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pdfAppendix 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 [email protected].
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 [email protected].
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)
| File Type | application/pdf |
| File Title | Source and Accuracy Statement - 2008 PPAS |
| Author | David V. Hornick |
| File Modified | 2011-11-15 |
| File Created | 2011-11-15 |