Monthly Wholesale Trade Survey – Estimation Procedures

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

collected in the MWTS. Each month, firms in the MWTS 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 MWTS

sample. The monthly totals are then benchmarked to the latest totals from the

AWTS. Period-to-period (e.g., month-to-month) change estimates are computed

using the benchmarked monthly totals. See Explanation of Revisions 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 Federal Insurance Contributions Act 

(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., 2-, 3-, and 4-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 the Estimates

Estimates in published tables are based on data from the Monthly Wholesale Trade

Survey, Annual Wholesale Trade Survey, and administrative records. To maintain

confidentiality, no estimates are published that would disclose the operations of an

individual firm. The total error of a published estimate may be considered to be

comprised of sampling error and nonsampling error. Individuals who use Monthly

Wholesale Trade Survey estimates to create new estimates should cite the Census

Bureau as the source of only the original 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 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 upon request. 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.

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.
• 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.

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.