Annual Survey of Manufactures Sampling and Estimating Methodologies

=> DESCRIPTION OF SURVEY SAMPLE

The annual survey of manufactures (ASM) contains two components. The mail
portion of the survey is a probability sample of about 64,000 manufacturing
establishments selected from a total of about 216,000 establishments. These
216,000 establishments represent all manufacturing establishments of
multiunit companies and all single-establishment companies mailed schedules
in the 1987 Census of Manufactures. This mail portion is supplemented
annually by a Social Security Administration list of new manufacturing
establishments opened after 1987 and a list of new multiunit manufacturing
establishments identified from the Census Bureau's Company Organization
Survey.

For the current panel, all establishments of companies with 1987 shipments
in manufacturing in excess of $500 million were included in the survey
panel with certainty. There are approximately 500 such companies
collectively accounting for approximately 18,000 establishments. For the
remaining portion of the mail survey, the establishment was defined as the
sampling unit. For this portion, all establishments with 250 employees or
more and establishments with a very large value of shipments also were
included in the survey panel with certainty. A total of 12,100
establishments were selected from this portion of the universe with
certainty. Therefore, of the 64,000 manufacturing establishments included
in the ASM panel, approximately 31,000 are selected with certainty. These
certainty establishments collectively account for approximately 80 percent
of the total value of shipments in the 1987 census.

Smaller establishments in the remaining portion of the mail survey were
sampled with probabilities ranging from 0.999 to 0.005 in accordance with
mathematical theory for optimum allocation of a sample. The probabilities
of selection assigned to the smaller establishments were proportional to
measures of size determined for each establishment. The measures of size
depend directly upon each establishment's 1987 product class values and the
historic variability of the year-to-year shipments of each product class.
Product classes displaying more volatile year-to-year change in shipments
at the establishment level were sampled at a heavier rate.

This method of assigning measures of size was used in order to maximize the
precision (that is, minimize the variance of estimates of the year-to-year
change) in the value of product class shipments.  Implicitly, it also gave
weight differences in employment, value added, and other general
statistics, since these are highly correlated with value of shipments.
Individual sample selection probabilities were obtained by multiplying each
establishment's final measure of size by an overall sampling fraction
coefficient calculated to yield a total expected sample size.

The sample selection procedure gave each establishment in the sampling
frame an independent chance of selection. This method of independent
selection permits the rotation of small establishments out of a given
sample panel without introducing a bias into the survey estimates.

The nonmail portion of the survey includes all single-establishment
companies that were tabulated as administrative records in the 1987 Census
of Manufactures. Although this portion contained approximately 134,000
establishments, it accounted for less than 2 percent of the estimate for
total value of shipments at the total manufacturing level.  This portion
was not sampled; rather, the data for every establishment in this group
were estimated based on selected information obtained annually from the
administrative records of the Internal Revenue Service and the Social
Security Administration. This administrative-records information, which
includes payroll, total employment, industry classification, and physical
location of the establishment, was obtained under conditions which
safeguard the confidentiality of both tax and census records. Estimates of
data other than payroll and employment for these small establishments were
developed from industry averages.

The corresponding estimates for the mail and nonmail establishments were
added together, along with the base-year differences, as defined in the
Description of Estimating Procedure section, to produce the figures shown
in this publication.

=> DESCRIPTION OF ESTIMATING PROCEDURES

Most of the ASM estimates for the years 1988-1991 were computed using a
difference estimation procedure. For each item, a base-year difference was
developed. This base-year difference is equal to the difference between the
1987 census published number for an item total and the linear ASM estimate
of the total for 1987. The ASM linear estimate was obtained by multiplying
each sample establish- ment's data by its sample weight (the reciprocal of
its probability of selection) and summing the weighted values.

These base-year differences were then added to the corresponding current-
year linear estimates, which include the sum of the estimates for the mail
and nonmailestablishments, to produce the estimates for the years 1983-
1991. Estimates developed by this procedure usually are far more reliable
than comparable linear estimates developed from the current sample data
alone.

However, the 1992 sample estimates for the purchased service items, shown
in files MC92A3A and MC92A3B, are strictly ASM linear estimates developed
only from ASM establishments that reported the specific item.

The remaining estimates in these files, showing the breakdown of
expenditures for new machinery and equipment and costs of parts (separated
into purchases from foreign sources and purchases from domestic sources),
were computed as ratio estimates. To do this, linear estimates of the new
machinery detail items were developed from the ASM establishments and were
ratio adjusted to the corresponding census total for new machinery. In a
similar fashion, the ASM linear estimates of the detailed purchased
materials items were ratio adjusted to the corresponding census total for
cost of parts.

=> QUALIFICATIONS OF THE DATA

The estimates developed from the sample are apt to differ somewhat from the
results of a survey covering all companies in the sampled lists but
otherwise conducted under essentially the same conditions as the actual
sample survey. The estimates of the magnitude of the sampling errors (the
differences between the estimates obtained and the results theoretically
obtained from a comparable, complete-coverage survey) are provided by the
standard errors of the estimates.

The particular sample selected for the ASM is one of a large number of
similar probability samples that, by chance, might have been selected under
the same specifications. Each of the possible samples would yield somewhat
different sets of results, and the standard errors are measures of the
variation of all the possible sample estimates around the theoretical,
comparable, complete-coverage values.

Estimates of the standard errors have been computed from the sample data
for selected statistics in this report. They are presented in the form of
relative standard errors (the standard errors divided by the estimated
values to which they refer).

In conjunction with its associated estimate, the relative standard error
may be used to define confidence intervals (ranges that would include the
comparable, complete-coverage value for specified percentages of all the
possible samples).

The complete-coverage value would be included in the range:

1. From one standard error below to one standard error above the derived
   estimate for about two-thirds of all possible samples.

2. From two standard errors below to two standard errors above the derived
   estimate for about 19 of 20 of all possible samples.

3. From three standard errors below to three standard errors above the
   derived estimate for nearly all samples.

An inference that the comparable, complete-survey result would be within
the indicated ranges would be correct in approximately the relative
frequencies shown. Those proportions, therefore, may be interpreted as
defining the confidence that the estimates from a particular sample would
differ from complete-coverage results by as much as one, two, or three
standard errors, respectively.

For example, suppose an estimated total is shown as 50,000 with an
associated relative standard error of 2 percent, that is, a standard error
of 1,000 (2 percent of 50,000). There is approximately 67 percent
confidence that the interval 49,000 to 51,000 includes the completecoverage
total, about 95 percent confidence that the interval 48,000 to 52,000
includes the complete-coverage total and almost certain confidence that the
interval 47,000 to 53,000 includes the complete-coverage total.

In addition to the sample errors, the estimates are subject to various
response and operational errors: errors of collection, reporting, coding,
transcription, imputation for nonresponse, etc. These operational errors
also would occur if a complete canvass were to be conducted under the same
conditions as the survey. Explicit measures of their effects generally are
not available. However, it is believed that most of the important
operational errors were detected and corrected in the course of the Census
Bureau's review of the data for reasonableness and consistency. The small
operational errors usually remain. To some extent, they are compensating in
the aggregated totals shown. When important operational errors were
detected too late to correct the estimates, the data were suppressed or
were specifically qualified in the files.

As derived, the estimated standard errors included part of the effect of
the operational errors. The total errors, which depend upon the joint
effect of the sampling and operational errors, are usually of the order of
size indicated by the standard error, or only moderately higher. However,
for particular estimates, the total error may considerably exceed the
standard errors shown.

The concept of complete coverage under the conditions prevailing for the
ASM is not identical to the complete coverage of the census of
manufactures, as the censuses have been conducted. Nearly all types of
operational errors that affect the ASM also occur in the censuses. The ASM
and the censuses, are conducted under quite different conditions, and
operational errors can be better controlled in the ASM than in the
censuses. As a result, for many of the census figures, the errors are of
the same order of size as the total errors of the corresponding annual
survey estimates. The differences between the census and ASM operating
conditions also disturb, to some degree, the comparability of the ASM and
census data.

Any figures shown in the files in this publication having an associated
standard error exceeding 15 percent may be of limited reliability. However,
the figure may be combined with higher-level totals, creating a broader
aggregate, which then may be of acceptable reliability.