2018 Source and Accuracy Statement

Source of the Data and Accuracy of the Estimates for the
June 2018 Current Population Survey Microdata File on Fertility and
Birth Expectation
Table of Contents
SOURCE OF THE DATA ..........................................................................................................................1
Basic CPS .................................................................................................................................................... 1
June 2018 Supplement ......................................................................................................................... 2
Estimation Procedure ........................................................................................................................... 2

ACCURACY OF THE ESTIMATES .........................................................................................................3
Sampling Error......................................................................................................................................... 3
Nonsampling Error ................................................................................................................................ 3
Nonresponse ............................................................................................................................................. 3
Sufficient Partial Interview ................................................................................................................. 4
Coverage ..................................................................................................................................................... 4
Comparability of Data ........................................................................................................................... 5
A Nonsampling Error Warning.......................................................................................................... 6
Standard Errors and Their Use.......................................................................................................... 6
Estimating Standard Errors ................................................................................................................ 7
Generalized Variance Parameters .................................................................................................... 7
Standard Errors of Estimated Numbers ........................................................................................ 9
Standard Errors of Estimated Percentages .................................................................................. 9
Standard Errors of Estimated Differences ..................................................................................10
Standard Errors of Ratios ..................................................................................................................11
Standard Errors of Fertility Ratios.................................................................................................12
Standard Errors of Quarterly or Yearly Averages ....................................................................13
Accuracy of State Estimates ..............................................................................................................13
Standard Errors of State Estimates................................................................................................13
Standard Errors of Regional Estimates ........................................................................................14
Standard Errors of Groups of States ..............................................................................................15
Technical Assistance............................................................................................................................16

REFERENCES.......................................................................................................................................... 22

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

Current Population Survey Coverage Ratios: June 2018 ..................................................... 5
Estimation Groups of Interest and Generalized Variance Parameters ......................... 8
Illustration of Standard Errors of Estimated Numbers........................................................ 9
Illustration of Standard Errors of Estimated Percentages ................................................10
Illustration of Standard Errors of Estimated Differences .................................................11
Illustration of Standard Errors of Ratios .................................................................................12

2
Table 7. Illustration of Standard Errors of Fertility Ratios ................................................................13
Table 8. Illustration of Standard Errors of Regional Estimates .......................................................15
Table 9. Parameters for Computation of Standard Errors for Labor Force Characteristics:
June 2018 .............................................................................................................................................17
Table 10. Parameters for Computation of Standard Errors for
Fertility and Birth Expectation Characteristics: June 2018 ..........................................18
Table 11. Parameters for Computation of Standard Errors for Fertility Ratios:
June 2018 ..........................................................................................................................................19
Table 12. Factors and Populations for State Parameters and Standard Errors: June 2018..20
Table 13. Factors and Populations for Census Region Parameters and Standard Errors:
June 2018 ..........................................................................................................................................21

Source of the Data and Accuracy of the Estimates for the
June 2018 Current Population Survey Microdata File on Fertility and
Birth Expectation
SOURCE OF THE DATA
The data in this microdata file are from the June 2018 Current Population Survey (CPS).
The U.S. Census Bureau conducts the CPS every month, although this file has only June data.
The June 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 U.S. Bureau of Labor Statistics
also jointly sponsor the supplemental questions for June.
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 population universe, is composed primarily of the
population in correctional institutions and nursing homes (98 percent of the 4.0 million
institutionalized people in Census 2010). Starting August 2017, college and university
dormitories were also excluded from the population universe because the majority of the
residents had usual residences elsewhere. Interviewers ask questions concerning labor
force participation about each member 15 years old and over 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.
Approximately 71,000 housing units were selected for sample from the sampling frame in
June. Based on eligibility criteria, nine percent of these housing units were sent directly to
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.

2
computer-assisted telephone interviewing (CATI). The remaining units were assigned to
interviewers for computer-assisted personal interviewing (CAPI). 3 Of all housing units in
sample, about 60,000 were determined to be eligible for interview. Interviewers obtained
interviews at about 51,000 of these units. Noninterviews occur when the occupants are not
found at home after repeated calls or are unavailable for some other reason.
June 2018 Supplement. In June 2018, in addition to the basic CPS questions, interviewers
asked supplementary questions of women 15 to 44 years of age on fertility.
Estimation Procedure. This survey’s estimation procedure adjusts weighted sample
results to agree with independently derived population estimates of the civilian
noninstitutionalized population of the United States and each state (including the District
of Columbia). These population estimates, used as controls for the CPS, are prepared
monthly to agree with the most current set of population estimates that are released as
part of the Census Bureau’s population estimates and projections 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), and 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
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
estimates.
The net international migration component of the population estimates 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 the survey date, it is
necessary to make short-term projections of these components to develop the estimate for
the survey date.

3

For further information on CATI and CAPI and the eligibility criteria, please see U.S. Census Bureau
(2006).

3
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, they 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. For example, errors could
occur because:
•
•
•
•
•

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 (measurement error).
Some individuals who should have been included in the survey frame were
missed (coverage error).
Responses are not collected from all those in the sample or the respondent is
unwilling to provide information (nonresponse error).
Values are estimated imprecisely for missing data (imputation error).
Forms may be lost, data may be incorrectly keyed, coded, or recoded, etc.
(processing error).

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 June 2018 basic CPS, the householdlevel nonresponse rate was 15.7 percent. The person-level nonresponse rate for the
Fertility supplement was an additional 8.6 percent.

4
Since the basic CPS nonresponse rate is a household-level rate and the Fertility supplement
nonresponse rate is a person-level rate, we cannot combine these rates to derive an overall
nonresponse rate. Nonresponding households may have fewer persons than interviewed
ones, so combining these rates may lead to an overestimate of the true overall nonresponse
rate for persons for the Fertility supplement.
Sufficient Partial Interview. 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 be answered in order to be considered a sufficient partial interview.
As part of the nonsampling error analysis, the item response rates, item refusal rates, and
edits are reviewed. For the Fertility supplement, the item refusal rates range from 1.4
percent to 4.6 percent. This survey is fully allocated. The item nonresponse rates range
from 18.1 percent to 27.9 percent.
Coverage. The concept of coverage in the survey sampling process is 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 June 2018 is estimated to be
about 11 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 partially corrects for 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 June 2018 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.

5
Table 1. Current Population Survey Coverage Ratios: June 2018
Total

White only

Black only

Residual raceA

HispanicB

Age
All
Male Female Male Female Male Female Male Female Male Female
group people
0.88
0.87
0.92
0.91
0.71
0.71
0.86
0.80
0.81
0.82
0-15 0.87
0.88
0.84
0.90
0.88
0.77
0.65
0.88
0.89
0.82
0.83
16-19 0.86
0.75
0.75
0.80
0.78
0.59
0.68
0.68
0.69
0.69
0.72
20-24 0.75
0.80
0.85
0.84
0.89
0.63
0.73
0.75
0.73
0.70
0.83
25-34 0.82
0.88
0.92
0.90
0.96
0.76
0.78
0.84
0.85
0.79
0.90
35-44 0.90
0.90
0.91
0.94
0.94
0.70
0.77
0.81
0.86
0.80
0.87
45-54 0.90
0.92
0.93
0.94
0.95
0.77
0.86
0.85
0.83
0.84
0.84
55-64 0.93
0.97
0.97
0.97
0.98
0.99
1.00
0.90
0.82
0.83
0.85
0.90
65+
0.89
0.88
0.90
0.91
0.93
0.74
0.78
0.80
0.81
0.78
0.85
15+
0.89
0.88
0.89
0.91
0.93
0.73
0.77
0.82
0.81
0.79
0.84
0+
Source: U.S. Census Bureau, Current Population Survey, June 2018.
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 results from differences in interviewer training and experience and in
differing survey processes. This is an example 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 from January 2003 through
December 2011, 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 controls 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.

6
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 Census
2010 files (see “Basic CPS”). 4 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 published 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.
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 (2006) and Brooks & Bailar (1978).

Standard Errors and Their Use. The 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 specified confidence that the interval includes
the average estimate calculated from all possible samples.
4

The phase-in process using the 2010 Census files began April 2014.

7
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 average over all possible samples of the differences between the sample estimates
and the true value.
Generalized Variance Parameters. While it is possible to compute and present an
estimate of 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 8 provide illustrations for
calculating standard errors. Table 9 provides the GVF parameters for labor force estimates,
and Tables 10 and 11 provides GVF parameters for characteristics from the June 2018

8
supplement. Tables 12 and 13 provide factors and population controls to derive state and
regional parameters.

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. The following table 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
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
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

Generalized variance parameters to
use in standard error calculations
Total or White
Total or 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
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 9). If the estimate is
using Fertility supplement data, the GVF parameters will come from the Fertility
supplement GVF table (Table 10).

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

Here x is the size of the estimate, and a and b are the parameters in Table 9 or 10
associated with the particular type of characteristic.

(1)

Illustration 1
Suppose there were 2,210,000 unemployed women of ages 15 to 44 in the civilian labor
force. Use the appropriate parameters from Table 9 and Formula (1) to get
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

2,210,000

-0.000028
2,788
78,000
2,082,000 to
2,338,000

Source: U.S. Census Bureau, Current Population Survey, Fertility Supplement, June 2018.

The standard error is calculated as

𝑠𝑠𝑥𝑥 = �−0.000028 × 2,210,0002 + 2,788 × 2,210,000,

which, rounded to the nearest thousand, is 78,000. The 90-percent confidence interval is
calculated as 2,210,000 ± 1.645 × 78,000.
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 9 or 10 as indicated by
the numerator.

The approximate standard error, 𝑠𝑠𝑦𝑦,𝑝𝑝 , of an estimated percentage can be obtained by using
the formula:

10
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 9 or 10 associated with the characteristic in the numerator of the
percentage.

Illustration 2
Suppose that 29.0 percent of the 63,890,000 women 15 to 44 years old were married when
the first child was born. Use the appropriate parameter from Table 10 and Formula (2) to
get
Table 4. Illustration of Standard Errors of Estimated Percentages
Percentage of women aged 15-44 who were
married when the first child was born (p)
Base (y)
b-parameter (b)
Standard error
90-percent confidence interval

29.0

63,890,000
5,564
0.42
28.3 to 29.7

Source: U.S. Census Bureau, Current Population Survey, Fertility Supplement, June 2018.

The standard error is calculated as
𝑠𝑠𝑦𝑦,𝑝𝑝 = �

5,564
× 29.0 × (100.0 − 29.0) = 0.42
63,890,000

The 90-percent confidence interval for the estimated percentage of women aged 15 to 44
who were married when the first child was born is from 28.3 to 29.7 percent (i.e., 29.0 ±
1.645 × 0.42).

Standard Errors of Estimated Differences. The standard error of the difference between
two sample estimates is approximately equal to
𝑠𝑠𝑥𝑥1 −𝑥𝑥2 = �𝑠𝑠𝑥𝑥1 2 + 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.

11
Illustration 3
Suppose that of the 6,592,000 women in 2018 between 20-29 years of age who were ever
married, 68.0 percent were in the labor force, and of the 6,597,000 women in 2016
between 20-29 years of age who were ever married, 66.0 percent were in the labor force.
Use the appropriate parameters from Table 9 and Formulas (2) and (3) to get
Table 5. Illustration of Standard Errors of Estimated Differences
Difference
2018 (x1)
2016 (x2)

Percentage women aged 20-29 ever
married in the labor force (p)
Base (y)
b-parameter (b)
Standard error
90-percent confidence
interval

68.0

6,592,000
2,788
0.96

66.4 to 69.6

66.0

6,597,000
2,788
0.97

64.4 to 67.6

Source: U.S. Census Bureau, Current Population Survey, Fertility Supplement, June 2018.

2.0

1.36

-0.2 to 4.2

The standard error of the difference is calculated as

𝑠𝑠𝑥𝑥1 −𝑥𝑥2 = �0.962 + 0.972 = 1.36

The 90-percent confidence interval around the difference is calculated as 2.0 ± 1.645 ×
1.36. Since this interval does include zero, we cannot conclude with 90 percent confidence
that the percentage of women in 2018 between 20-29 years of age who were ever married,
in the labor force, is different than the percentage of women in 2016 between 20-29 years
of age who were ever married, in the labor force.
Standard Errors of Ratios. Certain estimates may be calculated as the ratio of two
numbers. The standard error of a ratio, 𝑥𝑥⁄𝑦𝑦, may be computed using
𝑥𝑥

𝑠𝑠

2

𝑠𝑠𝑦𝑦 2

𝑠𝑠𝑥𝑥⁄𝑦𝑦 = 𝑦𝑦 �� 𝑥𝑥𝑥𝑥 � + � 𝑦𝑦 � − 2𝑟𝑟

𝑠𝑠𝑥𝑥 𝑠𝑠𝑦𝑦
𝑥𝑥 𝑦𝑦

(4)

The standard error of the numerator, 𝑠𝑠𝑥𝑥 , and that of the denominator, 𝑠𝑠𝑦𝑦 , may be calculated
using formulas described earlier. In Formula (4), 𝑟𝑟 represents the correlation between the
numerator and the denominator of the estimate.
For one type of ratio, the denominator is a count of families or households and the
numerator is a count of persons in those families or households with a certain
characteristic. If there is at least one person with the characteristic in every family or
household, use 0.7 as an estimate of 𝑟𝑟. An example of this type is the mean number of
children per family with children.

12
For all other types of ratios, 𝑟𝑟 is assumed to be zero. Examples are the average number of
children per family and the family poverty rate. If 𝑟𝑟 is actually positive (negative), then this
procedure will provide an overestimate (underestimate) of the standard error of the ratio.
Note: For estimates expressed as the ratio of x per 100 y or x per 1,000 y, multiply Formula
(4) by 100 or 1,000, respectively, to obtain the standard error.

Illustration 4
Suppose there were 30,539,000 ever-married women 15-44 years old and 33,351,000
never-married women 15-44 years old. The ratio of ever-married women, x, to nevermarried women, y, is 0.92. Use the appropriate parameters from Table 10 and Formulas
(1) and (4) to get
Table 6. Illustration of Standard Errors of Ratios

Women 15-44
a parameter (a)
b parameter (b)
Standard error
90-percent confidence
interval

Ever-married (x)
30,539,000
-0.000021
5,564
388,000
29,901,000 to
31,177,000

Never-married
(y)
33,351,000
-0.000021
5,564
403,000
32,688,000 to
34,014,000

Ratio

0.92
0.016

0.89 to 0.95

Source: U.S. Census Bureau, Current Population Survey, Fertility Supplement, June 2018.

Using Formula (4) with r = 0, the estimate of the standard error is
𝑠𝑠𝑥𝑥⁄𝑦𝑦 =

30,539,000
403,000 2
388,000 2
��
� +�
� = 0.016
33,351,000 30,539,000
33,351,000

The 90-percent confidence interval is calculated as 0.92 ± 1.645 × 0.016.

Standard Errors of Fertility Ratios. The standard error of a fertility ratio is a function of
the number of children ever born per 1,000 women and the number of women in a given
category. The formula for the standard error of a fertility ratio is
𝑏𝑏

𝑐𝑐

𝑠𝑠𝑥𝑥,𝑦𝑦 = 𝑥𝑥�𝑎𝑎 + 𝑥𝑥𝑥𝑥 + 1,000𝑦𝑦

(5)

where a, b, and c are the parameters from Table 11, x is the number of children ever born
or expected per 1,000 women, and y is the number of women in thousands. This formula
should be used when calculating standard errors for estimates involving the possibility of
more than one event per women, i.e., number of children ever born. For data involving at
most one event per woman, convert the ratio to a percentage and use Formula (2) and the
parameters in Table 9 or 10 to calculate the standard errors.

13
Illustration 5
Suppose that 8,411,000 women 40-44 years old had 1,994 children ever born per 1,000
women. Use Formula (5) and the parameters in Table 11 to get
Table 7. Illustration of Standard Errors of Fertility Ratios
Children ever born (x)
Base (y) in Thousands
a parameter (a)
b parameter (b)
c parameter (c)
Standard error
90-percent confidence interval

1,994
8,411
0.0000015
961
1,756
33
1,940 to 2,048

Source: U.S. Census Bureau, Current Population Survey, Fertility Supplement, June 2018.

The standard error is calculated as

961

1,756

𝑆𝑆𝑥𝑥,𝑦𝑦 = 1,994�0.0000015 + 1,994×8,411 + 1,000×8,411 = 33

The 90-percent confidence interval is from 1,940 to 2,048 children ever born per 1,000
women (i.e., 1,994 ± 1.645 × 33). 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 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).

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. Improved accuracy of state data was achieved with about the same sample size
as in the 1970 design.

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 was sampled 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 Estimates. The standard error for a state may be obtained by
determining new state-level a- and b-parameters and then using these adjusted parameters
in the standard error formulas mentioned previously. To determine a new state-level b-

14
parameter (bstate), multiply the b-parameter from Table 9 or 10 by the state factor from
Table 12. To determine a new state-level a-parameter (astate), use the following:
(1)

(2)

If the a-parameter from Table 9 or 10 is positive, multiply it by the state
factor from Table 12.

If the a-parameter in Table 9 or 10 is negative, calculate the new state-level
a-parameter as follows:

a state =

− bstate
POPstate

where POPstate is the state population found in Table 12.

(6)

To determine state-level parameters for the fertility ratio parameters found in Table 11,
multiply all parameters by the state factor from Table 12.
Note:

The Census Bureau recommends the use of 3-year averages to compare estimates
across states and 2-year averages to evaluate changes in state estimates over time.

Standard Errors of Regional Estimates. To compute standard errors for regional
estimates, follow the steps for computing standard errors for state estimates found in
“Standard Errors of State Estimates” using the regional factors found in Table 13.

Illustration 6
Suppose that of 24,317,000 women 15-44 years old in the South, 47.5 percent remain
childless. Use Formula (2) and the appropriate parameter and factor from Tables 10 and
13 to get:
Table 8. Illustration of Standard Errors of Regional Estimates
Percent of childless women in South (p)
Base (x)
b parameter (b)
South regional factor
Regional b parameter (bregion)
Standard error
90-percent confidence interval

47.5
24,317,000
4,364
1.11
4,844
0.70
46.3 to 48.7

Source: U.S. Census Bureau, Current Population Survey, Fertility Supplement, June 2018.

Obtain the region-level b parameter by multiplying the b parameter in Table 10 by the
regional factor in Table 13. This gives bregion = 4,364 × 1.11 = 4,844. The standard error of
the estimate of the percentage of women 15-44 years old in the South who are childless can
then be found by using Formula (2) and the new region-level b parameter. The standard
error is calculated as

15
4,844

𝑠𝑠𝑥𝑥,𝑦𝑦 = �24,317,000 × 47.5(100 − 47.5) = 0.70

and the 90-percent confidence interval for the percentage of women 15-44 years old in the
South who are childless is calculated as 47.5 ± 1.645 × 0.70.

Standard Errors of Groups of States. The standard error calculation for a group of states
is similar to the standard error calculation for a single state. First, calculate a new state
group factor for the group of states. Then, determine new state group a- and b-parameters.
Finally, use these adjusted parameters in the standard error formulas mentioned
previously.
Use the following formula to determine a new state group factor:
n

state group factor =

∑ ( POP × state factor )
i =1

i

i

n

∑ POP

i

i =1

(7)

where POPi and state factori are the population and factor for state i from Table 22. To
obtain a new state group b-parameter (bstate group), multiply the b-parameter from Table 18
or 19 by the state factor obtained by Formula (7). To determine a new state group aparameter (astate group), use the following:
(1)
(2)

If the a-parameter from Table 9 or 10 is positive, multiply it by the state
group factor determined by Formula (7).

If the a-parameter from Table 9 or 10 is negative, calculate the new state
group a parameter as follows:
a state group =

− bstate group
n

∑ POP
i =1

i

(8)

To determine state group-level parameters for the fertility ratio parameters found in Table
11, multiply all parameters by the state group factor calculated by Formula (7).
Illustration 7
Suppose the state group factor for the state group Illinois-Indiana-Michigan was required.
The appropriate factor would be
𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 =

12,580,894 × 1.16 + 6,598,681 × 1.14 + 9,879,776 × 1.15
= 1.15
12,580,894 + 6,598,681 + 9,879,776

16
Technical Assistance. If you require assistance or additional information, please contact
the Demographic Statistical Methods Division via e-mail at
[email protected].

17
Table 9. Parameters for Computation of Standard Errors for Labor Force
Characteristics: June 2018

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.

18
Table 10. Parameters for Computation of Standard Errors for Fertility and Birth
Expectation Characteristics: June 2018
Characteristic
FERTILITY
Total or White
Black
Hispanic
Asian, AIAN, NHOPI and two or more races
NUMBER OF BIRTHS
Total or White
Black
Hispanic
Asian, AIAN, NHOPI and two or more races

Persons

a

b

-0.000037
-0.000137
-0.000252
-0.000305

2,393
2,393
4,032
2,393

(X)
(X)
(X)
(X)

(X)
(X)
(X)
(X)

-0.000068
-0.000250
-0.000459
-0.000554

4,364
4,356
7,343
4,356

(X)
(X)
(X)
(X)

(X)
(X)
(X)
(X)

-0.000008
-0.000034
-0.000069
-0.000078

2,208
1,998
3,366
1,998

MARITAL STATUS, HOUSEHOLD & FAMILY CHARACTERISTICS
Total or White
-0.000021
5,564
Black
-0.000135
7,992
Hispanic
-0.000275
13,469
Asian, AIAN, NHOPI and two or more races
-0.000310
7,992
INCOME
Total or White
Black
Hispanic
Asian, AIAN, NHOPI and two or more races
EDUCATIONAL ATTAINMENT
Total or White
Black and two or more races
Hispanic
Asian, AIAN, NHOPI

NATIVITY – Born in:
Mexico, other N. America, S. America
Europe
Asia, Africa, Oceania
United States

Households, etc.
a
b

-0.000010
-0.000051
-0.000103
-0.000116

2,620
3,000
5,056
3,000

-0.000009
-0.000044
-0.000090
-0.000101

2,393
2,613
4,403
2,613

-0.000010
-0.000048
-0.000067
-0.000111

2,530
2,861
3,258
2,861

-0.000008
-0.000034
-0.000069
-0.000078

2,208
1,998
3,366
1,998

-0.000037
-0.000021
-0.000035
-0.000019

11,801
6,780
11,051
5,932

(X)
(X)
(X)
(X)

(X)
(X)
(X)
(X)

Source: U.S. Census Bureau, Current Population Survey, Internal data from the Fertility Supplement, June 2018.
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 Fertility Supplement 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

19
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. 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.

Table 11. Parameters for Computation of Standard Errors for Fertility Ratios: June 2018
a
0.0000015

b
961

c
1,756

Source: U.S. Census Bureau, Current Population Survey, Internal data from the Fertility Supplement, June
2018.
Note: Multiply the parameters by 1.3 to get foreign-born parameters.

20
Table 12. Factors and Populations for State Parameters and Standard Errors: June
2018
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

Factor
1.13
0.18
1.16
0.73
1.16
1.17
0.88
0.23
0.18
1.12
1.16
0.33
0.40
1.16
1.14
0.78
0.81
1.16
1.06
0.42
1.19
1.13
1.15
1.16
0.71
1.18

Population
4,807,676
710,126
7,010,312
2,963,855
39,226,312
5,582,566
3,538,202
955,498
692,428
20,968,512
10,331,291
1,368,587
1,730,355
12,580,894
6,598,681
3,115,966
2,855,257
4,384,773
4,576,687
1,326,879
5,979,687
6,817,355
9,879,776
5,566,518
2,916,507
6,023,367

State
Montana
Nebraska
Nevada
New Hampshire
New Jersey
New Mexico
New York
North Carolina
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania
Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming

Factor
0.22
0.51
0.72
0.35
1.15
0.44
1.19
1.18
0.18
1.15
1.07
1.06
1.16
0.28
1.12
0.23
1.14
1.17
0.51
0.20
1.19
1.17
0.50
1.16
0.16

Population
1,046,012
1,901,477
3,013,211
1,333,075
8,927,077
2,053,490
19,617,438
10,171,904
737,904
11,512,634
3,858,271
4,155,617
12,619,954
1,045,930
4,986,684
858,971
6,671,545
28,178,952
3,127,383
617,898
8,312,350
7,410,192
1,775,910
5,743,953
564,427

Source: U.S. Census Bureau, Current Population Survey, Internal data from the Fertility Supplement, June
2018.
Notes: These factors are for use with state-level fertility estimates for subpopulation groups. The state population
counts in this table are for the 0+ population. 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 Blacks, Asians, American Indian and Alaska Natives, Native Hawaiian and Other
Pacific Islanders, and Hispanics.

21
Table 13. Factors and Populations for Census Region Parameters and Standard
Errors: June 2018
Region
Northeast
Midwest
South
West

All Except South

Factor
1.08
1.09
1.11
1.03
1.06

Population
67,375,398
55,843,808
122,532,530
76,998,590
200,217,796

Source: U.S. Census Bureau, Current Population Survey, Internal data from the Fertility Supplement, June
2018.
Notes: These factors are for use with census region-level fertility estimates for subpopulation groups. The census
region population counts in this table are for the 0+ population. 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 Blacks, Asians, American Indian and Alaska Natives, Native Hawaiian and Other
Pacific Islanders, and Hispanics.

22
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, February 2006, “Household Data (“A” tables, monthly; “D”
tables, quarterly).” https://www.bls.gov/cps/eetech_methods.pdf

Bureau of Labor Statistics, April 2014, “Redesign of the Sample for the Current Population
Survey.” http://www.bls.gov/cps/sample_redesign_2014.pdf

U.S. Census Bureau. 2006. Current Population Survey: Design and Methodology. Technical
Paper 66. Washington, DC: Government Printing Office.
http://www.census.gov/prod/2006pubs/tp-66.pdf
All online references accessed April 15, 2019.