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Monthly Retail Trade and Food Services

Technical Documentation

SAMPLE DESIGN AND ESTIMATION PROCEDURES

The U.S. Census Bureau introduced the current samples with the 2016 Annual Retail Trade Survey 

(ARTS) and the April 2018 Monthly Retail Trade Survey (MRTS). These samples are designed to 

produce estimates based on the 2012 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, 

<http://www.census.gov/retail/mrts/historic_releases.html>.

Sampling Frame

The sampling frame used for the MRTS and the ARTS has two types of sampling units represented: 

single establishment firms and multiple-establishment firms. The information used to create these 

sampling units was extracted from data collected as part of the 2012 Economic Census and from 

establishment records contained on the Census Bureau’s Business Register as updated to December 

2015. The next few paragraphs give details about the Business Register and the construction of the 

sampling units. 

The Business Register is a multi-relational 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 structure of a firm’s primary 

identifier on the Business Register differs depending on whether it is a single-unit firm or 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 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 multi-unit 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 
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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 a multi-unit firm is a unique alpha number. The Census Bureau assigns the 

alpha number to the multi-unit firm and assigns a unique establishment identification number to each 

establishment within a multi-unit firm. All establishments owned or controlled by the same multiunit firm have the same alpha number. Different multi-unit firms have different alpha numbers, and 

different establishments within the same multi-unit firm have different establishment identification 

numbers. The Census Bureau assigns both the alpha number to the multi-unit firm and the 

establishment identification number 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 2012 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, we sum the establishment data for all retail 

establishments associated with the same firm identifier. No aggregation is necessary to put singleunit establishment information on a firm basis. Thus, the sampling units created for single-unit firms 

simultaneously represent establishment, EIN, and firm information. The sampling frame is an 

amalgam of establishments/EINs and firms/alphas.

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 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 2012 Economic Census. Accordingly, these values are on a 2012 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.
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Sample Design

The sample for MRTS uses a stratified, one-stage design with primary strata defined by 

industry. There are 85 primary strata. The primary strata are sub-stratified into 4, 7, 10, or 13 annual 

sales size strata. The largest sales size stratum within each industry stratum consists of firms, all of 

which are selected with certainty (probability equal to one). We determine a substratum boundary 

that divides the certainty units from the noncertainty units based on a statistical analysis of data from 

the 2012 Economic Census. Sample sizes are computed to meet multiple coefficient of variation 

constraints on estimated annual sales totals and end-of-year inventory totals. Constraints are specified 

at detailed industry levels and at broad industry levels up to the total retail level. Units are selected 

independently between strata using simple random sampling without replacement within the annual 

sales substrata. The selected noncertainty firms are divided into two approximately equal 

groups. One group is canvassed for both the monthly and the annual survey, while the other group is 

canvassed for only the annual survey. Sampling weights for the MRTS range from 1 to 500. The 

sample consists of approximately 13,000 employer firms.

Quarterly Birth Sampling 

Periodically, we update the sample to represent EINs issued since the initial sample selection. These 

new EINs, called births, are EINs, recently assigned by the IRS, that have an active payroll filing 

requirement on the IRS Business Master File (BMF). An active payroll filing requirement indicates 

that the EIN is required to file payroll for the next quarterly period. The Social Security 

Administration attempts to assign industry classification to each new EIN. 

EINs with an active payroll filing requirement on the IRS Business Master File are considered to be 

"BMF active" and EINs with an inactive payroll filing requirement are said to be "BMF inactive." 

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 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 two 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 

drawing the initial MRTS sample from the December 2015 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.
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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, 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
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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 2012 Economic Census. 

See <https://www.census.gov/programs-surveys/arts.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. Firms without paid employees, or 

nonemployers, are included in the estimates through imputation or administrative data provided by 

other federal agencies.

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. In

<http://www.census.gov/retail/mrts/www/benchmark/2018/pdf/Introduction.pdf> 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

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 
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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 both

the Annual Retail Trade Survey and the Monthly Retail Trade Survey. For more information on 

the random group method of variance estimation can be found at

<http://www.census.gov/retail/mrts/www/benchmark/2018/pdf/Reliability_of_Estimates.pdf>

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.
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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.

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 30.3 percent of the 

total monthly retail and food services sales estimate and about 32.9 percent of the total retail end-ofmonth inventory estimate. For the annual survey, imputed data amount to about 7.1 percent of the 
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total retail sales and food services estimate and about 8.5 percent of the total retail end-of-year 

inventory estimate.

Additionally, there may be nonsampling error introduced from the method used to account for data 

from nonemployer firms in the monthly estimates. The MRTS sample is comprised of only employer 

firms. In order to produce monthly estimates that include data from employers as well as 

nonemployers, the monthly estimates are benchmarked to Annual Retail Trade Survey (ARTS) 

estimates. The ARTS estimates include data for nonemployer firms obtained from the Census 

Bureau's Nonemployer Statistics Program. Because data for nonemployer firms are not available 

monthly, the benchmarking procedure assumes that the month-to-month changes in sales are the same 

for employer firms and nonemployer firms. Monthly estimates after December 2017 are multiplied 

by a carry forward factor (described in the revision methodology found at

<http://www.census.gov/retail/mrts/www/benchmark/2018/pdf/Introduction.pdf>, which provides 

an adjustment that accounts for differences between the annual and monthly sample estimates, 

including an adjustment for nonemployer firms.

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 <https://www.census.gov/content/dam/Census/about/about-thebureau/policies_and_notices/quality/statistical-quality-standards/Quality_Standards.pdf>.

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

Last Revised: May 25, 2018