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Appendix C. Sample Design, Data Collection, and Estimation

Monday, July 13, 2015


The primary goal for the 2012 Commodity Flow Survey (CFS) was to estimate shipping volumes (value, tons, and ton-miles) by commodity and mode of transportation at varying levels of geographic detail. A secondary objective was to estimate the volume of shipments moving from one geographic area to another (i.e., flows of commodities between states, regions, etc.) by mode and commodity. A detailed description of the sample design for the 2012 CFS is provided below.



The sample for the 2012 CFS was selected using a stratified three-stage design in which the first-stage sampling units were establishments, the second-stage sampling units were groups of four 1-week periods (reporting weeks) within the survey year, and the third-stage sampling units were shipments.

First Stage—Establishment Selection

To create the first-stage sampling frame, a subset of establishment records (as of July 2011) was extracted from the Census Bureau’s Business Register. The Business Register is a database of all known establishments located in the United States or its territories. An establishment is a single physical location where business transactions take place or services are performed. Establishments located in the United States, having nonzero payroll in 2010, and classified in mining (except oil and gas extraction), manufacturing, wholesale, electronic shopping and mail order, fuel dealers, and publishing industries, as defined by the 2007 NAICS, were included on the sampling frame. Certain manufacturers (Prepress services) and wholesalers (manufacturers’ sales offices, agents and brokers, and certain importers) were excluded from the frame.

Auxiliary establishments (e.g., truck transportation facilities, warehouses, and central administrative offices) with shipping activity were also included on the sampling frame. Auxiliary establishments are establishments that are primarily involved in rendering support services to other establishments within the same company, instead of for the public, government, or other business firms. All other establishments included on the sampling frame are referred to as nonauxiliary establishments.

Establishments classified in forestry, fishing, utilities, construction, and all other transportation, retail, and services industries were not included on the sampling frame. Farms and government-owned entities (except government-owned liquor stores) were also excluded from the sampling frame. The resulting frame comprised approximately 716,000 establishments as shown in the table below.

Trade area Establishments on frame
2012 CFS 2007 CFS
Mining 5,543 6,789
Manufacturing 305,805 327,826
Wholesale 345,511 356,477
Retail 27,697 25,190
Services 15,599 22,539
Auxiliaries 14,959 14,878
Total 716,114 753,699

For each establishment, sales, payroll, number of employees, a six-digit NAICS code, name and address, and a primary identifier were extracted, and a measure of size was computed. The measure of size was designed to approximate an establishment’s annual total value of shipments for the year 2009.

All of the establishments included on the sampling frame had state and county geographic codes. We used these codes to assign each establishment to one of the 83 CFS metropolitan areas (CFS Areas) defined as a state part of a metropolitan statistical area (MSA) or combined statistical area (CSA). Establishments not located in one of these specified metropolitan areas (MAs) were assigned to a Rest of State (ROS) CFS Area.


The sampling frame was stratified by geography, industry, and measure-of-size (MOS) class (with some exceptions for auxiliary establishments and hazardous materials establishments, as described below). The geography by industry cells form the primary strata for the main part of the sample.

Geographic strata were defined by a combination of the 50 states, the District of Columbia, and specific metropolitan areas (called CFS Areas) selected based on their population and importance as transportation gateways. These CFS Areas were defined using the 2009 Office of Management and Budget’s definitions. All other MAs were collapsed with the nonmetropolitan areas within the state into ROS CFS Area strata. When an MA crossed state boundaries, we considered the size of each state part of the MA when determining whether or not to create strata in each state in which the MA was defined. For example, the Chicago CSA makes up two CFS Areas: the Illinois part and the Indiana part. The Wisconsin part of Chicago was too small to be a separate CFS Area and was combined into the Remainder of Wisconsin CFS Area. The table below (second column) summarizes the number of CFS Areas used for sampling by type.

Geographic stratum (CFS Area) type Number of sampled CFS Areas Number of published CFS Areas
Actual CSA or MSA (state part). 83 82
CFS area = state (DC, RI). 2 2
ROS = whole state (AK, AR, ID, IA, ME, MS, MT, NM, ND, SD, VT, WV, WY). 13 13
ROS < whole state 36 35
Total number of CFS areas. 134 132

Between the time the CFS sample of establishments was selected and publication of the data, there were changes to the definitions of the MAs used by the CFS. For sampling purposes, the CFS Areas were defined using the 2009 OMB MA definitions. For tabulation and publication, the 2013 OMB definitions were used to define the CFS Areas. As a result, two CFS Areas used for sampling (Stockton, CA and Remainder of New Jersey) disappeared and, for many others, the counties making up the CFS Areas changed. The rightmost column of the table above shows the number of CFS Areas for which data were eventually published.

The industry strata were defined as follows. Within each of the geographic strata, we defined 48 industry groups based on the 2007 NAICS codes:

  • Three mining (four-digit NAICS).
  • Twenty-one manufacturing (three-digit NAICS).
  • Eighteen wholesale (four-digit NAICS).
  • Two retail (NAICS 4541 and 45431).
  • One services (NAICS 5111).
  • Three auxiliary (combinations of NAICS 484, 4931 and 551114).

For auxiliaries that responded to the Advance Survey and were found to be shippers, 134 primary strata were created, one in each geographic stratum, combining NAICS 484, 4931, and 551114. For auxiliary establishments that did not respond to the Advance Survey, two national strata were created as follows:

  • One stratum for nonresponding truck transportation establishments and warehousing and storage establishments (NAICS 484 and NAICS 4931).
  • One stratum for nonresponding corporate, subsidiary, and regional managing offices establishments (NAICS 551114).

In order to produce good estimates of shipments of hazardous materials (HAZMAT), 20 six-digit NAICS industries with high amounts of HAZMAT shipments were identified and used to form primary strata. The 2007 CFS data were used to identify these industries and in general, these industries were chosen because:

  • They had a large (weighted) total value or total tonnage of hazardous materials.
  • A high percentage of their (unweighted) shipments were HAZMAT shipments.

Thirteen of the 20 industries were made certainty strata, and the remaining seven industries were made into primary strata defined by state and the six-digit NAICS code.

The table below shows the number and types of primary strata for the main, auxiliary, and HAZMAT parts of the sample. Note that we are counting the number of strata before they are further stratified by MOS size class.

Part of the sample Number of primary strata
Main part of the sample (134 CFS areas x 45 industries) 6,030
Auxiliary part of the sample: Responders to the Advance Survey (134 CFS areas x 1 industry) 134
Nonresponders to the Advance Survey (2 industries) 2
HAZMAT part of the sample: Certainty (take-all) strata (13 six-digit NAICS codes) 13
Noncertainty strata (51 states [incl DC] x 7 six-digit NAICS codes) 357

Determining the Sample Sizes, Stratifying by MOS Size Class, and Sample Selection

The total desired sample size for the first stage sample was approximately 100,000 establishments and was fixed due to budget constraints. Therefore, in addition to defining the strata, a sample size was determined for each primary stratum. This was performed as follows:

  • A target coefficient of variation (CV) was assigned to each primary stratum (geography by industry cell).

  • Within each primary stratum, substrata defined by MOS were developed to minimize the sample size needed to achieve the target CV. The establishments in the largest MOS size class were taken with certainty. For the noncertainty substrata, the sample was allocated according to the Neyman allocation, since the Neyman allocation minimizes the sample size needed to achieve a target CV.

  • Once the minimum sample sizes for each primary stratum were determined, these were added together and compared to the desired total sample size of 100,000. If the total was not close enough to 100,000, we multiplied all of the target CVs by a fixed factor and repeated the process until the total sample size was close to 100,000.

  • The establishments in the geography by industry by MOS size class substrata were selected by simple random sampling without replacement. The total sample size was 102,565 establishments of which 46,265 were selected with certainty (see the table below).

Primary strata type 2012 frame 2012 sample
Establishments Total MOS (million dollars) Total sample Certainty component
Establishments MOS of sampled Establishments (million dollars) Establishments MOS of certainty Establishments (million dollars)
Main. 680,128 8,361,138 95,678 6,215,482 42,187 5620044
Auxiliary. 14,959 1,330,769 2,433 1,186,608 1,121 1087152
HAZMAT 21,027 775,739 4,454 685,595 2,957 669,835
Total. 716,114 10,467,646 102,565 8,087,685 46,265 7,377,031

Second Stage—Reporting Week Selection

The frame for the second stage of sampling consisted of the 52 weeks in 2012. Each establishment selected into the 2012 CFS sample was systematically assigned to report for four reporting weeks, one in each quarter of the reference year (2012). Each of the 4 weeks was in the same relative position in the quarter. For example, an establishment might have been requested to report data for the 5th, 18th, 31st, and 44th weeks of the reference year. In this instance, each reporting week corresponds to the 5th week of each quarter. Prior to assignment of weeks to establishments, we sorted the selected sample by primary stratum (geography by industry) and measure-of-size.

Third Stage—Shipment Selection

For each of the four reporting weeks in which an establishment was asked to report, the respondent was requested to construct a sampling frame consisting of all shipments made by the establishment in the reporting week. Each respondent was asked to count or estimate the total number of shipments comprising the sampling frame and to record this number on the questionnaire. For each assigned reporting week, if an establishment made more than 40 shipments during that week, we asked the respondent to select a systematic sample of the establishment’s shipments and to provide us with information only about the selected shipments. By design, this systematic sample consisted of between 20 and 40 shipments. If an establishment made 40 or fewer shipments during that week, we asked the respondent to provide information about all of the establishment’s shipments made during that week; i.e., no sampling was required.


Each establishment selected into the CFS sample was mailed a questionnaire for each of its four assigned reporting weeks; that is, an establishment was sent a questionnaire once every quarter of 2012. For a given establishment, the respondent was asked to provide the following information about each of the establishment’s reported shipments:

  • Shipment ID number
  • Shipment date (month, day)
  • Shipment value
  • Shipment weight in pounds
  • Commodity code from Standard Classification of Transported Goods (SCTG) list
  • Commodity description
  • An indication of whether the shipment was temperature controlled
  • United Nations or North American (UN/NA) number for hazardous material shipments
  • U.S. destination (city, state, zip code)—or gateway for export shipment
  • Modes of transport
  • An indication of whether the shipment was an export
  • City and country of destination for exports
  • Export mode

For a shipment that included more than one commodity, the respondent was instructed to report the commodity that made up the greatest percentage of the shipment’s weight.

In addition, establishments were asked to provide information about the use and extent of use of rush delivery services.


To correct for nonresponse or an unacceptable value in either the value or weight item for a given shipment, the missing item or unacceptable value (the one that has failed edit) is replaced by a predicted value obtained from a donor imputation model. Such a shipment is considered a “recipient” if its commodity code is valid and one of the two data items (either shipment value or shipment weight) is reported, greater than zero, and passed edit. The recipient’s item that is missing or failed edit is imputed as follows:

First a donor shipment for a given recipient with the same five-digit SCTG is selected at random from a pool of potential donor shipments (those with valid SCTGs and with reported and usable shipment value and weight). The donor pools are summarized below in order of preference (the lowest numbered donor pool with a matching shipment is used).

Donor pool Description of donor pool shipments
1 From same establishment and in the same detailed shipment size class.
2 From same company and in the same detailed shipment size class.
3 From same geographic area and in the same detailed shipment size class.
4 From same establishment and in the same broad shipment size class.
5 From same company and in the same broad shipment size class.
6 From same geographic area and in the same broad shipment size class.
7 From same establishment (no restriction on shipment size).
8 From same company (no restriction on shipment size).
9 From same geographic area (no restriction on shipment size).

Then, the donor’s value and weight data are used to calculate a ratio, which is applied to the recipient’s reported item, to impute the item that is missing or failed edit. If a donor cannot be found in one of the nine donor pools then the recipient’s item is imputed using the median value-to-weight ratio computed using all shipments in the same SCTG as that of the recipient.

Approximately 3 percent of shipment values are imputed, and, similarly, approximately 3 percent of shipment weights are imputed.


Estimated totals (e.g., value of shipments, tons, ton-miles) are produced as the sum of weighted shipment data (reported or imputed). Percentage change and percent-of-total estimates are derived using the appropriate estimated totals. Estimates of average miles per shipment are computed by dividing an estimate of the total miles traveled by the estimated number of shipments.

Each shipment has associated with it a single tabulation weight, which was used in computing all estimates to which the shipment contributes. The tabulation weight is a product of seven different component weights. A description of each component weight follows.

CFS respondents provided data for a sample of shipments made by their respective establishments in the survey year. For each establishment, we produced an estimate of that establishment’s total value of shipments for the entire survey year. To do this, we used four different weights: the shipment weight, the shipment nonresponse weight, the quarter weight, and the quarter nonresponse weight. Three additional weights are then applied to produce estimates representative of the entire universe. These are the establishment-level adjustment weight, the establishment (or first-stage sample) weight, and the nonresponse post-stratification adjustment weight.

Like establishments, we identified shipments as either certainty or noncertainty. (See the Nonsampling Error section below for a description of how certainty shipments were identified.) For noncertainty shipments, the shipment weight was defined as the ratio of the total number of shipments (as reported by the respondent) made by an establishment in a reporting week to the number of sampled shipments the respondent listed on the questionnaire for the same week. This weight uses data from the sampled shipments to represent all the establishment’s shipments made in the reporting week. However, a respondent may have failed to provide sufficient information about a particular sampled shipment. For example, a respondent may not have been able to provide value, weight, or a destination for one of the sampled shipments. If this data item could not be imputed or otherwise obtained, then this shipment did not contribute to tabulations and was deemed unusable. (A usable shipment is one that has valid entries for value, weight, and origin and destination ZIP Codes.) To account for these unusable shipments, we applied the shipment nonresponse weight. For noncertainty shipments from a particular establishment’s reporting week, this weight is equal to the ratio of the number of sampled shipments for the reporting week to the number of usable shipments for the same week. The shipment weight for certainty shipments from a particular establishment’s reporting week is equal to one.

The quarter weight inflates an establishment’s estimate for a particular reporting week to an estimate for the corresponding quarter. For noncertainty shipments, the quarter weight is equal to 13. The quarter weight for most certainty shipments is also equal to 13. However, if a respondent was able to provide information about all large (or certainty) shipments made in the quarter containing the reporting week, then the quarter weight for each of these shipments was set to one. For each establishment, the quarterly estimates were added to produce an estimate of the establishment’s value of shipments for the entire survey year. Whenever an establishment did not provide the Census Bureau with a response for each of its four reporting weeks, we computed a quarter nonresponse weight. The quarter nonresponse weight for a particular establishment is defined as the ratio of the number of quarters for which the establishment was in business in the survey year (usually four) to the total number of quarters (reporting weeks) for which we received usable shipment data from the establishment.

Using these four component weights and the reported (or imputed) shipment values, we computed an estimate of each establishment’s value of shipments for the entire survey year. This estimate was multiplied by a factor that adjusts this estimated value to a measure of the establishment’s value of shipments or receipts obtained from the 2012 Economic Census. This weight, the establishment-level adjustment weight, attempts to correct for any sampling or nonsampling errors caused by the selection of specific reporting weeks or that occur during the sampling of shipments by the respondent.

The adjusted value of shipments estimate for an establishment was then weighted by the establishment weight. This weight is equal to the reciprocal of the establishment’s probability of being selected into the first-stage sample (see Sample Design).

A final adjustment, the nonresponse post-stratification adjustment weight, calibrates the weighted shipment value (using all prior weighting factors) to the levels of tabulated revenue data from the 2012 Economic Census for specified post-stratification cells. This accounts for:

  • Establishments which did not respond to the survey or from which we did not receive any usable shipment data.
  • Changes in the universe of establishments between the time the first-stage sampling frame was constructed (2011) and the year in which the data were collected (2012).

For the preliminary 2012 CFS estimates, the nonresponse post-stratification cells were defined by industry categories, typically by three-digit NAICS codes (for Manufacturing) or four-digit NAICS codes (all other industries). There were approximately 45 nonresponse post-stratification cells.

For the final 2012 CFS estimates, the nonresponse post-stratification cells were defined by state-by-industry categories. The industry categories were the same as those described above for the preliminary estimates. There were approximately 2,300 state-by-industry nonresponse post-stratification cells.