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Survey Design

Target Population

The Annual Retail Trade Survey (ARTS) target population consists of all U.S. firms with paid employees that are primarily engaged in retail trade, as defined by the 2012 NAICS. Firms without paid employees, or nonemployers, are included in the estimates through imputation or administrative data provided by other federal agencies

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Sampling Frame

The sampling frame used for 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 October 2015. The next few paragraphs give details about the Business Register 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 Sample Design section.

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 paid 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 multi-unit firm owns or operates two or more establishments. The structure of a firm’s primary identifier on the sampling frame differs depending on whether it is a single-unit firm or a multi-unit 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 multi-unit firm is associated with a cluster of one or more EINs and EINs are associated with one or more establishments. A multi-unit 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 multi-unit 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 multi-unit 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 multi-unit 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 that are classified in the retail trade sector 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 multi-unit firms, associated Employer Identification Numbers (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 single-unit 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.

Sampling Unit

The sampling units used for the Annual Retail Trade Survey are firms. The firms consist of one or more establishments. An establishment is a single physical location where business transactions take place and for which payroll and employment records are kept. We create these sampling units from data collected as a part of the 2012 Economic Census and from establishment records contained in the Census Bureau’s Business Register as of December 2015. The Business Register is a database that contains records of known establishments in the U.S.

Sample Design

The sample for ARTS 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. Sampling weights for the Annual Retail Trade Survey range from 1 to 250. The sample consists of approximately 16,500 employer firms.

Frequency of Sample Redesign

Sample revisions are performed approximately every 5 to 7 years.

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Sample Maintenance

During the period for which the samples are used, updates are made on a quarterly basis to reflect changes in the business universe. These updates are designed to account for new businesses (births) and businesses that discontinue operations (deaths). The samples are also updated to reflect mergers, acquisitions, divestitures, splits, and other changes to the business universe.

We update the sample on a quarterly basis to represent EINs issued since the initial sample selection. These new EINs, called births, are EINs recently assigned by the Internal Revenue Service (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 BMF are said to be "BMF active," and EINs with an inactive payroll filing requirement are said to be "BMF inactive."

We sample EIN births 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 Service Annual Survey (SAS), the Annual Wholesale Trade Survey (AWTS), or the Annual Retail Trade Survey (ARTS), and it must meet certain criteria regarding its quarterly payroll. In the first phase, we stratify births by broad industry groups and a measure of size based on quarterly payroll. A relatively large sample is drawn and canvassed to obtain a more reliable measure of size, consisting of revenue in two recent months and a new or more detailed industry classification code. We contact births by telephone if they have not returned their questionnaire within 30 days.

Using this more reliable information, in the second phase we subject the selected births from the first phase to probability proportional-to-size sampling with overall probabilities equivalent to those used in drawing the initial ARTS 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 the time needed to accomplish the two-phase birth-selection procedure, we add births to the sample approximately nine months after they begin operation.

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 firm was selected with certainty and had only one establishment at the time of sampling, 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.

To be eligible for the sample canvass and tabulation, a single-establishment EIN or at least one EIN associated with a firm selected in the noncertainty sampling operations must meet both of the following requirements:

  • It must be on the active payroll filing requirement on the IRS BMF.
  • It must have been selected from the Business Register in either the initial sampling or during the quarterly birth-selection procedure.

We include any new establishments that a firm acquires, even if under new or different EINs, into the sample with the same sampling status as the original firm (i.e., with the same initial sampling weight). For noncertainty firms, additional evaluation may be done in some instances to determine the feasibility of adding the new establishments by evaluating the effect of the new establishments on the industry estimates.

Similarly, each quarter we check against the current Business Register to determine if any EINs on the survey have become BMF inactive. Typically, we do not canvass BMF inactive EINs during the reference year. Likewise, if any EIN on the survey was BMF inactive in a previous reference year or was part of an inactive sampling unit in the survey and is now BMF active on the current Business Register, we again include these EINs in the canvass. In both cases, we only tabulate data for that portion of the reference year that these EINs reported payroll to the IRS.

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Data Collection

Data Items Requested and Reference Period Covered

Data items requested vary by form type, but include annual sales, e-commerce sales, number of establishments covered by the report, sales taxes, end-of-year inventories, purchases, total operating expenses, and end-of-year accounts receivable for retail businesses located in the United States. Detailed operating expense items are requested every 5 years, with the most recent collection in 2012.

Questionnaires are mailed each year and request data for the previous year. The most current survey questionnaires can be found here.

Key Data Items

The following are the key ARTS data items: sales, inventories, purchases, expenses, and e-commerce sales if the reporting unit’s activity is 100% e-commerce.

Type of Request

ARTS is a mandatory survey.

Frequency and Mode of Contact

ARTS is an annual survey.  Firms receive a mailing with instructions to provide responses online via Centurion.   Due date and follow-up mailings are also conducted during the collection period.  Phone calls are also utilized to follow up with firms that fail to respond. Data may also be obtained in this manner.

Reporting Unit

The reporting unit is an entity about which data are collected. Reporting units are the vehicle for obtaining data and may or may not correspond to a survey unit for several reasons. First, the composition of the originally-sampled entity can change over the sample’s life cycle, as noted above. Second, for some surveys, an entity may request (or the Census Bureau may ask the entity) to report data in several separate pieces corresponding to different parts of the business or other entity type. For example, a large, diverse company in a company-based collection may request a separate form for each region or kind of business in which it operates or may ask to report separately for each of its establishments to align with its record keeping practices. For ARTS, reporting units are usually created to facilitate the collection and tabulation of data by industry.  The initial sample consisted of approximately 20,500 reporting units. 

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Compilation of Data


The Annual Retail Trade Survey uses an interactive data editing process that includes procedures for detecting and correcting errors. The data are automatically checked for consistency of variables within a record as well as consistency with historical data. Any record that fails the edits is flagged to be reviewed by ARTS staff.


Nonresponse is defined as the inability to obtain requested data from an eligible survey unit. Two types of nonresponse are often distinguished. Unit nonresponse is the inability to obtain any of the substantive measurements about a unit. In most cases of unit nonresponse, the Census Bureau was unable to obtain any information from the survey unit after several attempts to elicit a response. Item nonresponse occurs either when a question is unanswered or unusable.


The Annual Retail Trade Survey performs imputation, which is the procedure for determining a value for a specific data item where the response is missing or unusable.

Tabulation Unit

The tabulation unit houses the data used for estimation (or tabulation, in the case of a census). As with reporting units, the tabulation units may not correspond to a survey unit. Some programs consolidate establishment or plant-level data to a company level to create tabulation units, so that the tabulation unit is often equivalent to the survey unit. Other programs create artificial units that split a reporting unit’s data among the different industries in which the reporting unit operates. In this case, the tabulation unit represents a portion of a survey unit. For ARTS, the tabulation unit is either a reporting unit or an artificial unit created to split the reporting unit’s data among the different in-scope industries in which the reporting unit operates. 

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Estimation and Sampling Variance


Total estimates are computed using the Horvitz-Thompson estimator, i.e. the sum of weighted reported or imputed data, for all selected sampling units that meet the sample canvass and tabulation criteria. See the Sample Maintenance section. The weight for a given sampling unit is the reciprocal of its probability of selection into the ARTS sample. These estimates are input to a benchmarking procedure, as described below.


Firms without paid employees (nonemployers) are included in the ARTS estimates through administrative data provided by other Federal agencies and through imputation. Imputed nonemployer estimates for reference year 2016 have been updated to reflect values published by the Nonemployer Statistics program where applicable. ARTS nonemployer estimates for reference year 2017 are imputed because values from the Nonemployer Statistics program are not yet available.

ARTS estimates of total and detailed expenses and accounts receivable are not affected by this revision as these estimates are based only on employer businesses.

Sampling Error

The sampling error of an estimate based on a sample survey is the difference between the estimate and the result that would be obtained from a complete census conducted under the same survey conditions. This error occurs because characteristics differ among sampling units in the population and only a subset of the population is measured in a sample survey. 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 sample design. Because each unit in the sampling frame had a known probability of being selected into the sample, it was possible to estimate the sampling variability of the survey estimates.

Common measures of the variability among these estimates are the sampling variance, the standard error, and the coefficient of variation (CV), which is also referred to as the relative standard error (RSE). 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. It is also important to note that the standard error and CV only measure sampling variability. They do not measure any systematic biases in the estimates.

The Census Bureau recommends that individuals using these estimates incorporate sampling error information into their analyses, as this could affect the conclusions drawn from 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 Annual Retail Trade Survey.

Confidence Interval

The sample estimate and an estimate of its 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 and using a t-statistic with 15 (=G-1) degrees of freedom, 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.
  • For approximately 95 percent of the possible samples, the interval from 2.131 standard errors below to 2.131 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 sales, assume that an estimate of total sales 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 sales 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 plus or minus 1.753 times $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.

Non-sampling Error

Non-sampling error encompasses all factors other than sampling error that contribute to the total error associated with an estimate. This error may also be present in censuses and other nonsurvey programs. Non-sampling error arises from many sources: inability to obtain information on all units in the sample; response errors; differences in the interpretation of the questions; mismatches between sampling units and reporting units, requested data and data available or accessible in respondents’ records, or with regard to reference periods; mistakes in coding or keying the data obtained; and other errors of collection, response, coverage, and processing.

Although no direct measurement of non-sampling error was obtained, precautionary steps were taken in all phases of the collection, processing, and tabulation of the data in an effort to minimize its influence. Precise estimation of the magnitude of non-sampling errors would require special research or access to independent data, and, consequently, the magnitudes are often unavailable.

The Census Bureau recommends that individuals using these estimates factor in this information when assessing their analyses of these data, as non-sampling error could affect the conclusions drawn from the estimates.

Economic surveys at the Census Bureau are required to compute two different types of response rates: the Unit Response Rate and the Total Quantity Response Rate. Read more about ARTS response rates.

Quality Suppressions

Estimates can be suppressed from publication for quality reasons. An estimate with a coefficient of variation (CV) greater than 30 percent, with a total quantity response rate (TQRR) less than 50 percent, or with other concerns about data quality has been suppressed from publication, unless the estimate has consistently been published for prior years and the CV and TQRR are acceptably close to the thresholds. A suppressed estimate and its corresponding measure of sampling variability have been replaced with an "S" in the published tables.

For a description of the Census Bureau's standards for Releasing Information Products, see

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Linking Samples

The current sample was introduced with the 2016 Annual Retail Trade Survey. This sample is designed to produce estimates based on the 2012 North American Industry Classification System (NAICS).  All published estimates from the 2015 ARTS were restated from 2007 NAICS definitions to 2012 NAICS definitions. Definitions changed for NAICS 443 and 451, and changes were applied to the entire span of the time series. For more details on the restatement for those NAICS levels, please see the 2016 ARTS Summary of Changes.

Because the ARTS sample is selected from a sampling frame of firms with paid employees, the following methodology, which is used to link the samples, is applied to employer-only estimates. Then, the published ARTS estimates are obtained by summing the estimates for employers and nonemployers. See the Nonemployers section for more details.

Sales estimates from the new sample for reference year 2015 and subsequent years are linked to the prior sample estimates by multiplying the Horvitz-Thompson estimates from the new sample by a ratio. The ratio is calculated as follows:

  • The numerator is the census-adjusted (based on the 2012 Economic Census) sales estimate for employer firms for the industry restated to a 2012 NAICS basis from the prior sample.
  • The denominator is the 2015 Horvitz-Thompson sales estimate for employer firms for the industry on a 2012 NAICS basis from the new sample.

The resulting sales estimates (call these "modified" sales estimates) are implicitly benchmarked to 2012 Economic Census results via this linking procedure.

The following method is used to produce "modified" estimates for the following items: end-of-year inventories, purchases, and sales tax. First the sales ratio described above is multiplied by the Horvitz-Thompson estimate for the given item for 2015 and subsequent years. Then the estimates for 2010 through 2015 from the prior sample are input into the benchmarking program. Using this program, the estimates for 2011 through 2015 for each detailed industry are revised in a manner that:

  • Uses the benchmarked estimate for 2010 from the prior sample as a constraint, resulting in no revision to the 2010 estimate.
  • Uses the “modified” estimate for 2015 from the new sample as a constraint.
  • Minimizes the sum of squared differences between the year-to-year changes of the input and revised estimates for 2011 through 2015.

A similar method is used to produce "modified" estimates for total expenses, accounts receivable, and e-commerce. For accounts receivable, the estimates are benchmarked at the 3-digit NAICS aggregate industry levels with the same constraints given above because detail industry estimates can be very small. E-commerce benchmarks with mostly 3-digit NAICS aggregate industry levels, but splits out a few extra levels of detail, most notably NAICS 4541 (Electronic Shopping and Mail-Order Houses). For total expenses, the benchmarked estimate for 2012, instead of 2010, from the prior sample is used as a constraint.

Modified merchandise lines sales and e-commerce estimates within the NAICS 4541 industry group are obtained in a similar way to e-commerce, with additional raking to total sales and e-commerce for NAICS 4541 to ensure the lines properly sum to the totals.

Open-end and closed-end accounts receivable estimates are raked to the "modified" total accounts receivable to ensure they sum properly to the total.

Modified estimates at aggregate industry levels are computed by summing the modified estimates for the appropriate detailed industries comprising the aggregates.

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A new sample was introduced with the 2016 ARTS. This sample is designed to produce estimates based on the 2012 North American Industry Classification System (NAICS). In order to maintain the time series for each industry, an operation was performed to link estimates from the prior and new samples. For the linking operation to occur, two years of data were collected (2015 and 2016) from units in the new sample. The linking is done so that the new sample estimates are implicitly benchmarked using results of the 2012 Economic Census.

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Disclosure Avoidance

Disclosure is the release of data that reveals information or permits deduction of information about a particular survey unit through the release of either tables or microdata. Disclosure avoidance is the process used to protect each survey unit’s identity and data from disclosure. Using disclosure avoidance procedures, the Census Bureau modifies or removes the characteristics that put information at risk of disclosure. Although it may appear that a table shows information about a specific survey unit, the Census Bureau has taken steps to disguise or suppress a unit’s data that may be “at risk” of disclosure while making sure the results are still useful.

ARTS uses cell suppression for disclosure avoidance.

Cell suppression is a disclosure avoidance technique that protects the confidentiality of individual survey units by withholding cell values from release and replacing the cell values with a symbol, usually a “D”.  If the suppressed cell value were known, it would allow one to estimate an individual survey unit’s value too closely.

The cells that must be protected are called primary suppressions.

To make sure the cell values of the primary suppressions cannot be closely estimated by using other published cell values, additional cells may also be suppressed. These additional suppressed cells are called complementary suppressions.

The process of suppression does not usually change the higher-level totals. Values for cells that are not suppressed remain unchanged. Before the Census Bureau releases data, computer programs and analysts ensure primary and complementary suppressions have been correctly applied.

For more information on disclosure avoidance practices, see FCSM Statistical Policy Working Paper 22.

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Historical Estimates

Annual estimates prior to 1999 are derived from data that were collected and published based on the Standard Industrial Classification (SIC) system. For a description of how these estimates were derived, see Annual Benchmark Report for Retail Trade and Food Services: January 1992 to December 2000.

Because of the method used to derive annual estimates prior to 1999, these estimates should be used with caution. It is expected that for estimates for NAICS codes, that, by definition, are the same or nearly the same as a given SIC code, the quality of the estimates will be similar to that of the estimates released on an SIC basis. Estimates may be of less quality for NAICS codes that consist of more than one SIC component. Additionally, for reference years further from 1997, estimates are likely of less quality than for those years close to 1997. Note, however, that estimated year-to-year changes for 1992 through 1998 are dependent on the underlying SIC-based year-to-year changes. Year-to-year changes for 1999 and subsequent years are derived from data collected on a NAICS basis.

Special caution should be exercised when using the end-of-year retail inventory estimates prior to 1999. Retail inventory data has historically been analyzed at much broader industry levels than for sales. Determining clear relationships between NAICS and SIC codes was much more difficult at broader levels.

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