Source and Accuracy Statement

Attachment D

Source of the Data and Accuracy of the Estimates for the
October 2017 CPS Microdata File

SOURCE OF THE DATA
The data in this microdata file are from the October 2017 Current Population Survey (CPS). The
U.S. Census Bureau conducts the CPS every month, although this file has only October data.
The October survey uses two sets of questions, the basic CPS and a set of supplemental
questions. The CPS, sponsored jointly by the Census Bureau and the U.S. Bureau of Labor
Statistics, is the country’s primary source of labor force statistics for the civilian
noninstitutionalized population. The Census Bureau and the National Center for Educational
Statistics also jointly sponsor the supplemental questions for October.
Basic CPS. The monthly CPS collects primarily labor force data about the civilian
noninstitutionalized population living in the United States. The institutionalized population,
which is excluded from the 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). 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 2000 design, the United States was divided into 2,025
PSUs. These were then grouped into 824 strata and one PSU was selected for sample from each
stratum. 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.
In April 2014, the Census Bureau began phasing out the 2000 sample and replaced it with the
2010 sample, creating a mixed sampling frame. Two simultaneous changes occurred during this
1
2

For detailed information on the 2000 sample redesign, please see reference [1].
The PSUs correspond to substate areas (i.e., counties or groups of counties) that are geographically contiguous.

16-1

phase-in period. First, within the PSUs selected for both the 2000 and 2010 designs, sample
households from the 2010 design gradually replaced sample households from the 2000 design.
Second, new PSUs selected for only the 2010 design gradually replaced outgoing PSUs selected
for only the 2000 design. By July 2015, the new 2010 sample design was completely
implemented and the sample came entirely from the 2010 redesigned sample.
Approximately 72,000 housing units were selected for sample from the sampling frame in
October. Based on eligibility criteria, 10 percent of these housing units were sent directly to
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 61,000 were determined to be eligible for interview. Interviewers obtained
interviews at about 53,000 of these units. Noninterviews occur when the occupants are not
found at home after repeated calls or are unavailable for some other reason.
October 2017 Supplement. In October 2017, in addition to the basic CPS questions,
interviewers asked supplementary questions of household members three years old and over on
school enrollment.
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.

3

For further information on CATI and CAPI and the eligibility criteria, please see reference [2].

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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.
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).

16-3

To minimize these errors, the Census Bureau applies quality control procedures during all stages
of the production process including the design of the survey, the wording of questions, the
review of the work of interviewers and coders, and the statistical review of reports.
Two types of nonsampling error that can be examined to a limited extent are nonresponse and
undercoverage.
Nonresponse. The effect of nonresponse cannot be measured directly, but one indication of its
potential effect is the nonresponse rate. For the October 2017 basic CPS, the household-level
nonresponse rate was 13.8 percent. The person-level nonresponse rate for the School Enrollment
supplement was an additional 9.9 percent.
Since the basic CPS nonresponse rate is a household-level rate and the School Enrollment
supplement nonresponse rate is a person-level rate, we cannot combine these rates to derive an
overall nonresponse rate. Nonresponding households may have fewer persons than interviewed
ones, so combining these rates may lead to an overestimate of the true overall nonresponse rate
for persons for the School Enrollment supplement.
In accordance with Census Bureau and Office of Management and Budget Quality Standards, the
Census Bureau will conduct a nonresponse bias analysis to assess nonresponse bias in the School
Enrollment.
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 School Enrollment supplement, the item refusal rates range from 0.0
percent to 1.7 percent. The item allocation rates range from 4.5 percent to 20.6 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 October 2017 is estimated to be about 11 percent. CPS
coverage varies with age, sex, and race. Generally, coverage is larger for females than for males
and larger for non-Blacks than for Blacks. This differential coverage is a general problem for
most household-based surveys.

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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 October 2017 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. CPS Coverage Ratios: October 2017
Total
Age
All
group people
0-15
0.87
16-19 0.88
20-24 0.76
25-34 0.83
35-44 0.89
45-54 0.92
55-64 0.93
65+
0.96
15+
0.90
0+
0.89

White only

Black only

Residual race

Hispanic

Male

Female

Male

Female

Male

Female

Male

Female

Male

Female

0.87
0.92
0.76
0.81
0.87
0.89
0.92
0.98
0.88
0.88

0.87
0.84
0.77
0.85
0.91
0.94
0.95
0.95
0.90
0.90

0.90
0.96
0.79
0.84
0.90
0.91
0.93
0.98
0.91
0.91

0.92
0.87
0.79
0.87
0.95
0.95
0.97
0.96
0.93
0.92

0.76
0.78
0.67
0.66
0.73
0.82
0.85
0.96
0.78
0.77

0.74
0.72
0.64
0.76
0.80
0.89
0.87
0.97
0.82
0.81

0.85
0.84
0.69
0.79
0.83
0.83
0.91
0.88
0.83
0.83

0.79
0.82
0.78
0.80
0.84
0.91
0.87
0.88
0.84
0.83

0.79
0.94
0.78
0.72
0.81
0.81
0.85
0.84
0.81
0.80

0.79
0.83
0.78
0.81
0.87
0.92
0.88
0.86
0.85
0.83

Notes: (1) The Residual race group includes cases indicating a single race other than White or Black,
and cases indicating two or more races.
(2) Hispanics may be any race. 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
Census 2010-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.
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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 Census 2010-based controls results in about a 0.2 percent increase
from the 2000 census-based controls in the civilian noninstitutionalized population and in the
number of families and households. Thus, estimates of levels for data collected in 2012 and later
years will differ from those for earlier years by more than what could be attributed to actual
changes in the population. These differences could be disproportionately greater for certain
population subgroups than for the total population.
Users should also exercise caution because of changes caused by the phase-in of the 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 references [2] and [3].
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.
4

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

16-6

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.
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.
There are two ways to calculate standard errors for the CPS microdata file on School Enrollment.
They are:
•
•

Direct estimates created from replicate weighting methods;
Generalized variance estimates created from generalized variance function
parameters a and b.

While replicate weighting methods provide the most accurate variance estimates, this approach
requires more computing resources and more expertise on the part of the user. The Generalized
Variance Function (GVF) parameters provide a method of balancing accuracy with resource
usage as well as a smoothing effect on standard error estimates across time. For more
information on calculating direct estimates, see reference [4]. For more information on GVF
estimates, refer to the “Generalized Variance Parameters” section.
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
16-7

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 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, Table 4 provides the GVF parameters for labor force estimates, and
Table 5 provides GVF parameters for characteristics from the October 2017 supplement. Table
6 provides factors and population controls to derive 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
GVF parameters to
use in standard error calculations

Race/ethnicity group of interest
Total population

Total or White

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

Total or White

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

Black

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

Asian, AIAN, NHOPI

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

Asian, AIAN, NHOPI

Hispanic population

Hispanic

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

Black
Asian, AIAN, NHOPI

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Notes: (1) AIAN is American Indian and Alaska Native and NHOPI is Native Hawaiian and Other
Pacific Islander.
(2) AOIC is an abbreviation for alone or in combination. The AOIC population for a race group
of interest includes people reporting only the race group of interest (alone) and people
reporting multiple race categories including the race group of interest (in combination).
(3) Hispanics may be any race.
(4) Two or more races refers to the group of cases self-classified as having two or more races.

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 4 or 5 associated with
the particular type of characteristic. When calculating standard errors from cross-tabulations
involving different characteristics, use the set of parameters for the characteristic that will give
the largest standard error.
Illustration 1
Suppose there were 3,362,000 unemployed men (ages 16 and up) in the civilian labor force. Use
the appropriate parameters from Table 4 and Formula (1) to get
Illustration 1
Number of unemployed males in the civilian
labor force (x)
a-parameter (a)
b-parameter (b)
Standard error
90-percent confidence interval

3,362,000
-0.000031
2,947
98,000
3,201,000 to 3,523,000

The standard error is calculated as
𝑠𝑠𝑥𝑥 = �−0.000031 × 3,362,0002 + 2,947 × 3,362,000 = 98,000

The 90-percent confidence interval is calculated as 3,362,000 ± 1.645 × 98,000.

A conclusion that the average estimate derived from all possible samples lies within a range
computed in this way would be correct for roughly 90 percent of all possible samples.
Standard Errors of Estimated School Enrollment Numbers. The approximate standard error,
sx, of an estimated school enrollment number from this microdata file can be obtained by using
the formula:

16-9

𝑏𝑏

𝑠𝑠𝑥𝑥 = �− � � 𝑥𝑥 2 + 𝑏𝑏𝑏𝑏

(2)

𝑇𝑇

Here x is the size of the estimate, T is the population total in Table 3 for the total number of
persons in a specific age group, and b is the parameter in Table 5 associated with the particular
type of characteristic. If Table 3 does not contain the age group of interest, use the smallest age
group available in the table that does contain the age group of interest. When calculating
standard errors for numbers from cross-tabulations involving different characteristics, use the set
of parameters for the characteristic that will give the largest standard error.
Table 3. Population Totals for School Enrollment Age Groups:
October 2017
Age Group

Total

White

Black

3+
3-4
3-6
3-17
3-24
5-24
6-13
14 -17
15+
15 -17
15-19
15-24
16-17
16-24
18-19
18-24
20-21
20-24
22-24
25+
25-29
25-34
30-34
35+

310,070,226
9,165,161
18,350,106
71,067,484
92,382,926
83,217,765
34,048,740
24,991,619
260,368,881
21,366,139
21,366,139
42,681,581
16,763,274
38,078,716
16,763,274
38,078,716
21,315,442
21,315,442
21,315,442
217,687,300
22,731,454
44,090,874
21,359,420
173,596,426

237,735,230
5,716,228
11,491,170
50,774,462
66,410,796
60,694,568
23,808,268
18,388,002
202,323,543
15,362,775
15,362,775
30,999,109
12,337,177
27,973,511
12,337,177
27,973,511
15,636,334
15,636,334
15,636,334
171,324,434
16,612,710
32,585,700
15,972,990
138,738,734

40,971,396
1,835,784
3,670,481
11,112,141
14,324,312
12,488,528
5,557,731
3,718,626
32,977,628
3,118,373
3,118,373
6,330,544
2,510,428
5,722,599
2,510,428
5,722,599
3,212,171
3,212,171
3,212,171
26,647,084
3,459,013
6,355,648
2,896,635
20,291,436

Asian,
AIAN,
NHOPI
31,363,600
1,613,149
3,188,455
9,180,881
11,647,818
10,034,669
4,682,741
2,884,991
25,067,710
2,884,991
2,884,991
5,351,928
1,915,669
4,382,606
1,915,669
4,382,606
2,466,937
2,466,937
2,466,937
19,715,782
2,659,731
5,149,526
2,489,795
14,566,256

Hispanic
58,243,443
5,168,456
10,425,046
20,443,173
25,131,352
19,962,896
11,409,765
10,018,127
47,818,397
10,018,127
10,018,127
14,706,306
3,864,952
8,553,131
3,864,952
8,553,131
4,688,179
4,688,179
4,688,179
33,112,091
4,651,311
9,024,526
4,373,215
24,087,565

Notes: (1) AIAN is American Indian and Alaska Native and NHOPI is Native Hawaiian and Other
Pacific Islander.
(2) White, Black, and Asian, AIAN, NHOPI totals include Hispanics.

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(3) Hispanics may be any race.
Illustration 2
Suppose there were 4,319,000 three- and four-year-olds enrolled in school and 9,165,161 total
children in that age group. Use the appropriate b parameter from Table 5 and Formula (2) to get
Illustration 2
Number of three and four year olds enrolled
in school (x)
Total (T)
b parameter (b)
Standard error
90-percent confidence interval

4,319,000
9,165,161
2,912
82,000
4,184,000 to 4,454,000

The standard error is calculated as
𝑠𝑠𝑥𝑥 = �− �

2,912
� × 4,319,0002 + 2,912 × 4,319,000 = 82,000
9,165,161

The 90-percent confidence interval is calculated as 4,319,000 ± 1.645 × 82,000.

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 4 or 5 as indicated by the numerator.
The approximate standard error, 𝑠𝑠𝑦𝑦,𝑝𝑝 , of an estimated percentage can be obtained by using the
formula:
𝑏𝑏

𝑠𝑠𝑦𝑦,𝑝𝑝 = � 𝑝𝑝(100 − 𝑝𝑝)
𝑦𝑦

(3)

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 4 or 5 associated with the characteristic in the numerator of the percentage.

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Illustration 3
Suppose there were 16,533,000 people aged 18 to 21, and 50.3 percent were enrolled in college.
Use the appropriate parameter from Table 5 and Formula (3) to get
Illustration 3
Percentage of people aged 18-21 enrolled in
college (p)
Base (y)
b-parameter (b)
Standard error
90-percent confidence interval

50.3
16,533,000
2,530
0.62
49.3 to 51.3

The standard error is calculated as
2,530
𝑠𝑠𝑦𝑦,𝑝𝑝 = �
× 50.3 × (100.0 − 50.3) = 0.62
16,533,000

The 90-percent confidence interval for the estimated percentage of people aged 18 to 21 enrolled
in college is from 49.3 to 51.3 percent (i.e., 50.3 ± 1.645 × 0.62).
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

(4)

where 𝑠𝑠𝑥𝑥1 and 𝑠𝑠𝑥𝑥2 are the standard errors of the estimates, 𝑥𝑥1 and 𝑥𝑥2 . The estimates can be
numbers, percentages, ratios, etc. This will result in accurate estimates of the standard error of
the same characteristic in two different areas or for the difference between separate and
uncorrelated characteristics in the same area. However, if there is a high positive (negative)
correlation between the two characteristics, the formula will overestimate (underestimate) the
true standard error.
Illustration 3
Suppose that of the 7,248,000 employed men between 20-24 years of age, 30.1 percent were
part-time workers, and of the 6,932,000 employed women between 20-24 years of age, 39.4
percent were part-time workers. Use the appropriate parameters from Table 5 and Formulas (3)
and (4) to get

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Illustration 3
Men (x1)
Women (x2)
Percentage working
part-time (p)
Base (y)
b-parameter (b)
Standard error
90-percent confidence
interval

Difference

30.1

39.4

9.3

7,248,000
2,947
0.92

6,932,000
2,788
0.98

1.34

28.6 to 31.6

37.8 to 41.0

7.1 to 11.5

The standard error of the difference is calculated as
𝑠𝑠𝑥𝑥1 −𝑥𝑥2 = �0.922 + 0.982 = 1.34

The 90-percent confidence interval around the difference is calculated as 9.3 ± 1.645 × 1.34.
Since this interval does not include zero, we can conclude with 90-percent confidence that the
percentage of part-time women workers between 20-24 years of age is greater than the
percentage of part-time men workers between 20-24 years of age.
Standard Errors of Quarterly or Yearly Averages. For information on calculating standard
errors for labor force data from the CPS which involve quarterly or yearly averages, please see
the “Explanatory Notes and Estimates of Error: Household Data” section in Employment and
Earnings, a monthly report published by the U.S. Bureau of Labor Statistics.
Year-to-Year Factors.
In past years, the Census Bureau published a table of year factors for the School Enrollment
Supplement in the Source and Accuracy Statement. User demand for these factors has
diminished with the introduction of replicate weights. Data users producing estimates from prior
years should consult the Source and Accuracy Statements covering the years of their analysis to
estimate standard errors.
Technical Assistance. If you require assistance or additional information, please contact the
Demographic Statistical Methods Division via e-mail at [email protected].

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Table 4. Parameters for Computation of Standard Errors for Labor Force
Characteristics: October 2017
Characteristic

a

b

-0.000013
-0.000017
-0.000013

2,481
3,244
2,432

Civilian labor force, employed, not in labor force, and unemployed
Men
Women
Both sexes, 16 to 19 years

-0.000031
-0.000028
-0.000261

2,947
2,788
3,244

Black
Civilian labor force, employed, not in labor force, and unemployed
Total
Men
Women
Both sexes, 16 to 19 years

-0.000117
-0.000249
-0.000191
-0.001425

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

Asian, American Indian and Alaska Native, Native Hawaiian and
Other Pacific Islander
Civilian labor force, employed, not in labor force, and unemployed
Total
Men
Women
Both sexes, 16 to 19 years

-0.000245
-0.000537
-0.000399
-0.004078

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

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

-0.000087
-0.000172
-0.000158
-0.000909

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

Total or White
Civilian labor force, employed
Unemployed
Not in labor force

Notes: (1) These parameters are to be applied to basic CPS monthly labor force estimates.
(2) The Total or White, Black, and Asian, AIAN, NHOPI parameters are to be used for both alone and in
combination race group estimates.
(3) 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 aand b-parameters are zero.
(4) 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.

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(5) For the groups self-classified as having two or more races, use the Asian, AIAN, NHOPI

parameters for all employment characteristics.

Table 5. Parameters for Computation of Standard Errors for
School Enrollment Characteristics: October 2017
b
Characteristics

Black

Asian,
AIAN,
NHOPI

Hispanic

2,530
2,912

2,861
3,295

2,861
3,295

3,258
3,750

5,564
6,761

7,993
11,788

7,993
11,788

13,471
19,866

FAMILIES, HOUSEHOLDS, OR UNRELATED INDIVIDUALS
2,393
2,613
Income, earnings..............................................

2,613

4,403

1,998

3,367

Total or
White

PEOPLE
Persons enrolled in school:
Total............................................................
Children 13 and under................................
Marital status, household and family
characteristics, health insurance
Some household members..........................
All household members..............................

Marital status, household and family
characteristics, educational attainment,
population by age/sex.......................

2,208

1,998

Notes: (1) These parameters are to be applied to the October 2017 School Enrollment Supplement data.
(2) AIAN is American Indian and Alaska Native and NHOPI is Native Hawaiian and Other Pacific Islander.
(3) Hispanics may be any race. For a more detailed discussion on the use of parameters for race and
ethnicity, please see the “Generalized Variance Parameters” section.
(4) The Total or White, Black, and Asian, AIAN, NHOPI parameters are to be used for both alone and in
combination race group estimates.
(5) 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.
(6) 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.
(7) 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.

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Table 6. Factors for Region Parameters: October 2017
Geography
U.S. Totals
Regions:
Northeast
Midwest
South
West

Factor
1.00
1.08
1.09
1.11
1.03

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REFERENCES
[1]

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

[2]

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

[3]

Brooks, C.A. and 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/wp-content/uploads/sites/242/2014/04/spwp3.pdf

[4]

U.S. Census Bureau, July 15, 2009, “Estimating ASEC Variances with Replicate Weights
Part I: Instructions for Using the ASEC Public Use Replicate Weight File to Create
ASEC Variance Estimates.”
http://thedataweb.rm.census.gov/pub/cps/march/Use_of_the_Public_Use_Replicate_Wei
ght_File_final.doc

All online references accessed May 2, 2018.

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