Att E - Source and Accuracy

Attachment 16
Source of the Data and Accuracy of the Estimates for the November 2022
Current Population Survey Microdata File on Voting and Registration
Table of Contents
SOURCE OF THE DATA ..........................................................................................................................1
Basic CPS .................................................................................................................................................... 1
November 2022 Supplement ............................................................................................................. 2
Estimation Procedure ........................................................................................................................... 2

ACCURACY OF THE ESTIMATES .........................................................................................................3
Sampling Error......................................................................................................................................... 3
Nonsampling Error ................................................................................................................................ 3
Nonresponse ............................................................................................................................................. 4
Undercoverage ......................................................................................................................................... 5
Comparability of Data ........................................................................................................................... 5
A Nonsampling Error Warning.......................................................................................................... 7
Standard Errors and Their Use.......................................................................................................... 7
Estimating Standard Errors ................................................................................................................ 7
Generalized Variance Parameters .................................................................................................... 8
Standard Errors of Estimated Numbers ........................................................................................ 9
Standard Errors of Estimated Percentages ................................................................................10
Standard Errors of Estimated Differences ..................................................................................11
Accuracy of State Estimates ..............................................................................................................12
Standard Errors of State, Division, and Region Estimates ....................................................12
Standard Errors of Quarterly or Yearly Averages ....................................................................13
Technical Assistance............................................................................................................................13

REFERENCES.......................................................................................................................................... 19

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

Current Population Survey Coverage Ratios: November 2022......................................... 5
Estimation Groups of Interest and Generalized Variance Parameters ........................ 9
Illustration of Standard Errors of Estimated Numbers ....................................................10
Illustration of Standard Errors of Estimated Percentages ..............................................11
Illustration of Standard Errors of Estimated Differences ................................................12
Illustration of Standard Errors of State Estimates .............................................................13
Parameters for Computation of Standard Errors for Labor Force
Characteristics: November 2022 ..............................................................................................14
Table 8. Parameters for Computation of Standard Errors for Voting and Registration
Characteristics: November 2022 ...............................................................................................15
Table 9. Parameters for Computation of State Standard Errors for Voting and
Registration Characteristics of Total Population: November 2022.............................16
Table 10. Parameters for Computation of Division Standard Errors for Voting and
Registration Characteristics of Total Population: November 2022.............................18
Table 11. Parameters for Computation of Region Standard Errors for Voting and
Registration Characteristics of Total Population: November 2022.............................18

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Source of the Data and Accuracy of the Estimates for the
November 2022 Current Population Survey Microdata File on Voting and
Registration
SOURCE OF THE DATA
The data in this microdata file are from the November 2022 Current Population Survey
(CPS). The U.S. Census Bureau conducts the CPS every month, although this file has only
November data. The November 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 Social, Economic, and Housing Statistics
Division of the Census Bureau sponsors the supplemental questions for November.
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 reference 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 68,500 sampled addresses were selected from the sampling frame in
November. Based on eligibility criteria, eight 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 42,000 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. 4
November 2022 Supplement. In November 2022, in addition to the basic CPS questions,
interviewers asked supplementary questions of all persons 18 years of age and older on
voting and registration.

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 5 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

3
4

5

For further information on CATI and CAPI and the eligibility criteria, please reference U.S. Census Bureau
(2019).
Counts and estimates throughout this source and accuracy statement are rounded according to Disclosure
Review Board rounding rules.
For additional information on population controls, including details on the demographic characteristics
used and net international components, please refer to Chapters 1-3 and Appendix: History of the
Current Population Survey of U.S. Census Bureau (2019).

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accounting formula whereby the population from the 2020 Census data 6 is updated using
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:
6

In recent decades, the decennial census has usually provided all the data necessary to produce the
population base used in the population controls. However, changes in disclosure avoidance practices and
delays in the 2020 Census necessitated changes to the data sources that produce the base population for
the Vintage 2021 population estimates. The updated population controls use a Blended Base that draws
on the 2020 Census, 2020 Demographic Analysis Estimates, and Vintage 2020 Postcensal Population
Estimates. More information on this methodology can be found at U.S. Census Bureau (2021).

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•
•
•
•
•

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.
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 November 2022 basic CPS, the
household-level unweighted nonresponse rate was 28.7 percent. The person-level
unweighted nonresponse rate for the Voting and Registration supplement was an
additional 8.0 percent. Since the basic CPS nonresponse rate is a household-level rate and
the Voting and Registration 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 Voting
and Registration supplement.
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.

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
Voting and Registration supplement, the unweighted item refusal rates range from 0.1
percent to 4.7 percent. The unweighted item nonresponse rates range from 0.5 percent to
17.7 percent.
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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 November 2022 is
estimated to be about nine 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 November 2022 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: November 2022
Total

White alone

Black alone

Residual raceA

HispanicB

Age
All
Male Female Male Female Male Female Male Female Male Female
group people
0-15 0.85
0.85
0.85
0.90
0.90
0.68
0.69
0.80
0.82
0.83
0.84
16-19 0.81
0.83
0.80
0.85
0.85
0.71
0.65
0.83
0.73
0.83
0.88
20-24 0.79
0.82
0.76
0.85
0.78
0.68
0.66
0.78
0.76
0.82
0.82
25-34 0.83
0.82
0.83
0.88
0.87
0.60
0.66
0.76
0.79
0.84
0.88
35-44 0.88
0.86
0.91
0.90
0.93
0.71
0.79
0.75
0.93
0.82
0.95
45-54 0.90
0.88
0.92
0.90
0.94
0.74
0.80
0.89
0.90
0.80
0.88
55-64 0.93
0.91
0.95
0.91
0.97
0.86
0.83
0.91
0.99
0.87
0.90
65+
1.05
1.03
1.06
1.04
1.08
1.03
1.04
0.91
0.91
0.93
0.93
15+
0.91
0.89
0.92
0.92
0.95
0.76
0.79
0.83
0.87
0.84
0.89
0+
0.90
0.88
0.91
0.92
0.94
0.74
0.77
0.82
0.86
0.84
0.88
Source: U.S. Census Bureau, Current Population Survey, November 2022.
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 refer to 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. 7 These differences are examples of nonsampling variability not
7

Survey processes include, but are not limited to, question wording, universe, sampling frame, interview
modes, and weighting.

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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 2020 Census-based controls 8, with microdata files which reflect 2010 Censusbased 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. The discussion following includes 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 2020 Census-based controls results in
about a 0.7 percent increase from the 2010 Census-based controls in the civilian
noninstitutionalized population. 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 (refer to “Basic CPS”). 9 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
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.

8

9

In recent decades, the decennial census has usually provided all the data necessary to produce the
population base used in the population controls. However, changes in disclosure avoidance practices and
delays in the 2020 Census necessitated changes to the data sources that produce the base population for
the Vintage 2021 population estimates. The updated population controls use a Blended Base that draws
on the 2020 Census, 2020 Demographic Analysis Estimates, and Vintage 2020 Postcensal Population
Estimates. More information on this methodology can be found at .
The phase-in process using the 2010 Census files began April 2014.

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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.

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 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
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average over all possible samples of the differences between the sample estimates and the
true value.

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.
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 generalized variance
function (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 through 6 provide illustrations for calculating standard errors;
Table 7 provides the GVF parameters for labor force estimates;
Table 8 provides the GVF parameters for voting and registration characteristics
from the November 2022 supplement; and
Tables 9 through 11 provide GVF parameters for voting and registration
characteristics for Total by U.S. states, divisions, and regions.

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.

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Table 2. Estimation Groups of Interest and Generalized Variance Parameters
Race/ethnicity group of interest

Generalized variance parameters to
use in standard error calculations

Total populationA

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

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

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

Total

White
Black

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

Asian, AIAN, NHOPI

Source: U.S. Census Bureau, Current Population Survey, internal data files.
A
For standard error calculations using parameters from the CPS GVF table (Table 7), ‘Total or White’
should be used.
B
Hispanics may be any race.
C
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 7). If the estimate is
using Voting and Registration supplement data, the GVF parameters will come from the
Voting and Registration supplement GVF tables (Tables 8 through 11).
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 7 through Table
11 associated with the particular type of characteristic.

Illustration 1
Suppose there were 2,986,000 unemployed men (ages 16 and up) in the civilian labor
force. Table 3 shows how to use the appropriate parameters from Table 7 and Formula (1)
to estimate the standard error and confidence interval.
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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

Source: U.S. Census Bureau, Current Population Survey, November 2022.

2,986,000
-0.000031
2,947
92,000
2,835,000 to 3,137,000

The standard error is calculated as

𝑠𝑠𝑥𝑥 = �−0.000031 × 2,986,0002 + 2,947 × 2,986,000,

which, rounded to the nearest thousand, is 92,000. The 90-percent confidence interval is
calculated as 2,986,000 ± 1.645 × 92,000.
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 7 through Table 11 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 = �𝑦𝑦 𝑝𝑝(100 − 𝑝𝑝)

(2)

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 7 through Table 11 associated with the characteristic in the
numerator of the percentage.
Illustration 2
In November 2022, out of 254,700,000 people with at least an elementary school
education, 47.8 percent reported voting. Table 4 shows how to use the appropriate
parameter from Table 8 and Formula (2) to estimate the standard error and confidence
interval.
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Table 4. Illustration of Standard Errors of Estimated Percentages
Percentage of people with at least elementary education
that reported voting (p)
Base (y)
b-parameter (b)
Standard error
90-percent confidence interval

47.8

254,700,000
5,949
0.24
47.4 to 48.2

Source: U.S. Census Bureau, Current Population Survey, Voting and Registration, November 2022.

The standard error is calculated as
𝑠𝑠𝑦𝑦,𝑝𝑝 = �

5,949
× 47.8 × (100.0 − 47.8) = 0.24
254,700,000

and the 90-percent confidence interval for the estimated percentage of people with at least
an elementary school education who reported voting is from 47.4 to 48.2 percent (i.e., 47.8
± 1.645 × 0.24).

Standard Errors of Estimated Differences. The standard error of the difference between
two sample estimates is approximately equal to
2

𝑠𝑠|𝑥𝑥1−𝑥𝑥2| = ��𝑠𝑠𝑥𝑥1 � + �𝑠𝑠𝑥𝑥2 �

2

(3)

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 3
The November 2022 supplement showed that out of 124,000,000 men who had at least an
elementary school education, 57,940,000, or 46.7 percent, had voted, and of the
130,700,000 women who had at least an elementary school education, 63,910,000, or 48.9
percent, had voted. Table 5 shows how to use the appropriate parameters from Table 8 and
Formulas (2) and (3) to estimate the standard error and confidence interval.

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Table 5. Illustration of Standard Errors of Estimated Differences
Difference
Men (x1)
Women (x2)

Percentage with at least elementary
education that voted (p)
Base (y)
b-parameter (b)
Standard error
90-percent confidence interval

46.7

124,000,000
5,949
0.35
46.1 to 47.3

48.9

130,700,000
5,949
0.34
48.3 to 49.5

2.2

0.49
1.4 to 3.0

Source: U.S. Census Bureau, Current Population Survey, Voting and Registration, November 2022.

The standard error of the difference is calculated as

𝑠𝑠𝑥𝑥1−𝑥𝑥2 = �0.352 + 0.342 = 0.49

and the 90-percent confidence interval around the difference is calculated as 2.2 ± 1.645 ×
0.49. Since this interval does not include zero, we can conclude with 90-percent confidence
that the percentage of women with at least an elementary school education who voted is
greater than the percentage of men with at least an elementary school education who
voted.
Accuracy of State Estimates. The redesign of the CPS following the 1980 census provided
an opportunity to increase efficiency and accuracy of state data. All strata are now defined
within state boundaries. The sample is allocated among the states to produce state and
national estimates with the required accuracy while keeping total sample size to a
minimum.

Since the CPS is designed to produce both state and national estimates, the proportion of
the total population sampled and the sampling rates differ among the states. In general, the
smaller the population of the state, the larger the sampling proportion. For example, in
Vermont, approximately 1 in every 250 households is selected each month. In New York,
the sample is about 1 in every 2,000 households. Nevertheless, the size of the sample in
New York is four times larger than in Vermont because New York has a larger population.
Standard Errors of State, Division, and Region Estimates. Standard errors for state,
division, and region estimates may be obtained by using the state, division, and region
parameters. The state, division, and region parameters for Total population voting and
registration estimates are included in Tables 9, 10, and 11.

Illustration 4
In November 2022, about 6,068,000 people (39.8 percent) had completed at least a
bachelor’s degree out of about 15,240,000 people aged 18 and over living in New York
state. Table 6 shows how to use Formula (2) and the appropriate parameter from Table 9
to estimate the standard error and confidence interval.
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Table 6. Illustration of Standard Errors of State Estimates

Percentage of people in New York that
completed at least a bachelor’s degree (p)
Base (y)
New York State b parameter (bstate)
Standard error
90-percent confidence interval

39.8

15,240,000
8,490
1.16
37.9 to 41.7

Source: U.S. Census Bureau, Current Population Survey, Voting and Registration, November 2022.

The standard error of the estimate of the percentage of people living in New York that
completed at least a bachelor’s degree can be found by using Formula (2) and the statelevel b-parameter, 8,490. The standard error is calculated as
𝑠𝑠𝑦𝑦,𝑝𝑝 = �

8,490
× 39.8 × (100.0 − 39.8) = 1.16
15,240,000

And the 90-percent confidence interval is calculated as 39.8 ± 1.645 × 1.16.

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 reference Bureau of Labor Statistics (2006).

Technical Assistance. If you require assistance or additional information, please contact
the Demographic Statistical Methods Division via e-mail at
[email protected].

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Table 7. Parameters for Computation of Standard Errors for Labor Force
Characteristics: November 2022

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

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Table 8. Parameters for Computation of Standard Errors for Voting and Registration Characteristics: November 2022
Characteristics

a

Total

White

b

a

5,949

-0.000026

Black

b

a

5,949

-0.000097

b

Asian, AIAN, NHOPIA

HispanicB

a

b

a

b

5,949

-0.000222

5,949

-0.000128

5,949

5,762

-0.000124

5,762

Voting, registration, reasons for not
voting or registering (includes
breakdowns by:
Citizenship, Household relationship,
Family householder by presence of
children, Marital status, Duration of
residence, Tenure, Education level,
Family income of persons,
Occupation group)

-0.000022

Marital Status

-0.000022

5,762

-0.000025

5,762

-0.000094

5,762

-0.000215

Duration of Residence

-0.000022

5,762

-0.000025

5,762

-0.000094

5,762

-0.000215

CHARACTERISTICS OF ALL PERSONS, VOTING AND NONVOTING
Education of Persons

Persons by Family Income

-0.000022
-0.000022

5,762
5,762

HOUSEHOLD RELATIONSHIPS, VOTING AND NONVOTING

-0.000025
-0.000025

5,762
5,762

-0.000094
-0.000094

5,762
5,762

-0.000215
-0.000215

5,762
5,762
5,762

-0.000124
-0.000124
-0.000124

5,762
5,762
5,762

Householder, Spouse of householder
-0.000020
5,305
-0.000023
5,305 -0.000087
5,305 -0.000198
5,305
-0.000114
5,305
Nonrelative or Other Relative of
-0.000020
5,305
-0.000023
5,305 -0.000087
5,305 -0.000198
5,305
-0.000114
5,305
Householder
Source: U.S. Census Bureau, Current Population Survey, Internal data from the Voting and Registration Supplement, November 2022.
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 Voting and Registration Supplement data. The 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 foreignborn 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. 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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Table 9. Parameters for Computation of State Standard Errors for Voting and
Registration Characteristics of Total Population: November 2022
State
Alabama
Alaska
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
District of Columbia
Florida
Georgia
Hawaii
Idaho
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Mississippi
Missouri
Montana
Nebraska
Nevada
New Hampshire
New Jersey
New Mexico
New York
North Carolina

a

b

-0.001086
-0.001590
-0.001261
-0.001229
-0.000256
-0.001542
-0.001855
-0.002253
-0.001185
-0.000431
-0.001216
-0.001440
-0.001260
-0.000827
-0.001352
-0.001635
-0.001821
-0.002192
-0.001035
-0.001896
-0.001629
-0.000992
-0.000909
-0.001490
-0.001018
-0.001391
-0.001213
-0.001903
-0.001492
-0.001599
-0.001218
-0.001548
-0.000540
-0.000888

4,363
874
7,471
2,937
7,912
7,243
5,475
1,858
620
7,780
10,380
1,602
1,941
8,258
7,263
4,135
4,137
7,809
3,698
2,198
7,965
5,674
7,363
6,741
2,332
6,816
1,105
2,899
3,795
1,875
9,037
2,600
8,490
7,544

Source: U.S. Census Bureau, Current Population Survey, Internal data from the Voting and Registration
Supplement, November 2022.
Notes: These parameters are for use with state-level voting and registration estimates for the Total
population. Total state b-parameters were calculated by modeling all races, however a-parameters
were calculated using the total population controls.

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Table 9, cont. Parameters for Computation of State Standard Errors for Voting and
Registration Characteristics of Total Population: November 2022
State
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania
Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming

a

b

-0.001346
-0.000817
-0.001358
-0.001218
-0.000764
-0.002229
-0.001134
-0.001730
-0.001075
-0.000373
-0.001331
-0.001360
-0.001204
-0.001156
-0.001302
-0.001539
-0.001365

798
7,655
4,222
4,244
7,991
2,014
4,783
1,207
6,034
8,573
3,418
742
8,234
7,187
1,881
7,312
627

Source: U.S. Census Bureau, Current Population Survey, Internal data from the Voting and Registration
Supplement, November 2022.
Notes: These parameters are for use with state-level voting and registration estimates for the Total
population. Total state b-parameters were calculated by modeling all races, however a-parameters
were calculated using the total population controls.

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Table 10. Parameters for Computation of Division Standard Errors for Voting and
Registration Characteristics of Total Population: November 2022
Division
New England
Middle Atlantic
East North Central
West North Central
South Atlantic
East South Central
West South Central
Mountain
Pacific

a

b

-0.000369
-0.000247
-0.000198
-0.000310
-0.000142
-0.000355
-0.000231
-0.000255
-0.000169

4,597
8,313
7,435
5,275
7,659
5,503
7,418
5,177
7,158

Source: U.S. Census Bureau, Current Population Survey, Internal data from the Voting and Registration
Supplement, November 2022.
Notes: These parameters are for use with census division-level voting and registration estimates for the
Total population. Total division b-parameters were calculated by modeling all races, however aparameters were calculated using the total population controls.

Table 11. Parameters for Computation of Region Standard Errors for Voting and
Registration Characteristics of Total Population: November 2022
Region

a

b

Northeast
Midwest
South
West

-0.000156
-0.000119
-0.000069
-0.000104

7,182
6,504
6,968
6,512

All Except South

-0.000038

6,260

Source: U.S. Census Bureau, Current Population Survey, Internal data from the Voting and Registration
Supplement, November 2022.
Notes: These parameters are for use with census region-level voting and registration estimates for the Total
population. Total region b-parameters were calculated by modeling all races, however a-parameters
were calculated using the total population controls.

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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. (2012). Estimating Current Population Survey (CPS) Person Level
Supplement Variances Using Replicate Weights Part I: Instructions for Using CPS
Person Level Supplement Replicate Weights to Calculate Variances.
https://www2.census.gov/programs-surveys/cps/datasets/2018/supp/PERSONlevel_Use_of_the_Public_Use_Replicate_Weight_File.doc
U.S. Census Bureau. (2018). Estimating Current Population Survey (CPS) Household-level
Supplement Variances Using Replicate Weights Part I: Instructions for Using CPS
Household-level Supplement Replicate Weights to Calculate Variances.
https://www2.census.gov/programs-surveys/cps/datasets/2018/supp/HHlevel_Use_of_the_Public_Use_Replicate_Weight_File.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-Paper77.pdf
U.S. Census Bureau. (2021). METHODOLOGY FOR THE UNITED STATES POPULATION
ESTIMATES: VINTAGE 2021 Nation, States, Counties, and Puerto Rico – April 1, 2020
to July 1, 2021. https://www2.census.gov/programs-surveys/popest/technicaldocumentation/methodology/2020-2021/methods-statement-v2021.pdf
All online references accessed 4/3/2023.

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