2008 CPS-SPPA Source and Accuracy Statement

Appendix I

MEMORANDUM FOR:

Cheryl Landman
Chief, Demographic Surveys Division

From:

Ruth Ann Killion
Chief, Demographic Statistical Methods Division

Subject:

Source and Accuracy Statement for the May 2008 CPS Microdata
File on Public Participation in the Arts

Attached is the statement on the source of the data and accuracy of the estimates for the May
2008 CPS Microdata File on Public Participation in the Arts.
If you have any questions or need additional information, please contact David Hornick of the
Demographic Statistical Methods Division via email at dsmd.source.and.accuracy@census.gov.
Attachment
cc:

email:

L. Clement
(DSD)
G. Weyland
R. Schwartz
B. Kominski (HHES)
W. Savino
(ACSD)
A. Shields

P. Flanagan (DSMD)
J. Scott
S. Adeshiyan
X. Liu
B. Tran
T. Moore
HSSB (9)

Source of the Data and Accuracy of the Estimates for the
May 2008 CPS Microdata File on Public Participation in the Arts
Table of Contents
SOURCE OF THE DATA.............................................................................................................1
Basic CPS.............................................................................................................................1
May 2008 Supplement .........................................................................................................2
CPS Estimation Procedure ...................................................................................................2
PPAS Estimation Procedure ................................................................................................3
ACCURACY OF THE ESTIMATES ..........................................................................................4
Sampling Error .....................................................................................................................4
Nonsampling Error...............................................................................................................4
Nonresponse .........................................................................................................................5
Coverage ..............................................................................................................................5
Comparability of Data..........................................................................................................6
A Nonsampling Error Warning ............................................................................................7
Standard Errors and Their Use .............................................................................................7
Estimating Standard Errors ..................................................................................................8
Generalized Variance Parameters ........................................................................................8
Standard Errors of Estimated Numbers ...............................................................................9
Standard Errors of Estimated Percentages and Ratios .......................................................10
Standard Errors of Estimated Differences .........................................................................13
Standard Errors of Cross-Module Analysis ......................................................................14
Standard Errors of Quarterly or Yearly Averages .............................................................14
Technical Assistance ..........................................................................................................14
REFERENCES .............................................................................................................................20

Tables
Table 1.
Table 2.
Table 3.
Table 4.

Module Factors to Assign to Each Case in Analysis to Calculate the Final Weight ........4
CPS Coverage Ratios: May 2008 .....................................................................................6
Estimation Groups of Interest and Generalized Variance Parameters .............................9
Parameters for Computation of Standard Errors for Labor Force Characteristics: May
2008 ................................................................................................................................15
Table 5. Parameters for Computation of Standard Errors for Public Participation in the Arts
Characteristics: May 2008 .............................................................................................16

Source of the Data and Accuracy of the Estimates for the
May 2008 CPS Microdata File on Public Participation in the Arts
SOURCE OF THE DATA
The data in this microdata file are from the May 2008Current Population Survey (CPS). The
U.S. Census Bureau conducts the CPS every month, although this file has only May 2008 data.
The May 2008 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 entire population. The
National Endowment of the Arts sponsored the supplemental questions for May 2008.
Basic CPS. The monthly CPS collects primarily labor force data about the civilian
noninstitutional 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 (91 percent of the 4.1 million institutionalized people in Census
2000). 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.
In April 2004, the Census Bureau began phasing out the 1990 sample1 and replacing it with the
2000 sample, creating a mixed sampling frame. Two simultaneous changes occurred during this
phase-in period. First, primary sampling units (PSUs)2 selected for only the 2000 design
gradually replaced those selected for the 1990 design. This involved 10 percent of the sample.
Second, within PSUs selected for both the 1990 and 2000 designs, sample households from the
2000 design gradually replaced sample households from the 1990 design. This involved about
90 percent of the sample. The new sample design was completely implemented by July 2005.
In the first stage of the sampling process, PSUs are selected for sample. The United States is
divided into 2,025 PSUs. The PSUs were redefined for this design to correspond to the Office of
Management and Budget definitions of Core-Based Statistical Area definitions and to improve
efficiency in field operations. These PSUs are grouped into 824 strata. Within each stratum, a
single PSU is chosen for the sample, with its probability of selection proportional to its
population as of the most recent decennial census. This PSU represents the entire stratum from
which it was selected. In the case of strata consisting of only one PSU, the PSU is chosen with
certainty.
1

For detailed information on the 1990 sample redesign, please see reference [1].

2

The PSUs correspond to substate areas (i.e., counties or groups of counties) that are geographically contiguous.

2

Approximately 72,000 housing units were selected for sample from the sampling frame in May
2008. Based on eligibility criteria, 11 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 59,000 were determined to be eligible for interview. Interviewers obtained
interviews at about 54,000 of these units. Noninterviews occur when the occupants are not
found at home after repeated calls or are unavailable for some other reason.
May 2008 Supplement. In May 2008, in addition to the basic CPS questions, interviewers
asked supplementary questions on public participation in the arts of two randomly selected
household members aged 18 or older from about one-fourth the sampled CPS households. If the
selected person had a spouse or partner then questions were also asked of their spouse/partner.
The supplement contained questions about the sampled member’s participation in various artistic
activities from May 1, 2007 to May 1, 2008. It asked about the type of artistic activity, the
frequency of participation, training and exposure, musical and artistic preferences, school-age
socialization, and computer usage related to artistic information. These topics were separated
into a core set of questions and four modules. Module A was titled Reading and Music
Preference, module B was titled Participation Via Internet and Other Media, Module C was titled
Leisure Activities, and Module D was titled Arts Learning. Each module was administered to
only a portion of the sampled cases. Interviews were conducted during the period of May 18 24, 2008.
CPS Estimation Procedure. This survey’s estimation procedure adjusts weighted sample
results to agree with independently derived population estimates of the civilian noninstitutional
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 latest decennial 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].

3

The net international migration component in the population estimates includes a combination of
the following:
•
•
•
•
•

Legal migration to the United States.
Emigration of foreign-born and native people from the United States.
Net movement between the United States and Puerto Rico.
Estimates of temporary migration.
Estimates of net residual foreign-born population, which include unauthorized
migration.

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.
PPAS Estimation Procedure. The PPAS adjusts weighted sample results to agree with the
same independently derived population estimates of the civilian noninstitutional population of
the United States as the CPS. However, the age groups were modified to include only those who
are18 years old or older.
The questionnaire modules and the special core question were originally assigned to households
so that half of the sample would receive each module and the special core question. Problems
occurred during the selection of respondents that changed the probabilities used to assign the
modules, the special core question, and the selection of sample cases within the household. The
selection probabilities were corrected in the weighting. The module factor, as described later in
this section, was modified to account for the assignment of the modules and the special core
questions.
Each sampled person receives one or two weights for the PPA survey depending on the modules
asked. The first weight should be used to create estimates from the core and module C since
questions were asked about the respondent’s spouse/partner in these sections. The second weight
should be used to create estimates from modules A, B, and D since these sections did not include
questions about the respondent’s spouse/partner. Both weights were created using the same
weighting procedure but different person selection factors.
To account for the assignment of modules to a portion of the respondents, the data user must
apply a module factor to determine the final weight. The value of the factor is based on the
analysis the data user is conducting. Table 1 provides the factors for each module or
combination of modules (cross analysis of variables from two modules). These factors are
determined by summing the proportion of cases that were asked the module or combination of
modules of interest. The factor is the inverse of the proportion of cases receiving the module or
combination of modules.

4

Table 1. Module Factors to Assign to Each Case in Analysis to Calculate the
Final Weight
Analysis of Module
Module Factor to Assign

Core Questions Only
A or B
C or D or Special Core Question
A and B in combination
A and C or
A and D or
B and C or
B and D or
C and D in combination

1.000000
2.222222
1.818182
12.000000

5.454545

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 that 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).

5

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 May 2008 basic CPS, the household-level
nonresponse rate was 7.8 percent. The person-level nonresponse rate for the Public Participation
in the Arts supplement was an additional 18.4 percent.
Since the basic CPS nonresponse rate is a household-level rate and the Public Participation in the
Arts 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 Public Participation in the Arts supplement.
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 May 2008 is estimated to be about 12 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.
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 2
shows May 2008 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.

6

Table 2. CPS Coverage Ratios: May 2008
Total

White only

Black only

Residual race

Hispanic

All
Age
Male Female Male Female Male Female Male Female Male Female
group people
0-15
0.89
0.89
0.90
0.90
0.91
0.80
0.80
0.95
0.93
0.89
0.89
16-19 0.89
0.88
0.89
0.89
0.91
0.82
0.83
0.94
0.85
0.95
0.89
20-24 0.77
0.76
0.79
0.77
0.80
0.67
0.73
0.73
0.81
0.85
0.86
25-34 0.83
0.80
0.86
0.83
0.86
0.64
0.80
0.78
0.88
0.78
0.91
35-44 0.88
0.85
0.90
0.87
0.93
0.73
0.80
0.78
0.84
0.78
0.91
45-54 0.90
0.89
0.91
0.90
0.92
0.85
0.87
0.79
0.84
0.83
0.88
55-64 0.90
0.90
0.90
0.91
0.91
0.84
0.88
0.86
0.86
0.89
0.89
65+
0.93
0.92
0.94
0.91
0.94
1.01
0.97
0.89
0.82
0.86
0.93
15+
0.88
0.86
0.89
0.88
0.90
0.78
0.84
0.82
0.85
0.83
0.90
0+
0.88
0.87
0.89
0.88
0.91
0.79
0.83
0.85
0.87
0.84
0.89
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 2000-based controls, with microdata files from March 1994 through December 2002,
which reflect 1990 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 Census 2000-based controls results in about a 1 percent increase
from the 1990 census-based controls in the civilian noninstitutional population and in the number
of families and households. Thus, estimates of levels for data collected in 2003 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.
Note that certain microdata files from 2002, namely June, October, November, and the 2002
ASEC, contain both Census 2000-based estimates and 1990 census-based estimates and are

7

subject to the comparability issues discussed previously. All other microdata files from 2002
reflect the 1990 census-based controls.
Users should also exercise caution because of changes caused by the phase-in of the Census
2000 files (see “Basic CPS”). During this time period, CPS data were collected from sample
designs based on different censuses. Three features of the new CPS design have the potential of
affecting published estimates: (1) the temporary disruption of the rotation pattern from August
2004 through June 2005 for a comparatively small portion of the sample, (2) the change in
sample areas, and (3) the introduction of the new Core-Based Statistical Areas (formerly called
metropolitan areas). Most of the known effect on estimates during and after the sample redesign
will be the result of changing from 1990 to 2000 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.
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

8

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 is a
simple model that expresses the variance as a function of the expected value of the survey
estimate. The parameters of the generalized variance function are estimated using direct
replicate variances. These generalized variance parameters provide a relatively easy method to
obtain approximate standard errors for numerous characteristics. In this source and accuracy
statement, Table 4 provides the generalized variance parameters for labor force estimates, and
Table 5 provides generalized variance parameters for characteristics from the May 2008 Public
Participation in the Arts supplement.
The basic CPS questionnaire records the race and ethnicity of each respondent. With respect to
race, a respondent can be White, Black, Asian, American Indian and Alaskan Native (AIAN),
Native Hawaiian and Other Pacific Islander (NHOPI), or combinations of two or more of the
preceding. A respondent’s ethnicity can be Hispanic or non-Hispanic, regardless of race.
The generalized variance parameters to use in computing standard errors are dependent upon the
race/ethnicity group of interest. The following table summarizes the relationship between the

9

race/ethnicity group of interest and the generalized variance parameters to use in standard error
calculations for the basic CPS. For PPAS, the race/ethnicity parameters are given in Table 5.
Table 3. Estimation Groups of Interest and Generalized Variance Parameters
Race/ethnicity group of interest

Generalized variance parameters to
use in standard error calculations

Total population

Total or White

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

Total or White

Total Black, 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
API, AIAN, NHOPI

Notes: (1) API, AIAN, NHOPI are Asian and Pacific Islander, American Indian and Alaska Native,
Native Hawaiian and Other Pacific Islander, respectively.
(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, sx, of an estimated
number from this microdata file can be obtained by using the formula:
sx

ax 2 bx

(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 4,508,000 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

10

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

4,508,000
-0.000032
2,971
113,000
4,322,000 to 4,694,000

The standard error is calculated as
sx

0.000032 4,508,0002 2,971 4,508,000 113,000

The 90-percent confidence interval is calculated as 4,508,000 ± 1.645 × 113,000.
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 and Ratios. The reliability of an estimated
percentage or ratio using sample data depends on the size of both the numerator, x, and
denominator, y. This section presents two equations to calculate standard errors of estimated
percentages and ratios. The first equation is simplified and can be used for most percentage
estimates; the second equation can be used for all percentage and ratio estimates but is more
complex. Use the following questions to determine if the simplified equation can be used to
calculate the standard error of a percentage:
1) Do both the numerator and denominator use the same parameters from Table 4 or 5?
2) Is the denominator a CPS population control - a total by race/ethnicity (excluding the group
self-classified as having two or more races), sex, or age group, or state? See “CPS Estimation
Procedure” for more information on the specific CPS population controls and “PPAS Estimation
Procedure” for more information on the specific PPAS population controls.)
If the answer to either question is yes, then use the following simplified formula to find the
approximate standard error, sy,p, of the estimated percentage p:
s y ,p

b
p(100 p)
y

Here y is the total number of people, families, households, or unrelated individuals in the
denominator of the percentage, p is the percentage, and b is the parameter in Table 4 or 5
associated with the characteristic in the numerator of the percentage.
If the answer to both questions is no, or the estimate is not a percentage, compute the standard
error of the ratio using

(2)

11

sx y

x
y

sx
x

2

sy
y

2

2r

sxs y

(3)

xy

The standard error of the numerator, sx, and that of the denominator, sy, may be calculated using
standard error formulas described in this document. In Formula (3), r represents the correlation
between the numerator and the denominator of the estimate. If r has not been previously
calculated for a specific estimate, consider the type of ratio being estimated. For ratios where the
numerator is a subset of the denominator use

r

x sy

(4)

y sx

For ratios where the denominator is a count of families or households and the numerator is a
count of people in those families or households with a certain characteristic and there is at least
one person with the characteristic in every family or household, use 0.7 as an estimate of r. An
example of this type is the average number of children per family with children. For all other
types of ratios, r is assumed to be zero. Examples are the average number of children per family.
If r 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 (3)
by 100 or 1,000, respectively, to obtain the standard error.
Illustration 2
Suppose there were 116,300,000 women aged 18 and over, and 13.6 percent indicate they listen
to jazz. Use the appropriate parameter from Table 5 and Formula (2), since the denominator in
this percentage is treated as a CPS population control, to get

Illustration 2
Percentage of women 18+ who indicate they
listen to jazz (p)
Base (y)
b parameter (b)
Standard error
90-percent confidence interval

13.6
116,300,000
35,647
0.6
12.6 to 14.6

The standard error is calculated as
s y, p

35,647
13.6 (100 13.6) 0.6
116,300,000

The 90-percent confidence interval for the estimated percentage of women aged 18 years old or
older who listen to jazz is from 12.61 to 14.59 percent (i.e., 13.6 ± 1.645 × 0.6).

12

Illustration 3
Suppose the ratio of men to women working part-time was 9,223,000 to 17,667,000, or 0.52.
Use Formulas (1) and (3) with r = 0 and the appropriate parameters from Table 4 to get
Illustration 3
Males (x)
Number who work parttime
a parameter (a)
b parameter (b)
Standard error
90-percent confidence
interval

Females (y)

Ratio

9,223,000

17,667,000

0.52

-0.000032
2,971
157,000

-0.000031
2,782
199,000

0.01

8,965,000 to 9,481,000

17,340,000 to 17,994,000 0.50 to 0.54

The standard error is calculated as

sx y

9,223,000
17,667,000

157,000
9,223,000

2

199,000
17,667,000

2

0.01

and the 90-percent confidence interval is calculated as 0.52 ± 1.645 × 0.01.
Illustration 4
Suppose that the number of unemployed males was 4,508,000 and the total number unemployed
was 8,193,000. The ratio of unemployed males to the total number unemployed would be 0.55
or 55 percent. The numerator and denominator in this percentage do not use the same
parameters from Table 4, and the denominator is not a CPS population control. Therefore, use
Formulas (3) and (4) for the standard error and correlation, r, along with Formula (1) and the
appropriate parameters from Table 4 to get

Number Unemployed
a parameter (a)
b parameter (b)
correlation (r)
Standard error
90-percent confidence
interval

Illustration 4
Unemployed Males (x) Unemployed Total (y)
4,508,000
8,193,000
-0.000032
-0.000016
2,971
3,096
113,000
156,000
4,322,000 to 4,694,000

7,936,000 to 8,450,000

The correlation is calculated as

r

4,508,000 156,000
8,193,000 113,000

0.76

Ratio (%)
55.0
0.76
0.9
53.5 to 56.5

13

The standard error is calculated as
2

2

4,508,000
113,000
156,000
113,000 156,000
sx y
2 0.76
8,193,000 4,508,000
8,193,000
4,508,000 8,193,000
and the 90-percent confidence interval is calculated as 0.55 ± 1.645 × 0.009.

0.009

Standard Errors of Estimated Differences. The standard error of the difference between two
sample estimates is approximately equal to
s x1

x2

s x1

2

s x2

2

(3)

where s x1 and s x2 are the standard errors of the estimates, x1 and x2. 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 5
Suppose that of the 68,300,000 people with a high school diploma but no college, 9.5 percent
attended a live opera, and of the 61,400,000 people with some college or associate degree, 21.3
percent attended a live opera. Use the appropriate parameters from Table 5 and Formulas (2)
and (3) to get
Illustration 5
High School
Some College or
Diploma (x1)
Associates (x2)
Percentage working
part-time (p)
Base
b parameter (b)
Standard error
90-percent confidence
interval

Difference

9.5

21.3

11.8

68,300,000
40,263
0.71

61,400,000
40,263
1.05

1.27

8.3 to 10.7

19.6 to 23.0

9.7 to 13.9

The standard error of the difference is calculated as

sx

y

0.712 1.052 1.27

The 90-percent confidence interval around the difference is calculated as 11.8 ± 1.645 × 1.27.
Since this interval does not include zero, we can conclude with 90 percent confidence that the
percentage of people with some college or associate degree who attended a live opera is greater
than the percentage of people with a high school diploma who attended a live opera.

14

Standard Errors for Cross-Module Analysis. The standard errors of estimates from crossmodule analysis may be obtained by determining new a and b parameters and using these
adjusted parameters in the standard error formulas mentioned previously. To determine a new
cross-module b parameter, multiply the Core b parameter from Table 5 by the factor provided in
Table 1. For example, the cross-module factor to apply to Module A and B is 12.0.
To determine the new a parameter, use the following formula:

a cross

module

bcross module
POPitem

where POPitem is the population found in Table 5.
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.
Technical Assistance. If you require assistance or additional information, please contact the
Demographic Statistical Methods Division via e-mail at dsmd.source.and.accuracy@census.gov.

15

Table 4. Parameters for Computation of Standard Errors for Labor Force Characteristics:
May 2008
Characteristic

a

b

Civilian labor force, employed
Not in labor force
Unemployed

-0.000016
-0.000009
-0.000016

3,068
1,833
3,096

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

-0.000032
-0.000031
-0.000022

2,971
2,782
3,096

-0.000151
-0.000311
-0.000252
-0.001632

3,455
3,357
3,062
3,455

-0.000141
-0.000253
-0.000266
-0.001528

3,455
3,357
3,062
3,455

-0.000346
-0.000729
-0.000659
-0.004146

3,198
3,198
3,198
3,198

Total or White

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

Notes: (1) These parameters are to be applied to basic CPS monthly labor force estimates.
(2) API, AIAN, NHOPI are Asian and Pacific Islander, American Indian and Alaska Native,
Native Hawaiian and Other Pacific Islander, respectively.
(3) 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.
(4) 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.
(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.

16

Table 5. Parameters for Computation of Standard Errors for Public Participation in the Arts Characteristics: May 2008 1
Module C or Special
Core
Modules A or B
Core Question
Module D
Characteristic
Population
a
b
a
b
a
b
a
b
All Adults

-0.000118

26,532

-0.000266

59,862

-0.000170

38,332

-0.000220

49,404

224,826,742

Male

-0.000186

20,220

-0.000551

59,862

-0.000301

32,699

-0.000455

49,404

108,545,640

Female

-0.000174

20,220

-0.000515

59,862

-0.000281

32,699

-0.000425

49,404

116,281,102

Hispanic2

-0.001017

30,967

-0.002524

76,829

-0.001635

49,784

-0.001892

57,588

30,444,019

Nonhispanic White

-0.000152

23,545

-0.000388

59,862

-0.000248

38,332

-0.000320

49,404

154,461,582

Nonhispanic African American

-0.001210

30,967

-0.003001

76,829

-0.001945

49,784

-0.002250

57,588

25,597,094

Nonhispanic Other

-0.002162

30,967

-0.005845

83,729

-0.003476

49,784

-0.004784

68,532

14,324,047

Age

-0.000075

16,951

-0.000226

50,822

-0.000129

28,929

-0.000173

38,917

224,826,742

Income

-0.000118

26,532

-0.000266

59,862

-0.000170

38,332

-0.000220

49,404

224,826,742

Education

-0.000118

26,532

-0.000266

59,862

-0.000170

38,332

-0.000220

49,404

224,826,742

-0.001406

17,961

-0.003052

38,994

-0.003000

38,332

-0.002448

31,280

12,775,516

Connecticut

-0.003866

13,328

-0.012019

41,439

-0.006152

21,211

-0.008411

28,999

3,447,696

Maine

-0.002795

3,642

-0.008512

11,091

-0.004929

6,422

-0.006483

8,447

1,302,995

Massachusetts

-0.004164

26,532

-0.009921

63,217

-0.006833

43,540

-0.007753

49,404

6,371,844

-0.003511

3,642

-0.010693

11,091

-0.006191

6,422

-0.008144

8,447

1,037,252

-0.005915

3,642

-0.018013

11,091

-0.010430

6,422

-0.013719

8,447

615,729

-0.000818

32,608

-0.002100

83,729

-0.001421

56,653

-0.001719

68,532

39,861,959

-0.003088

26,532

-0.007358

63,217

-0.005067

43,540

-0.005750

49,404

8,592,019

Sex

Ethnicity and Race

State and Region
New England

Rhode Island
Remainder New England
Mid-Atlantic
New Jersey

3

17

Table 5. Parameters for Computation of Standard Errors for Public Participation in the Arts Characteristics: May 2008 1
Module C or Special
Core
Modules A or B
Core Question
Module D
Characteristic
Population
a
b
a
b
a
b
a
b
New York

-0.001883

35,847

-0.004397

83,729

-0.003530

67,209

-0.004409

83,952

19,041,198

Pennsylvania

-0.002170

26,532

-0.005170

63,217

-0.003560

43,540

-0.004040

49,404

12,228,742

South Atlantic

-0.000464

26,532

-0.001046

59,862

-0.000670

38,332

-0.000863

49,404

57,236,836

Florida

-0.001323

23,885

-0.003107

56,111

-0.001811

32,699

-0.002736

49,404

18,059,796

Georgia

-0.003065

29,092

-0.006943

65,909

-0.004856

46,095

-0.005205

49,404

9,492,256

Maryland

-0.003328

18,440

-0.007907

43,814

-0.005416

30,011

-0.006378

35,346

5,541,450

North Carolina

-0.003229

29,092

-0.007317

65,909

-0.005117

46,095

-0.005484

49,404

9,008,211

South Carolina

-0.005477

23,885

-0.012867

56,111

-0.008790

38,332

-0.011329

49,404

4,360,741

Virginia

-0.003164

23,885

-0.007433

56,111

-0.005078

38,332

-0.006544

49,404

7,549,167

-0.005539

9,901

-0.013857

24,772

-0.008752

15,645

-0.009666

17,279

1,787,633

-0.002264

3,254

-0.005811

8,354

-0.004053

5,826

-0.004085

5,873

1,437,582

-0.000511

23,408

-0.001536

70,275

-0.001082

49,525

-0.001079

49,404

45,765,789

Illinois

-0.001840

23,408

-0.005004

63,666

-0.003013

38,332

-0.003883

49,404

12,721,800

Michigan

-0.002360

23,408

-0.006419

63,666

-0.003865

38,332

-0.004981

49,404

9,918,880

-0.002072

23,408

-0.005635

63,666

-0.003392

38,332

-0.004372

49,404

11,299,174

-0.001648

19,487

-0.005474

64,735

-0.002765

32,699

-0.003526

41,702

11,825,935

-0.000702

13,901

-0.002021

40,039

-0.001170

23,173

-0.001682

33,315

19,811,330

Iowa

-0.002638

7,786

-0.007308

21,568

-0.004657

13,745

-0.006111

18,036

2,951,442

Kansas

-0.003924

10,729

-0.012003

32,819

-0.007602

20,786

-0.008428

23,044

2,734,129

Minnesota

-0.002077

10,729

-0.006355

32,819

-0.004025

20,786

-0.004462

23,044

5,164,487

Missouri

-0.004036

23,408

-0.010977

63,666

-0.006609

38,332

-0.008518

49,404

5,800,136

Nebraska

-0.004446

7,786

-0.012316

21,568

-0.007849

13,745

-0.010299

18,036

1,751,178

North Dakota

-0.004249

2,655

-0.011724

7,325

-0.007113

4,444

-0.008641

5,399

624,786

West Virginia
Remainder S. Atlantic

4

East North Central

Ohio
Remainder E.N. Central
West North Central

5

18

Table 5. Parameters for Computation of Standard Errors for Public Participation in the Arts Characteristics: May 2008 1
Module C or Special
Core
Modules A or B
Core Question
Module D
Characteristic
Population
a
b
a
b
a
b
a
b
South Dakota

-0.003381

2,655

-0.009329

7,325

-0.005660

4,444

-0.006876

5,399

785,172

East South Central

-0.001495

26,532

-0.003374

59,862

-0.002160

38,332

-0.002784

49,404

17,743,068

Alabama

-0.006352

29,092

-0.014392

65,909

-0.010065

46,095

-0.010788

49,404

4,579,659

-0.001814
-0.000771

23,885
26,532

-0.004263
-0.001739

56,111
59,862

-0.002484
-0.001114

32,699
38,332

-0.003753
-0.001436

49,404
49,404

13,163,409
34,414,531

-0.001221

29,092

-0.002766

65,909

-0.001935

46,095

-0.002073

49,404

23,827,505

-0.002256

23,885

-0.005300

56,111

-0.003621

38,332

-0.004666

49,404

10,587,026

-0.000853

18,281

-0.002373

50,822

-0.001790

38,332

-0.002306

49,404

21,419,886

Colorado

-0.003768

18,281

-0.007677

37,246

-0.006016

29,188

-0.006245

30,295

4,851,354

Nevada

-0.004013

10,394

-0.011315

29,310

-0.007298

18,905

-0.008509

22,041

2,590,269

-0.004597

2,400

-0.021254

11,097

-0.008513

4,445

-0.010235

5,344

522,125

-0.001359

18,281

-0.003777

50,822

-0.002849

38,332

-0.003671

49,404

13,456,138

-0.000549

26,532

-0.001405

67,885

-0.000793

38,332

-0.001248

60,282

48,321,085

California

-0.000733

26,532

-0.001814

65,718

-0.001189

43,075

-0.001364

49,404

36,220,464

Oregon

-0.004889

18,281

-0.013591

50,820

-0.010251

38,332

-0.013212

49,404

3,739,264

-0.004117

26,532

-0.010196

65,718

-0.006683

43,075

-0.007665

49,404

6,445,194

-0.003298

6,319

-0.008149

15,615

-0.005088

9,750

-0.009870

18,913

1,916,163

-0.002385

26,532

-0.004037

44,900

-0.003968

44,138

-0.004442

49,404

11,122,535

-0.001763

33,497

-0.003748

71,232

-0.002838

53,925

-0.003030

57,587

19,003,804

Dallas-Fort Worth, TX

-0.001406

33,497

-0.002989

71,232

-0.002263

53,925

-0.002417

57,587

23,827,505

Denver-Aurora-

-0.003494

16,951

-0.007140

34,641

-0.005380

26,100

-0.005941

28,823

4,851,354

Remainder East South Central6
West South Central
Texas
Remainder W.S. Central

7

Mountain

Wyoming
Remainder Mountain

8

Pacific

Washington
Remainder Pacific

9

Metropolitan Areas
Boston-Worcester-Manchester,
MA-NH
Chicago-Naperville-Michigan
City, IL-IN

19

Table 5. Parameters for Computation of Standard Errors for Public Participation in the Arts Characteristics: May 2008 1
Module C or Special
Core
Modules A or B
Core Question
Module D
Characteristic
Population
a
b
a
b
a
b
a
b
Boulder, CO
Detroit-Warren-Flint, MI
Los Angeles-Long BeachRiverside, CA
Miami-Fort Lauderdale-Miami
Beach, FL
NY-Newark-Bridgeport, NY-NJCT-PA
Philadelphia-Camden-Vineland,
PA-NJ-DE-MD

-0.000972

33,497

-0.002067

71,232

-0.001565

53,925

-0.001671

57,587

34,466,615

-0.001101

39,872

-0.002204

79,815

-0.001489

53,925

-0.001794

64,962

36,220,464

-0.002208

39,872

-0.004419

79,815

-0.002986

53,925

-0.003597

64,962

18,059,796

-0.000921

39,872

-0.001843

79,815

-0.001245

53,925

-0.001500

64,962

43,309,655

-0.001271

33,497

-0.002702

71,232

-0.002046

53,925

-0.002184

57,587

26,362,211

San Jose-Francisco-Oakland, CA
Washington-Baltimore-Northern
Virginia , DC-MD-VA-WV

-0.001101

39,872

-0.002204

79,815

-0.001489

53,925

-0.001794

64,962

36,220,464

-0.000151

23,407

-0.000333

51,440

-0.000212

32,699

-0.000186

28,823

154,557,079

Occupation

-0.000075

16,951

-0.000244

54,832

-0.000130

29,237

-0.000220

49,404

224,826,742

Notes: (1) These parameters are to be applied to the May 2008 Public Participation in the Arts Supplement data.
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)

Hispanics may be any race.
Remainder New England includes New Hampshire and Vermont.
Remainder S. Atlantic includes Delaware and the District of Columbia.
Remainder E.N. Central includes Indiana and Wisconsin.
Remainder E. S. Central includes Kentucky, Mississippi, and Tennessee.
Remainder W.S. Central includes Arkansas, Louisiana, and Oklahoma.
Remainder Mountain includes Arizona, Idaho, New Mexico, Montana, and Utah.
Remainder Pacific includes Alaska and Hawaii.

20

References
[1]

Bureau of Labor Statistics. 1994. Employment and Earnings. Volume 41 Number 5,
May 1994. Washington, DC: Government Printing Office.

[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. (http://www.fcsm.gov/working-papers/spp.html)