For a description of Census Bureau publication standards and the total 

quantity response rate, see http://www.census.gov/quality/standards/Quality_Standards.pdf.

Source: Retail Indicators Branch, U.S. Census Bureau

Last Revised: April 29, 2011