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APPENDIX C.
Accuracy of the Data
CONTENTS
Confidentiality of the Data C-1
Calculation of Standard Errors
Confidence Intervals
Control of Nonsampling Error
Editing of Unacceptable Data C-9
Errors in the Data C-2
Estimation Procedure C-5
Occupied Housing Units
Persons
Sample Design C-1
Use of Table to Compute Standard Errors
INTRODUCTION
The data contained in this data product are based on the 1990 census
sample. The data are estimates of the actual figures that would have
been obtained from a complete count. Estimates derived from a sample
are expected to be different from the 100-percent figures because they
are subject to sampling and nonsampling errors. Sampling error in data
arises from the selection of persons and housing units to be included
in the sample. Nonsampling error affects both sample and 100-percent
data, and is introduced as a result of errors that may occur during the
collection and processing phases of the census. Provided below is a
detailed discussion of both types of errors and a description of the
estimation procedures.
SAMPLE DESIGN
Every person and housing unit in the United States was asked certain
basic demographic and housing questions (for example, race, age,
marital status, housing value, or rent). A sample of these persons and
housing units was asked more detailed questions about such items as
income, occupation, and housing costs in addition to the basic
demographic and housing information. The primary sampling unit for the
1990 census was the housing unit, including all occupants. For persons
living in group quarters, the sampling unit was the person. Persons in
group quarters were sampled at a 1-in-6 rate.
The sample designation method depended on the data collection
procedures. Approximately 95 percent of the population was enumerated
by the mailback procedure. In these areas, the Bureau of the Census
either purchased a commercial mailing list, which was updated by the
United States Postal Service and Census Bureau field staff, or prepared
a mailing list by canvassing and listing each address in the area prior
to Census Day. These lists were computerized and the appropriate units
were electronically designated as sample units. The questionnaires were
either mailed or hand-delivered to the addresses with instructions to
complete and mail back the form.
Housing units in governmental units with a precensus (1988) estimated
population of fewer than 2,500 persons were sampled at 1-in-2.
Governmental units were defined for sampling purposes as all
incorporated places, all counties, all county equivalents such as
parishes in Louisiana, and all minor civil divisions in Connecticut,
Maine, Massachusetts, Michigan, Minnesota, New Hampshire, New Jersey,
New York, Pennsylvania, Rhode Island, Vermont, and Wisconsin. Housing
units in census tracts and block numbering areas (BNA's) with a
precensus housing unit count below 2,000 housing units were sampled at
1-in-6 for those portions not in small governmental units (governmental
units with a population less than 2,500). Housing units within census
tracts and BNA's with 2,000 or more housing units were sampled at
1-in-8 for those portions not in small governmental units.
In list/enumerate areas (about 5 percent of the population), each
enumerator was given a blank address register with designated sample
lines. Beginning about Census Day, the enumerator systematically
canvassed an assigned area and listed all housing units in the address
register in the order they were encountered. Completed questionnaires,
including sample information for any housing unit listed on a
designated sample line, were collected. For all governmental units with
fewer than 2,500 persons in list/enumerate areas, a 1-in-2 sampling
rate was used. All other list/enumerate areas were sampled at 1-in-6.
Housing units in American Indian reservations, tribal jurisdiction
statistical areas, and Alaska Native villages were sampled according to
the same criteria as other governmental units, except the sampling
rates were based on the size of the American Indian and Alaska Native
population in those areas as measured in the 1980 census. Trust lands
were sampled at the same rate as their associated American Indian
reservations. Census designated places in Hawaii were sampled at the
same rate as governmental units because the Census Bureau does not
recognize incorporated places in Hawaii.
The purpose of using variable sampling rates was to provide relatively
more reliable estimates for small areas and decrease respondent burden
in more densely populated areas while maintaining data reliability.
When all sampling rates were taken into account across the Nation,
approximately one out of every six housing units in the Nation was
included in the 1990 census sample.
CONFIDENTIALITY OF THE DATA
To maintain the confidentiality required by law (Title 13, United
States Code), the Bureau of the Census applies a confidentiality edit
to the 1990 census data to assure that published data do not disclose
information about specific individuals, households, or housing units.
As a result, a small amount of uncertainty is introduced into the
estimates of census characteristics. The sample itself provides
adequate protection for most areas for which sample data are published
since the resulting data are estimates of the actual counts; however,
small areas require more protection. The edit is controlled so that the
basic structure of the data is preserved.
The confidentiality edit is implemented by selecting a small subset of
individual households from the internal sample data files and blanking
a subset of the data items on these household records. Responses to
those data items were then imputed using the same imputation procedures
that were used for nonresponse. A larger subset of households is
selected for the confidentiality edit for small areas to provide
greater protection for these areas. The editing process is implemented
in such a way that the quality and usefulness of the data were
preserved.
ERRORS IN THE DATA
Since statistics in this data product are based on a sample, they
may differ somewhat from 100-percent figures that would have been
obtained if all housing units, persons within those housing units, and
persons living in group quarters had been enumerated using the same
questionnaires, instructions, enumerators, etc. The sample estimate
also would differ from other samples of housing units, persons within
those housing units, and persons living in group quarters. The
deviation of a sample estimate from the average of all possible samples
is called the sampling error. The standard error of a sample estimate
is a measure of the variation among the estimates from all the possible
samples and thus is a measure of the precision with which an estimate
from a particular sample approximates the average result of all
possible samples. The sample estimate and its estimated standard error
permit the construction of interval estimates with prescribed
confidence that the interval includes the average result of all
possible samples. Described below is the method of calculating standard
errors and confidence intervals for the data in this product.
In addition to the variability which arises from the sampling
procedures, both sample data and 100-percent data are subject to
nonsampling error. Nonsampling error may be introduced during any of
the various complex operations used to collect and process census data.
For example, operations such as editing, reviewing, or handling
questionnaires may introduce error into the data. A detailed discussion
of the sources of nonsampling error is given in the section on
"Control of Nonsampling Error" in this appendix.
Nonsampling error may affect the data in two ways. Errors that are
introduced randomly will increase the variability of the data and
should therefore be reflected in the standard error. Errors that tend
to be consistent in one direction will make both sample and 100-percent
data biased in that direction. For example, if respondents consistently
tend to under-report their income, then the resulting counts of
households or families by income category will tend to be understated
for the higher income categories and overstated for the lower income
categories. Such biases are not reflected in the standard error.
Calculation of Standard Errors
Totals and Percentages--Tables A through C in this
appendix contain the information necessary to calculate the standard
errors of sample estimates in this data product. To calculate the
standard error, it is necessary to know the basic standard error for
the characteristic (given in table A or B) that would result under a
simple random sample design (of persons, households, or housing units)
and estimation technique; the design factor for the particular
characteristic estimated (given in table C); and the number of persons
or housing units in the tabulation area and the percent of these in the
sample. For machine-
readable products, the percent-in-sample is included in a data matrix on
the file for each tabulation area. In printed reports, the
percent-in-sample is provided in data tables at the end of the
statistical tables that compose the report. The design factors reflect
the effects of the actual sample design and complex ratio estimation
procedure used for the 1990 census. Tape purchasers will receive table
C, the table of design factors, as a supplement to the technical
documentation. Table C is included in this appendix for printed
reports.
The steps given below should be used to calculate the standard error of
an estimate of a total or a percentage contained in this product. A
percentage is defined here as a ratio of a numerator to a denominator
where the numerator is a subset of the denominator. For example, the
proportion of Black teachers is the ratio of Black teachers to all
teachers.
1. Obtain the standard error from table A or B (or use the formula
given below the table) for the estimated total or percentage,
respectively.
2. Find the geographic area to which the estimate applies in the
appropriate percent-in-sample table or appropriate matrix, and obtain
the person or housing unit "percent-in-sample" figure for this
area. Use the person "percent-in-sample" figure for person and
family characteristics. Use the housing unit "percent-in-sample"
figure for housing unit characteristics.
3. Use table C to obtain the design factor for the characteristic (for
example, employment status, school enrollment) and the range that
contains the percent- in-sample with which you are working. Multiply
the basic standard error by this factor.
The unadjusted standard errors of zero estimates or of very small
estimated totals or percentages will approach zero. This is also the
case for very large percentages or estimated totals that are close to
the size of the tabulation areas to which they correspond.
Nevertheless, these estimated totals and percentages still are subject
to sampling and nonsampling variability, and an estimated standard
error of zero (or a very small standard error) is not appropriate. For
estimated percentages that are less than 2 or greater than 98, use the
basic standard errors in table B that appear in the "2 or 98"
row. For an estimated total that is less than 50 or within 50 of the
total size of the tabulation area, use a basic standard error of 16.
An illustration of the use of the tables is given in the section
entitled "Use of Tables to Compute Standard Errors."
Sums and Differences--The standard errors estimated from
these tables are not directly applicable to sums of and differences
between two sample estimates. To estimate the standard error of a sum
or difference, the tables are to be used somewhat differently in the
following three situations:
1. For the sum of or difference between a sample estimate and a
100-percent value, use the standard error of the sample estimate. The
complete count value is not subject to sampling error.
2. For the sum of or difference between two sample estimates, the
appropriate standard error is approximately the square root of the
sum of the two individual standard errors squared; that is, for
standard errors:
SExand SEyof estimates XandY:
SE|M(X|m+Y|M)|m=SE|M(X|m-Y|M)|m=|M(SEX)2|m+|M(SEY)2
This method, however, will underestimate (overestimate) the
standard error if the two items in a sum are highly positively
(negatively) correlated or if the two items in a difference are highly
negatively (positively) correlated. This method may also be used for
the difference between (or sum of) sample estimates from two censuses
or from a census sample and another survey. The standard error for
estimates not based on the 1990 census sample must be obtained from an
appropriate source outside of this appendix.
For the differences between two estimates, one of which is a
subclass of the other, use the tables directly where the calculated
difference is the estimate of interest. For example, to determine the
estimate of non-Black teachers, one may subtract the estimate of Black
teachers from the estimate of total teachers. To determine the standard
error of the estimate of non-Black teachers apply the above formula
directly.
Ratios--Frequently, the statistic of interest is the
ratio of two variables, where the numerator is not a subset of the
denominator. For example, the ratio of teachers to students in public
elementary schools. The standard error of the ratio between two sample
estimates is estimated as follows:
1. If the ratio is a proportion, then follow the procedure outlined for
"Totals and Percentages."
2. If the ratio is not a proportion, then approximate the standard
error using the formula below.
SE|M(X|m/Y|M)|m=XY|M(SEX|M)2X2|m+|M(SEY|M)2Y2
Medians--For the standard error of the median of a
characteristic, it is necessary to examine the distribution from which
the median is derived, as the size of the base and the distribution
itself affect the standard error. An approximate method is given here.
As the first step, compute one-half of the number on which the median
is based (refer to this result as N/2). Treat N/2 as if it were an
ordinary estimate and obtain its standard error as instructed above.
Compute the desired confidence interval about N/2. Starting with the
lowest value of the characteristic, cumulate the frequencies in each
category of the characteristic until the sum equals or first exceeds
the lower limit of the confidence interval about N/2. By linear
interpolation, obtain a value of the characteristic corresponding to
this sum. This is the lower limit of the confidence interval of the
median. In a similar manner, continue cumulating frequencies until the
sum equals or exceeds the count in excess of the upper limit of the
interval about N/2. Interpolate as before to obtain the upper limit of
the confidence interval for the estimated median.
When interpolation is required in the upper open-ended interval of a
distribution to obtain a confidence bound, use 1.5 times the lower
limit of the open-ended confidence interval as the upper limit of the
open-ended interval.
Confidence Intervals
A sample estimate and its estimated standard error may be
used to construct confidence intervals about the estimate. These
intervals are ranges that will contain the average value of the
estimated characteristic that results over all possible samples, with a
known probability. For example, if all possible samples that could
result under the 1990 census sample design were independently selected
and surveyed under the same conditions, and if the estimate and its
estimated standard error were calculated for each of these samples,
then:
1. Approximately 68 percent of the intervals from one estimated
standard error below the estimate to one estimated standard error
above the estimate would contain the average result from all possible
samples;
2. Approximately 90 percent of the intervals from 1.645 times the
estimated standard error below the estimate to 1.645 times the
estimated standard error above the estimate would contain the average
result from all possible samples.
3. Approximately 95 percent of the intervals from two estimated
standard errors below the estimate to two estimated standard errors
above the estimate would contain the average result from all possible
samples.
The intervals are referred to as 68 percent, 90 percent, and
95 percent confidence intervals, respectively.
The average value of the estimated characteristic that could be derived
from all possible samples is or is not contained in any particular
computed interval. Thus, we cannot make the statement that the average
value has a certain probability of falling between the limits of the
calculated confidence interval. Rather, one can say with a specified
probability of confidence that the calculated confidence interval
includes the average estimate from all possible samples (approximately
the 100-percent value).
Confidence intervals also may be constructed for the ratio, sum of, or
difference between two sample figures. This is done by first computing
the ratio, sum, or difference, then obtaining the standard error of the
ratio, sum, or difference (using the formulas given earlier), and
finally forming a confidence interval for this estimated ratio, sum, or
difference as above. One can then say with specified confidence that
this interval includes the ratio, sum, or difference that would have
been obtained by averaging the results from all possible samples.
The estimated standard errors given in this appendix do not include all
portions of the variability due to nonsampling error that may be
present in the data. The standard errors reflect the effect of simple
response variance, but not the effect of correlated errors introduced
by enumerators, coders, or other field or processing personnel. Thus,
the standard errors calculated represent a lower bound of the total
error. As a result, confidence intervals formed using these estimated
standard errors may not meet the stated levels of confidence (i.e., 68,
90, or 95 percent). Thus, some care must be exercised in the
interpretation of the data in this data product based on the estimated
standard errors.
A standard sampling theory text should be helpful if the user needs
more information about confidence intervals and nonsampling errors.
Use of Tables to Compute Standard Errors
The following is a hypothetical example of how to compute a standard
error of a total and a percentage. Suppose a particular data table
shows that for City A 9,948 persons out of all 15,888 persons age 16
years and over were in the civilian labor force. The percent-in-sample
table lists City A with a percent-in-sample of 16.0 percent (Persons
column). The column in table C which includes 16.0 percent-in-sample
shows the design factor to be 1.1 for "Employment status."
The basic standard error for the estimated total 9,948 may be obtained
from table A or from the formula given below table A. In order to avoid
interpolation, the use of the formula will be demonstrated here.
Suppose that the total population of City A was 21,220. The formula for
the basic standard error, SE, is
SE|M(9,948|M)|m=5|M(9,948|M)|M(1|m-9,948|m/21,220|M)
= 163 persons.
The standard error of the estimated 9,948 persons 16 years and over
who were in the civilian labor force is found by multiplying the basic
standard error 163 by the design factor, 1.1 from table C. This yields
an estimated standard error of 179 for the total number of persons 16
years and over in City A who were in the civilian labor force.
The estimated percent of persons 16 years and over who were in the
civilian labor force in City A is 62.6. From table B, the unadjusted
standard error is found to be approximately 0.85 percentage points. The
standard error for the estimated 62.6 percent of persons 16 years and
over who were in the civilian labor force is 0.85 x 1.1 = 0.94
percentage points.
A note of caution concerning numerical values is necessary. Standard
errors of percentages derived in this manner are approximate.
Calculations can be expressed to several decimal places, but to do so
would indicate more precision in the data than is justifiable. Final
results should contain no more than two decimal places when the
estimated standard error is one percentage point (i.e., 1.00) or more.
In the previous example, the standard error of the 9,948 persons 16
years and over in City A who were in the civilian labor force was found
to be 179. Thus, a 90 percent confidence interval for this estimated
total is found to be:
9,948|m-1.645|M(179|M)to9,948|m+1.645|M(179|M)
or
9,654 to 10,242
One can say, with about 90 percent confidence, that this interval
includes the value that would have been obtained by averaging the
results from all possible samples.
The following is an illustration of the calculation of standard errors
and confidence intervals when a difference between two sample estimates
is obtained. For example, suppose the number of persons in City B age
16 years and over who were in the civilian labor force was 9,314 and
the total number of persons 16 years and over was 16,666. Further
suppose the population of City B was 25,225. Thus, the estimated
percentage of persons 16 years and over who were in the civilian labor
force is 55.9 percent. The unadjusted standard error determined using
the formula provided at the bottom of table B is 0.86 percentage
points. We find that City B had a percent-in-sample of 15.7. The range
which includes 15.7 percent-in-sample in table C shows the design factor to
be 1.1 for "Employment Status." Thus, the approximate standard error of the
percentage (55.9 percent) is 0.86 x 1.1 = 0.95 percentage points.
Now suppose that one wished to obtain the standard error of the
difference between City A and City B of the percentages of persons who
were 16 years and over and who were in the civilian labor force. The
difference in the percentages of interest for the two cities is:
62.6-55.9=6.7percent.
Using the results of the previous example:
SE|M(6.7|M)|m=|M(SE|M(62.6|M)|M)2|m+|M(SE|M(55.9|M)|M)2|m=|M(0.94|M)
2|m+|M(0.95|M)2
= 1.34 percentage points
The 90 percent confidence interval for the difference is formed
as before:
6.70|m-1.645|M(1.34|M)to6.70|m+1.645|M(1.34|M)
or
4.50 to 8.90
One can say with 90 percent confidence that the interval
includes the difference that would have been obtained by averaging the
results from all possible samples.
For reasonably large samples, ratio estimates are normally distributed,
particularly for the census population. Therefore, if we can calculate
the standard error of a ratio estimate then we can form a confidence
interval around the ratio. Suppose that one wished to obtain the
standard error of the ratio of the estimate of persons who were 16
years and over and who were in the civilian labor force in City A to
the estimate of persons who were 16 years and over and who were in the
civilian labor force in City B. The ratio of the two estimates of
interest is:
9948/9314|m=1.07
SE|M(1.07|M)|m=994893141792|M(9948|M)2|m+1882|M(9314|M)2
= .029
Using the results above, the 90 percent confidence interval for
this ratio would be:
1.07|m-1.645|M(.029|M)to1.07|m+1.645|M(.029|M)
or
1.02 to 1.12
ESTIMATION PROCEDURE
The estimates which appear in this publication were
obtained from an iterative ratio estimation procedure (iterative
proportional fitting) resulting in the assignment of a weight to each
sample person or housing unit record. For any given tabulation area, a
characteristic total was estimated by summing the weights assigned to
the persons or housing units possessing the characteristic in the
tabulation area. Estimates of family or household characteristics were
based on the weight assigned to the family member designated as
householder. Each sample person or housing unit record was assigned
exactly one weight to be used to produce estimates of all
characteristics. For example, if the weight given to a sample person or
housing unit had the value 6, all characteristics of that person or
housing unit would be tabulated with the weight of 6. The estimation
procedure, however, did assign weights varying from person to person or
housing unit to housing unit. The estimation procedure used to assign
the weights was performed in geographically defined "weighting
areas." Weighting areas generally were formed of contiguous
geographic units which agreed closely with census tabulation areas
within counties. Weighting areas were required to have a minimum sample
of 400 persons. Weighting areas never crossed State or county
boundaries. In small counties with a sample count below 400 persons,
the minimum required sample condition was relaxed to permit the entire
county to become a weighting area.
Within a weighting area, the ratio estimation procedure for persons was
performed in four stages. For persons, the first stage applied 17
household-type groups. The second stage used two groups: sampling rate
of 1-in-2; sampling rate less than 1-in-2. The third stage used the
dichotomy householders/nonhouseholders. The fourth stage applied 180
aggregate age-sex-race-Hispanic origin categories. The stages were as
follows:
PERSONS
STAGE I: TYPE OF HOUSEHOLD
Group Persons in Housing Units With a Family With Own Children Under 18
1 2 persons in housing unit
2 3 persons in housing unit
3 4 persons in housing unit
4 5 to 7 persons in housing unit
5 8 or more persons in housing unit
Persons in Housing Units With a Family Without Own Children
Under 18
6- 10 2 through 8 or more persons in housing unit
Persons in All Other Housing Units
11 1 person in housing unit
12-16 2 through 8 or more persons in housing unit
Persons in Group Quarters
17 Persons in Group Quarters
STAGE II: SAMPLING RATES
1 Sampling rate of 1-in-2
2 Sampling rate less than 1-in-2
STAGE III: HOUSEHOLDER/NONHOUSEHOLDER
1 Householder
2 Nonhouseholder
STAGE IV: AGE/SEX/RACE/HISPANIC ORIGIN
Group White
Persons of Hispanic Origin
Male
1 0 to 4 years
2 5 to 14 years
3 15 to 19 years
4 20 to 24 years
5 25 to 34 years
6 35 to 54 years
7 55 to 64 years
8 65 to 74 years
9 75 years and over
Female
10-18 Same age categories as groups
1 through 9.
Persons Not of Hispanic Origin
19-36 Same sex and age categories as groups 1 through 18.
Black
37-72 Same age/sex/Hispanic origin cate gories as
groups 1 through 36.
Asian or Pacific Islander
73-108 Same age/sex/Hispanic origin cate gories as groups 1
through 36.
American Indian, Eskimo, or Aleut
109-144 Same age/sex/Hispanic origin cate gories as groups 1
through 36.
Other Race (includes those races not listed above)
145-180 Same age/sex/Hispanic origin cate gories as groups 1
through 36.
Within a weighting area, the first step in the estimation procedure
was to assign an initial weight to each sample person record. This
weight was approximately equal to the inverse of the probability of
selecting a person for the census sample.
The next step in the estimation procedure, prior to iterative
proportional fitting, was to combine categories in each of the four
estimation stages, when needed to increase the reliability of the ratio
estimation procedure. For each stage, any group that did not meet
certain criteria for the unweighted sample count or for the ratio of
the 100-percent to the initially weighted sample count, was combined,
or collapsed, with another group in the same stage according to a
specified collapsing pattern. At the fourth stage, an additional
criterion concerning the number of complete count persons in each
race/Hispanic origin category was applied.
As the final step, the initial weights underwent four stages of ratio
adjustment applying the grouping procedures described above. At the
first stage, the ratio of the complete census count to the sum of the
initial weights for each sample person was computed for each stage I
group. The initial weight assigned to each person in a group was then
multiplied by the stage I group ratio to produce an adjusted weight.
In stage II, the stage I adjusted weights were again adjusted by the
ratio of the complete census count to the sum of the stage I weights
for sample persons in each stage II group. Next, at stage III, the
stage II weights were adjusted by the ratio of the complete census
count to the sum of the stage II weights for sample persons in each
stage III group. Finally, at stage IV, the stage III weights were
adjusted by the ratio of the complete census count to the sum of the
stage III weights for sample persons in each stage IV group. The four
stages of ratio adjustment were performed two times (two iterations) in
the order given above. The weights obtained from the second iteration
for stage IV were assigned to the sample person records. However, to
avoid complications in rounding for tabulated data, only whole number
weights were assigned. For example, if the final weight of the persons
in a particular group was 7.25 then 1/4 of the sample persons in this
group were randomly assigned a weight of 8, while the remaining 3/4
received a weight of 7.
The ratio estimation procedure for housing units was essentially the
same as that for persons, except that vacant units were treated
differently. The occupied housing unit ratio estimation procedure was
done in four stages, and the vacant housing unit ratio estimation
procedure was done in a single stage. The first stage for occupied
housing units applied 16 household type categories, while the second
stage used the two sampling categories described above for persons. The
third stage applied three units-in-structure categories; i.e. single units,
multi-unit less than 10 and multi-unit 10 or more. The fourth stage could
potentially use 200 tenure-race-Hispanic origin-value/rent groups. The
stages for ratio estimation for housing units were as follows:
OCCUPIED HOUSING UNITS
STAGE I: TYPE OF HOUSEHOLD
Group Housing Units With a Family With Own Children Under 18
1 2 persons in housing unit
2 3 persons in housing unit
3 4 persons in housing unit
4 5 to 7 persons in housing unit
5 8 or more persons in housing unit
Housing Units With a Family Without Own Children Under 18
6-10 2 through 8 or more persons in housingunit
All Other Housing Units
11 1 person in housing unit
12-16 2 through 8 or more persons in housing unit
STAGE II: SAMPLING RATE CATEGORY
1 Sampling rate of 1-in-2
2 Sampling rate less than 1-in-2
STAGE III: UNITS IN STRUCTURE
1 Single unit structure
2 Multi-unit structure consisting of fewer than 10 individual
units
3 Multi-unit structure consisting of 10 or more individual units
STAGE IV: TENURE/RACE AND HISPANIC ORIGIN OF HOUSEHOLDER/VALUE OR RENT
Group Owner
White Householder
Householder of Hispanic Origin
Value
1 Less than $20,000
2 $20,000 to $39,999
3 $40,000 to $59,999
4 $60,000 to $79,999
5 $80,000 to $99,999
6 $100,000 to $149,999
7 $150,000 to $249,999
8 $250,000 to $299,999
9 $300,000 or more
10 Other1/
Householder Not of Hispanic Origin
11-20 Same value categories as groups 1 through 10
Black Householder
21-40 Same Hispanic origin/value categories as groups 1 through 20
Asian or Pacific Islander Householder
41-60 Same Hispanic origin/value cate gories as groups 1
through 20
American Indian, Eskimo, or Aleut Householder
61-80 Same Hispanic origin/value categories as groups 1 through
20
Householder of Other Race
81-100 Same Hispanic origin/value categories as groups 1 through 20
Renter
White Householder
Householder of Hispanic origin
Rent
101 Less than $100
102 $100 to $199
103 $200 to $299
104 $300 to $399
105 $400 to $499
106 $500 to $599
107 $600 to $749
108 $750 to $999
109 $1,000 or more
110 No cash rent
Householder Not of Hispanic Origin
111-120 Same rent categories as groups 101 through 110
Black Householder
121-140 Same Hispanic origin/rent categories as groups 101
through 120
Asian or Pacific Islander House holder
141-160 Same Hispanic origin/rent categories as groups 101
through 120
American Indian, Eskimo, or Aleut Householder
161-180 Same Hispanic origin/rent categories as groups 101
through 120
Householder of Other Race
181-200 Same Hispanic origin/rent categories as groups 101
through 120
Vacant Housing Units
1 Vacant for rent
2 Vacant for sale
3 Other vacant
(1) Value of units in this category results from other factors besides
housing value alone, for example, inclusion of more than 10 acres of land,
or presence of a business establishment on the premises.
The estimates produced by this procedure realize some of the gains
in sampling efficiency that would have resulted if the population had
been stratified into the ratio estimation groups before sampling, and
if the sampling rate had been applied independently to each group. The
net effect is a reduction in both the standard error and the possible
bias of most estimated characteristics to levels below what would have
resulted from simply using the initial, unadjusted weight. A by-product
of this estimation procedure is that the estimates from the sample
will, for the most part, be consistent with the complete count figures
for the population and housing unit groups used in the estimation
procedure.
Control of Nonsampling Error
As mentioned earlier, both sample and 100-percent data are subject
to nonsampling error. This component of error could introduce serious
bias into the data, and the total error could increase dramatically
over that which would result purely from sampling. While it is
impossible to completely eliminate nonsampling error from an operation
as large and complex as the decennial census, the Bureau of the Census
attempted to control the sources of such error during the collection
and processing operations. Described below are the primary sources of
nonsampling error and the programs instituted for control of this
error. The success of these programs, however, was contingent upon how
well the instructions actually were carried out during the census. As
part of the 1990 census evaluation program, both the effects of these
programs and the amount of error remaining after their application will
be evaluated.
Undercoverage--It is possible for some households or
persons to be missed entirely by the census. The undercoverage of
persons and housing units can introduce biases into the data.
Several coverage improvement programs were implemented during the
development of the census address list and census enumeration and
processing to minimize undercoverage of the population and housing
units. These programs were developed based on experience from the 1980
census and results from the 1990 census testing cycle. In developing
and updating the census address list, the Census Bureau used a variety
of specialized procedures in different parts of the country.
In the large urban areas, the Census Bureau purchased and geocoded
address lists. Concurrent with geocoding, the United States Postal
Service (USPS) reviewed and updated this list. After the postal check,
census enumerators conducted a dependent canvass and update operation.
In the fall of 1989, local officials were given the opportunity to
examine block counts of address listings (local review) and identify
possible errors. Prior to mailout, the USPS conducted a final review.
In small cities, suburban areas, and selected rural parts of the
country, the Census Bureau created the address list through a listing
operation. The USPS reviewed and updated this list, and the Census
Bureau reconciled USPS corrections and updated through a field
operation. In the fall of 1989, local officials participated in
reviewing block counts of address listings. Prior to mailout, the USPS
conducted a final review.
The Census Bureau (rather than the USPS) conducted a listing
operation in the fall of 1989 and delivered census questionnaires in
selected rural and seasonal housing areas in March of 1990. In some
inner-city public housing developments, whose addresses had been
obtained via the purchased address list noted above, census
questionnaires were also delivered by Census Bureau enumerators.
Coverage improvement programs continued during and after mailout. A
recheck of units initially classified as vacant or nonexistent improved
further the coverage of persons and housing units. All local officials
were given the opportunity to participate in a post-census local
review, and census enumerators conducted an additional recanvass. In
addition, efforts were made to improve the coverage of unique
population groups, such as the homeless and parolees/probationers.
Computer and clerical edits and telephone and personal visit followup
also contributed to improved coverage.
More extensive discussion of the programs implemented to improve
coverage will be published by the Census Bureau when the evaluation of
the coverage improvement program is completed.
Respondent and Enumerator Error--The person answering
the questionnaire or responding to the questions posed by an enumerator
could serve as a source of error, although the questions were phrased
as clearly as possible based on precensus tests, and detailed
instructions for completing the questionnaire were provided to each
household. In addition, respondents' answers were edited for
completeness and consistency, and problems were followed up as
necessary.
The enumerator may misinterpret or otherwise incorrectly record
information given by a respondent; may fail to collect some of the
information for a person or household; or may collect data for
households that were not designated as part of the sample. To control
these problems, the work of enumerators was monitored carefully. Field
staff were prepared for their tasks by using standardized training
packages that included hands-on experience in using census materials. A
sample of the households interviewed by enumerators for nonresponse
were reinterviewed to control for the possibility of data for
fabricated persons being submitted by enumerators. Also, the estimation
procedure was designed to control for biases that would result from the
collection of data from households not designated for the sample.
Processing Error--The many phases involved in processing
the census data represent potential sources for the introduction of
nonsampling error. The processing of the census questionnaires includes
the field editing, followup, and transmittal of completed
questionnaires; the manual coding of write-in responses; and the
electronic data processing. The various field, coding and computer
operations undergo a number of quality control checks to insure their
accurate application.
Nonresponse--Nonresponse to particular questions on the
census questionnaire allows for the introduction of bias into the data,
since the characteristics of the nonrespondents have not been observed
and may differ from those reported by respondents. As a result, any
imputation procedure using respondent data may not completely reflect
this difference either at the elemental level (individual person or
housing unit) or on the average. Some protection against the
introduction of large biases is afforded by minimizing nonresponse. In
the census, nonresponse was reduced substantially during the field
operations by the various edit and followup operations aimed at
obtaining a response for every question. Characteristics for the
nonresponses remaining after this operation were imputed by the
computer by using reported data for a person or housing unit with
similar characteristics.
EDITING OF UNACCEPTABLE DATA
The objective of the processing operation is to produce a set of
data that describes the population as accurately and clearly as
possible. To meet this objective, questionnaires were edited during
field data collection operations for consistency, completeness, and
acceptability. Questionnaires also were reviewed by census clerks for
omissions, certain specific inconsistencies, and population coverage.
For example, write-in entries such as "Don't know" or "NA"
were considered unacceptable. For some district offices, the initial
edit was automated; however, for the majority of the district offices,
it was performed by clerks. As a result of this operation, a telephone
or personal visit followup was made to obtain missing information.
Potential coverage errors were included in the followup, as well as a
sample of questionnaires with omissions and/or inconsistencies.
Subsequent to field operations, remaining incomplete or inconsistent
information on the questionnaires was assigned using imputation
procedures during the final automated edit of the collected data.
Imputations, or computer assignments of acceptable codes in place of
unacceptable entries or blanks, are needed most often when an entry for
a given item is lacking or when the information reported for a person
or housing unit on that item is inconsistent with other information for
that same person or housing unit. As in previous censuses, the general
procedure for changing unacceptable entries was to assign an entry for
a person or housing unit that was consistent with entries for persons
or housing units with similar characteristics. The assignment of
acceptable codes in place of blanks or unacceptable entries enhances
the usefulness of the data.
Another way in which corrections were made during the computer editing
process was through substitution; that is, the assignment of a full set
of characteristics for a person or housing unit. When there was an
indication that a housing unit was occupied but the questionnaire
contained no information for the people within the household or the
occupants were not listed on the questionnaire, a previously accepted
household was selected as a substitute, and the full set of
characteristics for the substitute was duplicated. The assignment of
the full set of housing characteristics occurred when there was no
housing information available. If the housing unit was determined to be
occupied, the housing characteristics were assigned from a previously
processed occupied unit. If the housing unit was vacant, the housing
characteristics were assigned from a previously processed vacant
unit.
Table A. Unadjusted Standard Error for Estimated
Totals
\[Based on a 1-in-6 simple random sample\]
Size of publication area 2/
Estimated
Total 1/
500 1,000 2,500 5,000 10,000 25,000 50,000 100,000
50 16 16 16 16 16 16 16 16
100 20 21 22 22 22 22 22 22
250 25 30 35 35 35 35 35 35
500 - 35 45 45 50 50 50 50
1,000 - - 55 65 65 70 70 70
2,500 - - - 80 95 110 110 110
5,000 - - - - 110 140 150 150
10,000 - - - - - 170 200 210
15,000 - - - - - 170 230 250
25,000 - - - - - - 250 310
75,000 - - - - - - - 310
100,000 - - - - - - - -
250,000 - - - - - - - -
500,000 - - - - - - - -
1,000,000 - - - - - - - -
5,000,000 - - - - - - - -
10,000,000 - - - - - - - -
-------------------------------------------------------------------------
Estimated
Total 1/
250,000 500,000 1,000,000 5,000,000 10,000,000 25,000,000
50 16 16 16 16 16 16
100 22 22 22 22 22 22
250 35 35 35 35 35 35
500 50 50 50 50 50 50
1,000 70 70 70 70 70 70
2,500 110 110 110 110 110 110
5,000 160 160 160 160 160 160
10,000 220 220 220 220 220 220
15,000 270 270 270 270 270 270
25,000 340 350 350 350 350 350
75,000 510 570 590 610 610 610
100,000 550 630 670 700 700 710
250,000 - 790 970 1 090 1 100 1 100
500,000 - - 1 120 1 500 1 540 1 570
1,000,000 - - - 2 000 2 120 2 190
5,000,000 - - - - 3 540 4 470
10,000,000 - - - - - 5 480
(1) For estimated totals larger than 10,000,000, the
standard error is somewhat larger than the table values. The formula
given below should be used to calculate the standard error.
SE|M(Y|M)|m=5Y|M(1|m-YN|M)
N |m= Sizeofarea
Y |m=
Estimateofcharacteristictotal
(2) The total count of persons in the area if the estimated total is a
person characteristic, or the total count of housing units in the area
if the estimated total is a housing unit characteristic.
Table B. Unadjusted Standard Error in Percentage Points for Estimated
Percentage
\[Based on a 1-in-6 simple random sample\]
Base of percentage1/
Estimated
Percentage
500 750 1,000 1,500 2,500 5,000 7,500 10,000
2 or 98 1.4 1.1 1.0 0.8 0.6 0.4 0.4 0.3
5 or 95 2.2 1.8 1.5 1.3 1.0 0.7 0.6 0.5
10 or 90 3.0 2.4 2.1 1.7 1.3 0.9 0.8 0.7
15 or 85 3.6 2.9 2.5 2.1 1.6 1.1 0.9 0.8
20 or 80 4.0 3.3 2.8 2.3 1.8 1.3 1.0 0.9
25 or 75 4.3 3.5 3.1 2.5 1.9 1.4 1.1 1.0
30 or 70 4.6 3.7 3.2 2.6 2.0 1.4 1.2 1.0
35 or 65 4.8 3.9 3.4 2.8 2.1 1.5 1.2 1.1
50 5.0 4.1 3.5 2.9 2.2 1.6 1.3 1.1
--------------------------------------------------------------------------
Estimated
Percentage
25,000 50,000 100,000 250,000 500,000
2 or 98 0.2 0.1 0.1 0.1 0.1
5 or 95 0.3 0.2 0.2 0.1 0.1
10 or 90 0.4 0.3 0.2 0.1 0.1
15 or 85 0.5 0.4 0.3 0.2 0.1
20 or 80 0.6 0.4 0.3 0.2 0.1
25 or 75 0.6 0.4 0.3 0.2 0.1
30 or 70 0.6 0.5 0.3 0.2 0.1
35 or 65 0.7 0.5 0.3 0.2 0.2
50 0.7 0.5 0.4 0.2 0.2
(1) For a percentage and/or base of percentage not shown
in the table, the formula given below may be used to calculate the
standard error. This table should only be used for proportions, that
is, where the numerator is a subset of the denominator.
SE|M(p|M)|m=5Bp|M(100|m-p|M)
B |m=
Baseofestimatedpercentage
p |m=
Estimatedpercentage
|
|
|
