Att D - Source and Accuracy Statement

Attachment C

Source of the Data and Accuracy of the Estimates for the
October 2020 Current Population Survey Microdata File on School Enrollment
Table of Contents
SOURCE OF THE DATA ..........................................................................................................................1
Basic CPS........................................................................................................................................................ 1
October 2020 Supplement ..................................................................................................................... 2
Estimation Procedure .............................................................................................................................. 2

ACCURACY OF THE ESTIMATES .........................................................................................................3
Sampling Error ............................................................................................................................................ 3
Nonsampling Error ................................................................................................................................... 3
Nonresponse ................................................................................................................................................ 4
Undercoverage ............................................................................................................................................ 4
Comparability of Data .............................................................................................................................. 5
A Nonsampling Error Warning ............................................................................................................ 6
Standard Errors and Their Use ............................................................................................................ 7
Estimating Standard Errors .................................................................................................................. 7
Generalized Variance Parameters ...................................................................................................... 8
Standard Errors of Estimated Numbers .......................................................................................... 9
Standard Errors of Estimated School Enrollment Numbers .................................................10
Standard Errors of Estimated Percentages ..................................................................................12
Standard Errors of Estimated Differences ....................................................................................13
Standard Errors of Quarterly or Yearly Averages .....................................................................13
Year-to-Year factors................................................................................................................................14
Technical Assistance...............................................................................................................................14
REFERENCES.......................................................................................................................................... 17

Tables
Table 1.
Table 2.
Table 3.
Table 4.
Table 5.
Table 6.
Table 7.
Table 8.

Current Population Survey Coverage Ratios: October 2020............................................... 5
Estimation Groups of Interest and Generalized Variance Parameters .......................... 9
Illustration of Standard Errors of Estimated Numbers .......................................................10
Population Controls for School Enrollment Age Groups: October 2020 .....................11
Illustration of Standard Errors of Estimated School Enrollment Numbers ...............11
Illustration of Standard Errors of Estimated Percentages .................................................12
Illustration of Standard Errors of Estimated Differences ..................................................13
Parameters for Computation of Standard Errors for Labor Force
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Characteristics: October 2020 .......................................................................................................15
Table 9. Parameters for Computation of Standard Errors for School Enrollment
Characteristics: October 2020 .......................................................................................................16

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Source of the Data and Accuracy of the Estimates for the
October 2020 Current Population Survey Microdata File on School
Enrollment
SOURCE OF THE DATA
The data in this microdata file are from the October 2020 Current Population Survey (CPS).
The U.S. Census Bureau conducts the CPS every month, although this file has only October
data. The October survey uses two sets of questions, the basic CPS and a set of
supplemental questions. The CPS, sponsored jointly by the Census Bureau and the U.S.
Bureau of Labor Statistics, is the country’s primary source of labor force statistics for the
civilian noninstitutionalized population. The Census Bureau and the National Center for
Educational Statistics jointly sponsor the supplemental questions for October.
Basic CPS. The monthly CPS collects primarily labor force data about the civilian
noninstitutionalized population living in the United States. The institutionalized
population, which is excluded from the universe, consists primarily of the population in
correctional institutions and nursing homes (98 percent of the 4.0 million institutionalized
people in the 2010 Census). Starting in August 2017, college and university dormitories
were also excluded from the universe because most of the residents had usual residences
elsewhere. Interviewers ask questions concerning labor force participation of each
member 15 years old and older in sample households. Typically, the week containing the
nineteenth of the month is the interview week. The week containing the twelfth is the
reference week (i.e., the week about which the labor force questions are asked).
The CPS uses a multistage probability sample based on the results of the decennial census,
with coverage in all 50 states and the District of Columbia. The sample is continually
updated to account for new residential construction. When files from the most recent
decennial census become available, the Census Bureau gradually introduces a new sample
design for the CPS.

Every ten years, the CPS first-stage sample is redesigned 1 reflecting changes based on the
most recent decennial census. In the first stage of the sampling process, primary sampling
units (PSUs) 2 were selected for sample. In the 2010 sample design, the United States was
divided into 1,987 PSUs. These PSUs were then grouped into 852 strata. Within each
stratum, a single PSU was chosen for the sample, with its probability of selection
proportional to its population as of the most recent decennial census. In the case of strata
consisting of only one PSU, the PSU was chosen with certainty.
1
2

For detailed information on the 2010 sample redesign, please see Bureau of Labor Statistics (2014).
The PSUs correspond to substate areas (i.e., counties or groups of counties) that are geographically
contiguous.

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Approximately 69,000 sampled addresses were selected from the sampling frame in
October. Based on eligibility criteria, six percent of these sampled addresses were sent
directly to computer-assisted telephone interviewing (CATI). The remaining sampled
addresses were assigned to interviewers for computer-assisted personal interviewing
(CAPI). 3 Of all addresses in sample, about 59,000 were determined to be eligible for
interview. Interviewers obtained interviews at about 47,000 of the housing units at these
addresses. Noninterviews occur when the occupants are not found at home after repeated
calls or are unavailable for some other reason.
October 2020 Supplement. In October 2020, in addition to the basic CPS questions,
interviewers asked supplementary questions of household members three years old and
older on school enrollment.

Estimation Procedure. This survey’s estimation procedure adjusts weighted sample
results to agree with independently derived population controls of the civilian
noninstitutionalized population of the United States, each state, and the District of
Columbia. These population controls 4 are prepared monthly as part of the Census Bureau’s
Population Estimates Program.
The population controls for the nation are distributed by demographic characteristics in
two ways:
•
•

Age, sex, and race (White alone, Black alone, and all other groups combined).
Age, sex, and Hispanic origin.

The population controls for the states are distributed by:
•
•
•

Race (Black alone and all other race groups combined).
Age (0-15, 16-44, and 45 and over).
Sex.

The independent estimates by age, sex, race, and Hispanic origin, and for states by selected
age groups and broad race categories, are developed using the basic demographic
accounting formula whereby the population from the 2010 Census data is updated using
3
4

For further information on CATI and CAPI and the eligibility criteria, please see U.S. Census Bureau
(2019).
For additional information on population controls, including details on the demographic characteristics
used and net international components, please see Chapters 1-3 and Appendix: History of the Current
Population Survey of U.S. Census Bureau (2019).

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data on the components of population change (births, deaths, and net international
migration) with net internal migration as an additional component in the state population
controls.
The net international migration component of the population controls includes:
•
•
•
•

Net international migration of the foreign born;
Net migration between the United States and Puerto Rico;
Net migration of natives to and from the United States; and
Net movement of the Armed Forces population to and from the United States.

Because the latest available information on these components lags behind the survey date,
it is necessary to make short-term projections of these components to develop the estimate
for the survey date.
ACCURACY OF THE ESTIMATES
A sample survey estimate has two types of error: sampling and nonsampling. The accuracy
of an estimate depends on both types of error. The nature of the sampling error is known
given the survey design; the full extent of the nonsampling error is unknown.

Sampling Error. Since the CPS estimates come from a sample, they may differ from figures
from an enumeration of the entire population using the same questionnaires, instructions,
and enumerators. For a given estimator, the difference between an estimate based on a
sample and the estimate that would result if the sample were to include the entire
population is known as sampling error. Standard errors, as calculated by methods
described in “Standard Errors and Their Use,” are primarily measures of the magnitude of
sampling error. However, the estimation of standard errors may include some
nonsampling error.
Nonsampling Error. For a given estimator, the difference between the estimate that
would result if the sample were to include the entire population and the true population
value being estimated is known as nonsampling error. There are several sources of
nonsampling error that may occur during the development or execution of the survey. It
can occur because of circumstances created by the interviewer, the respondent, the survey
instrument, or the way the data are collected and processed. Some nonsampling errors,
and examples of each, include:
•

Measurement error: The interviewer records the wrong answer, the respondent
provides incorrect information, the respondent estimates the requested.
information, or an unclear survey question is misunderstood by the respondent.
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•
•
•
•

Coverage error: Some individuals who should have been included in the survey
frame were missed.
Nonresponse error: Responses are not collected from all those in the sample or
the respondent is unwilling to provide information.
Imputation error: Values are estimated imprecisely for missing data.
Processing error: Forms may be lost, data may be incorrectly keyed, coded, or
recoded, etc.

To minimize these errors, the Census Bureau applies quality control procedures during all
stages of the production process including the design of the survey, the wording of
questions, the review of the work of interviewers and coders, and the statistical review of
reports.

Two types of nonsampling error that can be examined to a limited extent are nonresponse
and undercoverage.
Nonresponse. The effect of nonresponse cannot be measured directly, but one indication
of its potential effect is the nonresponse rate. For the October 2020 basic CPS, the
household-level unweighted nonresponse rate was 19.7 percent. The person-level
unweighted nonresponse rate for the School Enrollment supplement was an additional
11.0 percent.
Since the basic CPS nonresponse rate is a household-level rate and the School Enrollment
supplement nonresponse rate is a person-level rate, we cannot combine these rates to
derive an overall nonresponse rate. Nonresponding households may have more or fewer
persons than interviewed ones, so combining these rates may lead to an under- or
overestimate of the true overall nonresponse rate for persons for the School Enrollment
supplement.
In accordance with Census Bureau and Office of Management and Budget Quality
Standards, the Census Bureau will conduct an analysis to assess nonresponse bias in the
School Enrollment.
Responses are made up of complete interviews and sufficient partial interviews. A
sufficient partial interview is an incomplete interview in which the household or person
answered enough of the questionnaire for the supplement sponsor to consider the
interview complete. The remaining supplement questions may have been edited or
imputed to fill in missing values. Insufficient partial interviews are considered to be
nonrespondents. Refer to the supplement overview attachment in the technical
documentation for the specific questions deemed critical by the sponsor as necessary to
answer in order to be considered a sufficient partial interview.
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As a result of sufficient partial interviews being considered responses, individual
items/questions have their own response and refusal rates. As part of the nonsampling
error analysis, the item response rates, item refusal rates, and edits are reviewed. For the
School Enrollment supplement, the unweighted item refusal rates range from 0.25 percent
to 4.86 percent. The unweighted item allocation rates range from 4.64 percent to 30.68
percent.

Undercoverage. The concept of coverage with a survey sampling process is defined as the
extent to which the total population that could be selected for sample “covers” the survey’s
target population. Missed housing units and missed people within sample households
create undercoverage in the CPS. Overall CPS undercoverage for October 2020 is estimated
to be about ten percent. CPS coverage varies with age, sex, and race. Generally, coverage is
higher for females than for males and higher for non-Blacks than for Blacks. This
differential coverage is a general problem for most household-based surveys.
The CPS weighting procedure mitigates bias from undercoverage, but biases may still be
present when people who are missed by the survey differ from those interviewed in ways
other than age, race, sex, Hispanic origin, and state of residence. How this weighting
procedure affects other variables in the survey is not precisely known. All of these
considerations affect comparisons across different surveys or data sources.

A common measure of survey coverage is the coverage ratio, calculated as the estimated
population before poststratification divided by the independent population control. Table
1 shows October 2020 CPS coverage ratios by age and sex for certain race and Hispanic
groups. The CPS coverage ratios can exhibit some variability from month to month.
Table 1. Current Population Survey Coverage Ratios: October 2020
Total

White alone

Black alone

Residual raceA

HispanicB

Age
All
Male Female Male Female Male Female Male Female Male Female
group people
0-15 0.86
0.87
0.86
0.89
0.89
0.81
0.78
0.80
0.79
0.83
0.82
16-19 0.89
0.92
0.87
0.95
0.89
0.85
0.80
0.80
0.86
0.87
0.81
20-24 0.79
0.82
0.76
0.84
0.78
0.74
0.67
0.80
0.75
0.80
0.75
25-34 0.82
0.80
0.83
0.84
0.87
0.65
0.70
0.75
0.79
0.74
0.82
35-44 0.90
0.88
0.92
0.92
0.95
0.72
0.83
0.84
0.87
0.82
0.88
45-54 0.90
0.90
0.90
0.92
0.93
0.82
0.80
0.87
0.84
0.83
0.86
55-64 0.96
0.95
0.97
0.97
0.98
0.88
0.89
0.88
0.91
0.85
0.90
65+
1.01
1.01
1.02
1.03
1.03
0.96
0.98
0.91
0.90
0.93
0.88
15+
0.91
0.90
0.92
0.93
0.94
0.79
0.82
0.83
0.85
0.82
0.85
0+
0.90
0.90
0.91
0.92
0.93
0.79
0.81
0.82
0.83
0.82
0.84

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Source: U.S. Census Bureau, Current Population Survey, October 2020.
A
The Residual race group includes cases indicating a single race other than White or Black, and cases
indicating two or more races.
B
Hispanics may be any race.
Note: For a more detailed discussion on the use of parameters for race and ethnicity, please see the
“Generalized Variance Parameters” section.

Comparability of Data. Data obtained from the CPS and other sources are not entirely
comparable. This is due to differences in interviewer training and experience and in
differing survey processes. 5 These differences are examples of nonsampling variability not
reflected in the standard errors. Therefore, caution should be used when comparing
results from different sources.

Data users should be careful when comparing the data from this microdata file, which
reflects 2010 Census-based controls, with microdata files which reflect 2000 Census-based
controls. Ideally, the same population controls should be used when comparing any
estimates. In reality, the use of the same population controls is not practical when
comparing trend data over a period of 10 to 20 years. Thus, when it is necessary to
combine or compare data based on different controls or different designs, data users
should be aware that changes in weighting controls or weighting procedures can create
small differences between estimates. See the discussion following for information on
comparing estimates derived from different populations or different sample designs.

Microdata files from previous years reflect the latest available census-based controls.
Although the most recent change in population controls had relatively little impact on
summary measures such as averages, medians, and percentage distributions, it did have a
significant impact on levels. For example, use of 2010 Census-based controls results in
about a 0.2 percent increase from the 2000 Census-based controls in the civilian
noninstitutionalized population and in the number of families and households. Thus,
estimates of levels for data collected in 2012 and later years will differ from those for
earlier years by more than what could be attributed to actual changes in the population.
These differences could be disproportionately greater for certain population subgroups
than for the total population.

Users should also exercise caution because of changes caused by the phase-in of the 2010
Census files (see “Basic CPS”). 6 During this time period, CPS data were collected from
sample designs based on different censuses. Two features of the new CPS design have the
potential of affecting estimates: (1) the temporary disruption of the rotation pattern from
5
6

Survey processes include, but are not limited to, question wording, universe, sampling frame, interview
modes, and weighting.
The phase-in process using the 2010 Census files began April 2014.

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August 2014 through June 2015 for a comparatively small portion of the sample and (2)
the change in sample areas. Most of the known effect on estimates during and after the
sample redesign will be the result of changing from 2000 to 2010 geographic definitions.
Research has shown that the national-level estimates of the metropolitan and
nonmetropolitan populations should not change appreciably because of the new sample
design. However, users should still exercise caution when comparing metropolitan and
nonmetropolitan estimates across years with a design change, especially at the state level.

Caution should also be used when comparing Hispanic estimates over time. No
independent population control totals for people of Hispanic origin were used before 1985.

A Nonsampling Error Warning. Since the full extent of the nonsampling error is
unknown, one should be particularly careful when interpreting results based on small
differences between estimates. The Census Bureau recommends that data users
incorporate information about nonsampling errors into their analyses, as nonsampling
error could impact the conclusions drawn from the results. Caution should also be used
when interpreting results based on a relatively small number of cases. Summary measures
(such as medians and percentage distributions) probably do not reveal useful information
when computed on a subpopulation smaller than 75,000.
For additional information on nonsampling error, including the possible impact on CPS
data, when known, refer to U.S. Census Bureau (2019) and Brooks & Bailar (1978).

Standard Errors and Their Use. A sample estimate and its standard error enable one to
construct a confidence interval. A confidence interval is a range about a given estimate that
has a specified probability of containing the average result of all possible samples. For
example, if all possible samples were surveyed under essentially the same general
conditions and using the same sample design, and if an estimate and its standard error
were calculated from each sample, then approximately 90 percent of the intervals from
1.645 standard errors below the estimate to 1.645 standard errors above the estimate
would include the average result of all possible samples.
A particular confidence interval may or may not contain the average estimate derived from
all possible samples, but one can say with the specified confidence that the interval
includes the average estimate calculated from all possible samples. Standard errors may
also be used to perform hypothesis testing, a procedure for distinguishing between
population parameters using sample estimates. The most common type of hypothesis is
that the population parameters are different. An example of this would be comparing the
percentage of men who were part-time workers to the percentage of women who were
part-time workers.
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Tests may be performed at various levels of significance. A significance level is the
probability of concluding that the characteristics are different when, in fact, they are the
same. For example, to conclude that two characteristics are different at the 0.10 level of
significance, the absolute value of the estimated difference between characteristics must be
greater than or equal to 1.645 times the standard error of the difference.
The Census Bureau uses 90-percent confidence intervals and 0.10 levels of significance to
determine statistical validity. Consult standard statistical textbooks for alternative criteria.

Estimating Standard Errors. The Census Bureau uses replication methods to estimate the
standard errors of CPS and School, Enrollment estimates. These methods primarily
measure the magnitude of sampling error. However, they do measure some effects of
nonsampling error as well. They do not measure systematic biases in the data associated
with nonsampling error. Bias is the average over all possible samples of the differences
between the sample estimates and the true value.
There are two ways to calculate standard errors for the CPS microdata file on School
Enrollment.

1. Direct estimates created from replicate weighting methods;
2. Generalized variance estimates created from generalized variance function
(GVF) parameters a and b.
While replicate weighting methods provide the most accurate variance estimates, this
approach requires more computing resources and more expertise on the part of the user.
The GVF parameters provide a method of balancing accuracy with resource usage as well
as a smoothing effect on standard error estimates. For more information on calculating
direct estimates, see U.S. Census Bureau (2009). For more information on GVF estimates,
refer to the “Generalized Variance Parameters” section.

Generalized Variance Parameters. While it is possible to estimate the standard error
based on the survey data for each estimate in a report, there are a number of reasons why
this is not done. A presentation of the individual standard errors would be of limited use,
since one could not possibly predict all of the combinations of results that may be of
interest to data users. Additionally, data users have access to CPS microdata files, and it is
impossible to compute in advance the standard error for every estimate one might obtain
from those data sets. Moreover, variance estimates are based on sample data and have
variances of their own. Therefore, some methods of stabilizing these estimates of variance,
for example, by generalizing or averaging over time, may be used to improve their
reliability.
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Experience has shown that certain groups of estimates have similar relationships between
their variances and expected values. Modeling or generalizing may provide more stable
variance estimates by taking advantage of these similarities. The GVF is a simple model
that expresses the variance as a function of the expected value of the survey estimate. The
parameters of the GVF are estimated using direct replicate variances. These GVF
parameters provide a relatively easy method to obtain approximate standard errors for
numerous characteristics.
In this source and accuracy statement:
•
•

•
•

Tables 3 and 5 through 7 provide illustrations for calculating standard errors;
Table 4 provides the October 2020 population totals for school enrollment
groups;
Table 8 provides the GVF parameters for labor force estimates; and
Table 9 provides GVF parameters for characteristics from the October 2020
supplement.

The basic CPS questionnaire records the race and ethnicity of each respondent. With
respect to race, a respondent can be White, Black, Asian, American Indian and Alaskan
Native (AIAN), Native Hawaiian and Other Pacific Islander (NHOPI), or combinations of two
or more of the preceding. A respondent’s ethnicity can be Hispanic or non-Hispanic,
regardless of race.
The GVF parameters to use in computing standard errors are dependent upon the
race/ethnicity group of interest. Table 2 summarizes the relationship between the
race/ethnicity group of interest and the GVF parameters to use in standard error
calculations.

Table 2. Estimation Groups of Interest and Generalized Variance Parameters
Generalized variance parameters to
use in standard error calculations

Race/ethnicity group of interest
Total population

White alone, White alone or in combination (AOIC), or
White non-Hispanic population

Black alone, Black AOIC, or Black non-Hispanic population

Asian alone, Asian AOIC, or Asian non-Hispanic population
AIAN alone, AIAN AOIC, or AIAN non-Hispanic population

Total or White
Total or White
Black

Asian, American Indian and Alaska
Native (AIAN), Native Hawaiian and
Other Pacific Islander (NHOPI)
Asian, AIAN, NHOPI

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NHOPI alone, NHOPI AOIC, or NHOPI non-Hispanic
population
Populations from other race groups
HispanicA population

Two or more racesB – employment/unemployment and
educational attainment characteristics
Two or more racesB – all other characteristics

Asian, AIAN, NHOPI
Asian, AIAN, NHOPI
HispanicA
Black

Asian, AIAN, NHOPI

Source: U.S. Census Bureau, Current Population Survey, internal data files.
A
Hispanics may be any race.
B
Two or more races refers to the group of cases self-classified as having two or more races.

When calculating standard errors for an estimate of interest from cross-tabulations
involving different characteristics, use the set of GVF parameters for the characteristic that
will give the largest standard error. If the estimate of interest is strictly from basic CPS
data, the GVF parameters will come from the CPS GVF table (Table 8). If the estimate is
using School Enrollment supplement data, the GVF parameters will come from the School
Enrollment supplement GVF table (Table 9).
Standard Errors of Estimated Numbers. The approximate standard error, 𝑠𝑠𝑥𝑥 , of an
estimated number from this microdata file can be obtained by using the formula:
𝑠𝑠𝑥𝑥 = √𝑎𝑎𝑥𝑥 2 + 𝑏𝑏𝑏𝑏

(1)

Here x is the size of the estimate, and a and b are the parameters in Table 8 or 9 associated
with the particular type of characteristic.

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Illustration 1
Suppose there were 5,670,000 unemployed men (ages 16 and up) in the civilian labor
force. Table 3 shows how to use the appropriate parameters from Table 8 and Formula (1)
to estimate the standard error and confidence interval.
Table 3. Illustration of Standard Errors of Estimated Numbers

Number of unemployed males in the civilian labor force (x)
a-parameter (a)
b-parameter (b)
Standard error
90-percent confidence interval

5,670,000
-0.000031
2,947
125,000
5,464,000 to 5,876,000

Source: U.S. Census Bureau, Current Population Survey, School Enrollment, October 2020.

The standard error is calculated as

𝑠𝑠𝑥𝑥 = �−0.000031 × 5,670,0002 + 2,947 × 5,670,000,

which, rounded to the nearest thousand, is 125,000. The 90-percent confidence interval is
calculated as 5,670,000 ± 1.645 × 125,000.
A conclusion that the average estimate derived from all possible samples lies within a
range computed in this way would be correct for roughly 90 percent of all possible
samples.

Standard Errors of Estimated School Enrollment Numbers. The approximate standard
error, 𝑠𝑠𝑥𝑥 , of an estimated school enrollment number from this microdata file can be
obtained by using the formula:
𝑏𝑏

𝑠𝑠𝑥𝑥 = �− � � 𝑥𝑥 2 + 𝑏𝑏𝑏𝑏
𝑇𝑇

(2)

Here x is the size of the estimate, T is the population control from Table 4 for the age group
of interest, and b is the parameter in Table 9 associated with the particular type of
characteristic. If Table 4 does not explicitly contain the age group of interest, obtain T by
summing the controls for the age groups available in the table that do contain the age
group of interest. When calculating standard errors for numbers from cross-tabulations
involving different characteristics, use the set of parameters for the characteristic that will
give the largest standard error.
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Table 4. Population Controls for School Enrollment Age Groups: October 2020

Age
Group
3-4
5
6
7-11
12-13
14
15-17
18
19
20-24
25-29
30-34
35-64
65+

Total

White Only

Black Only

7,908,848
4,046,816
4,054,088
20,259,943
8,388,898
4,179,805
12,442,925
4,117,765
4,150,618
20,916,678
22,473,470
22,393,956
123,473,323
55,116,473

5,666,372
2,895,841
2,902,665
14,558,111
6,040,875
3,032,184
9,104,574
3,021,530
3,041,331
15,323,245
16,280,141
16,398,428
95,433,260
46,040,122

1,197,485
611,698
613,098
3,066,351
1,277,916
626,830
1,809,201
601,440
609,482
3,078,214
3,462,493
3,264,850
15,904,915
5,334,800

Asian, AIAN,
NHOPIA
1,044,991
539,277
538,325
2,635,481
1,070,107
520,791
1,529,150
494,795
499,805
2,515,219
2,730,836
2,730,678
12,135,148
3,741,551

HispanicB
2,065,622
1,055,056
1,047,101
5,283,393
2,175,276
1,072,815
3,093,158
1,000,858
993,017
4,813,548
4,848,668
4,597,506
21,241,193
4,939,893

Source: U.S. Census Bureau, Population Estimates, October 2020.
A
AIAN is American Indian and Alaska Native, and NHOPI is Native Hawaiian and Other Pacific Islander.
B
Hispanics may be any race.
Notes: White, Black, and Asian, AIAN, NHOPI totals include Hispanics. The Asian, AIAN, NHOPI parameters
are to be used for Asian, AIAN, NHOPI alone and all race in-combination group estimates.

Illustration 2
Suppose there were 3,189,000 three- and four-year-olds enrolled in school and 7,908,848
total children in that age group. Table 5 shows how to use the appropriate b parameter
from Table 9 and Formula (2) to estimate the standard error and confidence interval.
Table 5. Illustration of Standard Errors of School Enrollment Numbers
Number of three- and four-year-olds enrolled in school (x)
3,189,000
Total (T)
7,908,848
b-parameter (b)
4,256
Standard error
90,000
90-percent confidence interval
3,041,000 to 3,337,000

Source: U.S. Census Bureau, Current Population Survey, School Enrollment Supplement, October 2020.

The standard error is calculated as

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𝑠𝑠𝑥𝑥 = �− �

4,256
� × 3,189,0002 + 4,256 × 3,189,000
7,908,848

which, rounded to the nearest thousand, is 90,000. The 90-percent confidence interval is
calculated as 3,189,000 ± 1.645 × 90,000.
A conclusion that the average estimate derived from all possible samples lies within a
range computed in this way would be correct for roughly 90 percent of all possible
samples.

Standard Errors of Estimated Percentages. The reliability of an estimated percentage,
computed using sample data for both numerator and denominator, depends on both the
size of the percentage and its base. Estimated percentages are relatively more reliable than
the corresponding estimates of the numerators of the percentages, particularly if the
percentages are 50 percent or more. When the numerator and denominator of the
percentage are in different categories, use the parameter from Table 8 or 9 as indicated by
the numerator.
The approximate standard error, 𝑠𝑠𝑦𝑦,𝑝𝑝 , of an estimated percentage can be obtained by using
the formula:
𝑏𝑏

𝑠𝑠𝑦𝑦,𝑝𝑝 = � 𝑝𝑝(100 − 𝑝𝑝)

(3)

𝑦𝑦

Here y is the total number of people, families, households, or unrelated individuals in the
base or denominator of the percentage, p is the percentage 100*x/y (0 ≤ p ≤ 100), and b is
the parameter in Table 8 or 9 associated with the characteristic in the numerator of the
percentage.

Illustration 3
Suppose there were 16,995,000 people aged 18 to 21, and 50.0 percent were enrolled in
college. Table 6 shows how to use the appropriate parameters from Table 9 and Formula
(3) to estimate the standard error and confidence interval.
Table 6. Illustration of Standard Errors of Estimated Percentages

Percentage of people aged 18-21 enrolled in college (p)
Base (y)
b-parameter (b)
Standard error
90-percent confidence interval

50.0
16,995,000
4,256
0.79
48.7 to 51.3

Source: U.S. Census Bureau, Current Population Survey, School Enrollment, October 2020.

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The standard error is calculated as

4,256
× 50.0 × (100.0 − 50.0) = 0.79
𝑠𝑠𝑦𝑦,𝑝𝑝 = �
16,995,000

and the 90-percent confidence interval for the estimated percentage of people aged 18 to
21 enrolled in college is from 48.7 to 51.3 percent (i.e., 50.0 ± 1.645 × 0.79).
Standard Errors of Estimated Differences. The standard error of the difference between
two sample estimates is approximately equal to
2

𝑠𝑠𝑥𝑥1 −𝑥𝑥2 = ��𝑠𝑠𝑥𝑥1 � + �𝑠𝑠𝑥𝑥2 �

2

(4)

where 𝑠𝑠𝑥𝑥1 and 𝑠𝑠𝑥𝑥2 are the standard errors of the estimates, 𝑥𝑥1 and 𝑥𝑥2 . The estimates can be
numbers, percentages, ratios, etc. This will result in accurate estimates of the standard
error of the same characteristic in two different areas or for the difference between
separate and uncorrelated characteristics in the same area. However, if there is a high
positive (negative) correlation between the two characteristics, the formula will
overestimate (underestimate) the true standard error.
Illustration 4
Suppose that of the 6,720,000 employed men between 20-24 years of age, 28.0 percent
were part-time workers, and of the 6,505,000 employed women between 20-24 years of
age, 40.3 percent were part-time workers. Table 7 shows how to use the appropriate
parameters from Table 8 and Formulas (3) and (4) to estimate the standard error and
confidence interval.
Table 7. Illustration of Standard Errors of Estimated Differences
Difference
Men (x1)
Women (x2)

Percentage working part-time (p)
Base (y)
b-parameter (b)
Standard error
90-percent confidence interval

28.0
6,720,000
2,947
0.94
26.5 to 29.5

40.3
6,505,000
2,788
1.02
38.6 to 42.0

Source: U.S. Census Bureau, Current Population Survey, School Enrollment, October 2020.

The standard error of the difference is calculated as

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12.3
1.39
10.0 to 14.6

𝑠𝑠𝑥𝑥1 −𝑥𝑥2 = �0.942 + 1.022 = 1.39

and the 90-percent confidence interval around the difference is calculated as 12.3 ± 1.645 ×
1.39. Since this interval does not include zero, we can conclude with 90-percent confidence
that the percentage of part-time women workers between 20-24 years of age is greater
than the percentage of part-time men workers between 20-24 years of age.
Standard Errors of Quarterly or Yearly Averages. For information on calculating
standard errors for labor force data from the CPS which involve quarterly or yearly
averages, please see Bureau of Labor Statistics (2006).

Year-to-Year Factors.
In past years, the Census Bureau published a table of year factors for the School Enrollment
Supplement in the Source and Accuracy Statement. User demand for these factors has
diminished with the introduction of replicate weights. Data users producing estimates
from prior years should consult the Source and Accuracy Statements covering the years of
their analysis to estimate standard errors.
Technical Assistance. If you require assistance or additional information, please contact
the Demographic Statistical Methods Division via e-mail at
dsmd.source.and.accuracy@census.gov.

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Table 8. Parameters for Computation of Standard Errors for Labor Force
Characteristics: October 2020

Characteristic

Total or White
Civilian labor force, employed
Unemployed
Not in labor force
Civilian labor force, employed, not in labor force, and unemployed
Men
Women
Both sexes, 16 to 19 years

Black
Civilian labor force, employed, not in labor force, and unemployed
Total
Men
Women
Both sexes, 16 to 19 years
Asian, American Indian and Alaska Native (AIAN), Native
Hawaiian and Other Pacific Islander (NHOPI)
Civilian labor force, employed, not in labor force, and unemployed
Total
Men
Women
Both sexes, 16 to 19 years
Hispanic, may be of any race
Civilian labor force, employed, not in labor force, and unemployed
Total
Men
Women
Both sexes, 16 to 19 years

a

b

-0.000013
-0.000017
-0.000013

2,481
3,244
2,432

-0.000031
-0.000028
-0.000261

2,947
2,788
3,244

-0.000117
-0.000249
-0.000191
-0.001425

3,601
3,465
3,191
3,601

-0.000245
-0.000537
-0.000399
-0.004078

3,311
3,397
2,874
3,311

-0.000087
-0.000172
-0.000158
-0.000909

3,316
3,276
3,001
3,316

Source: U.S. Census Bureau, Internal Current Population Survey data files for the 2010 Design.
Notes: These parameters are to be applied to basic CPS monthly labor force estimates. The Total or White,
Black, and Asian, AIAN, NHOPI parameters are to be used for both alone and in combination race
group estimates. For nonmetropolitan characteristics, multiply the a- and b-parameters by 1.5. If the
characteristic of interest is total state population, not subtotaled by race or ethnicity, the a- and bparameters are zero. For foreign-born and noncitizen characteristics for Total and White, the a- and
b-parameters should be multiplied by 1.3. No adjustment is necessary for foreign-born and
noncitizen characteristics for Black, Hispanic, and Asian, AIAN, NHOPI parameters. For the groups

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self-classified as having two or more races, use the Asian, AIAN, NHOPI parameters for all
employment characteristics.

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Table 9. Parameters for Computation of Standard Errors for School Enrollment
Characteristics: October 2020
b

Characteristics

Total

White

Black

HispanicB

PEOPLE
Total
Male
Female

Asian, AIAN,
NHOPIA

3,995
2,732
2,684

3,638
2,591
2,930

4,278
2,707
3,051

5,260
3,468
3,629

5,495
4,065
3,601

Level of enrollment below college
(ages 3 to 24)
Total enrolled
Nursery School
Kindergarten
Elementary School
High School

3,615
4,144
3,615
3,615
3,615

3,615
4,142
3,615
4,142
3,615

4,459
4,459
3,919
4,459
3,919

4,631
3,953
3,953
6,093
3,505

4,644
4,644
4,644
4,644
4,644

6,973
4,707

5,844
4,165

6,934
5,061

7,077
4,862

7,435
5,657

6,367

6,519

6,706

4,786

5,352

5,487

Age
3 to 5
6 to 14
15 to 24
25 and over

Marital status, household and family
characteristics
Some household members
All household members

4,256
3,674
4,256
3,674

4,216
3,483
4,216
3,483

FAMILIES, HOUSEHOLDS, OR UNRELATED INDIVIDUALS
Income, earnings
6,618
5,580
Marital status, household, and family
characteristics, educational attainment,
population by age/sex

5,045

4,516

4,044
4,044
4,456
4,044

4,401
6,024
4,401
6,024

4,334
4,334
4,334
5,220

Source: U.S. Census Bureau, Current Population Survey, Internal data from the School Enrollment, October 2020.
A AIAN is American Indian and Alaska Native, and NHOPI is Native Hawaiian and Other Pacific Islander.
B Hispanics may be any race.
Notes: These parameters are to be applied to the School Enrollment data. The Total or White, Black, and Asian, AIAN,
NHOPI parameters are to be used for both alone and in combination race group estimates. For nonmetropolitan
characteristics, multiply the a- and b-parameters by 1.5. If the characteristic of interest is total state population,
not subtotaled by race or ethnicity, the a- and b-parameters are zero. For foreign-born and noncitizen
characteristics for Total and White, the a- and b-parameters should be multiplied by 1.3. No adjustment is
necessary for foreign-born and noncitizen characteristics for Black, Asian, AIAN, NHOPI, and Hispanic parameters.

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For the group self-classified as having two or more races, use the Asian, AIAN, NHOPI parameters for all
characteristics except employment, unemployment, and educational attainment, in which case use Black
parameters. For a more detailed discussion on the use of parameters for race and ethnicity, please see the
“Generalized Variance Parameters” section.

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REFERENCES
Brooks, C.A., & Bailar, B.A. (1978). Statistical Policy Working Paper 3 - An Error Profile:
Employment as Measured by the Current Population Survey. Subcommittee on
Nonsampling Errors, Federal Committee on Statistical Methodology, U.S.
Department of Commerce, Washington, DC.
https://s3.amazonaws.com/sitesusa/wpcontent/uploads/sites/242/2014/04/spwp3.pdf
Bureau of Labor Statistics. (2006). Household Data (“A” tables, monthly; “D” tables,
quarterly). https://www.bls.gov/cps/eetech_methods.pdf

Bureau of Labor Statistics. (2014). Redesign of the Sample for the Current Population
Survey. http://www.bls.gov/cps/sample_redesign_2014.pdf

U.S. Census Bureau. (2009). Estimating ASEC Variances with Replicate Weights Part I:
Instructions for Using the ASEC Public Use Replicate Weight File to Create ASEC
Variance Estimates.
http://usa.ipums.org/usa/resources/repwt/Use_of_the_Public_Use_Replicate_Weig
ht_File_final_PR.doc
U.S. Census Bureau. (2019). Current Population Survey: Design and Methodology.
Technical Paper 77. Washington, DC: Government Printing Office.
https://www2.census.gov/programs-surveys/cps/methodology/CPS-Tech-Paper-77.pdf
All online references accessed June 2, 2021.

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