Source and Accurcy Statement

1Source of the Data and Accuracy of the Estimates for the

2013 Annual Social and Economic Supplement Microdata File

Table of Contents

SOURCE OF THE DATA 1

Basic CPS 1

The 2013 Annual Social and Economic Supplement 3

Estimation Procedure 4

ACCURACY OF THE ESTIMATES 5

Sampling Error 5

Nonsampling Error 5

Nonresponse 6

Sufficient Partial Interview 6

Coverage 6

Comparability of Data 7

A Nonsampling Error Warning 8

Estimation of Median Incomes 8

Standard Errors and Their Use 9

Estimating Standard Errors 9

Generalized Variance Parameters 10

Standard Errors of Estimated Numbers 11

Standard Errors of Estimated Percentages 13

Standard Errors of Estimated Differences 13

Standard Errors of Estimated Ratios 15

Standard Errors of Estimated Medians 17

Standard Errors of Averages for Grouped Data 19

Standard Errors of Estimated Per Capita Deficits 21

Accuracy of State Estimates 22

Standard Errors of State Estimates 23

Standard Errors of Regional Estimates 24

Standard Errors of Groups of States 24

Standard Errors of Data for Combined Years 25

Standard Errors of Differences of 2-Year Averages 27

Standard Errors of Quarterly or Yearly Averages 28

Technical Assistance 28

REFERENCES 34

Tables

Table 1. Description of the March Basic CPS and ASEC Sample Cases 3

Table 2. CPS Coverage Ratios: March 2013 7

Table 3. Estimation Groups of Interest and Generalized Variance Parameters 11

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

March 2013 29

Table 5. Parameters for Computation of Standard Errors for People and Families:

2013 ASEC 30

Table 6. CPS Year Factors: ASEC 1947 to 2012 31

Table 7. CPS Year-to-Year Correlation Coefficients for Income and Health Insurance Characteristics: ASEC 1961 to 2013 32

Table 8. CPS Year-To-Year Correlation Coefficients for Poverty Characteristics:

ASEC 1971 to 2013 32

Table 9. Factors and Populations for State Standard Errors and Parameters: 2013 ASEC 33

Table 10.Factors and Populations for Regional Standard Errors and Parameters:

2013 ASEC 33

1Source of the Data and Accuracy of the Estimates for the

2013 Annual Social and Economic Supplement Microdata File

SOURCE OF THE DATA

The data in this microdata file are from the 2013 Annual Social and Economic Supplement (ASEC) of the Current Population Survey (CPS). The U.S. Census Bureau conducts the ASEC over a 3-month period in February, March, and April, with most of the data collection occurring in the month of March. The ASEC 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 Census Bureau and the Bureau of Labor Statistics also jointly sponsor the ASEC.

1Basic CPS. The monthly CPS collects primarily labor force data about the civilian noninstitutionalized population living in the United States. The institutionalized population, which is excluded from the population universe, is composed primarily of the population in correctional institutions and nursing homes (98 percent of the 4.0 million institutionalized people in Census 2010). Interviewers ask questions concerning labor force participation about each member 15 years old and over in sample households. Typically, the week containing the nineteenth of the month is the interview week. The week containing the twelfth is the reference week (i.e., the week about which the labor force questions are asked).

The CPS uses a multistage probability sample based on the results of the decennial census, with coverage in all 50 states and the District of Columbia. The sample is continually updated to account for new residential construction. When files from the most recent decennial census become available, the Census Bureau gradually introduces a new sample design for the CPS.

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.

Approximately 72,500 housing units were selected for sample from the sampling frame for the basic CPS. Based on eligibility criteria, 12 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 59,300 were determined to be eligible for interview. Interviewers obtained interviews at about 52,900 of these units. Noninterviews occur when the occupants are not found at home after repeated calls or are unavailable for some other reason. Table 1 summarizes historical changes in the CPS design.

Table 1. Description of the March Basic CPS and ASEC Sample Cases
Time period	Number of sample PSUs	Basic CPS housing units eligible		Total (ASEC/ADS1 + basic CPS) housing units eligible
		Interviewed	Not interviewed	Interviewed	Not interviewed
2013	824	52,900	6,400	75,500	7,700
2012	824	53,300	5,800	75,100	7,200
2011	824	53,400	5,300	75,900	6,500
2010	824	54,100	4,600	77,000	5,700
2009	824	54,100	4,600	76,200	5,700
2008	824	53,800	5,100	75,900	6,400
2007	824	53,700	5,600	75,500	7,100
2006	824	54,000	5,400	76,000	7,100
2005	754/824 2	54,400	5,700	76,500	7,500
2004	754	55,000	5,200	77,700	7,000
2003	754	55,500	4,500	78,300	6,800
2002	754	55,500	4,500	78,300	6,600
2001	754	46,800	3,200	49,600	4,300
2000	754	46,800	3,200	51,000	3,700
1999	754	46,800	3,200	50,800	4,300
1998	754	46,800	3,200	50,400	5,200
1997	754	46,800	3,200	50,300	3,900
1996	754	46,800	3,200	49,700	4,100
1995	792	56,700	3,300	59,200	3,800
1990 to 1994	729	57,400	2,600	59,900	3,100
1989	729	53,600	2,500	56,100	3,000
1986 to 1988	729	57,000	2,500	59,500	3,000
1985	629/729 3	57,000	2,500	59,500	3,000
1982 to 1984	629	59,000	2,500	61,500	3,000
1980 to 1981	629	65,500	3,000	68,000	3,500
1977 to 1979	614	55,000	3,000	58,000	3,500
1976	624	46,500	2,500	49,000	3,000
1973 to 1975	461	46,500	2,500	49,000	3,000
1972	449/461 4	45,000	2,000	45,000	2,000
1967 to 1971	449	48,000	2,000	48,000	2,000
1963 to 1966	357	33,400	1,200	33,400	1,200
1960 to 1962	333	33,400	1,200	33,400	1,200
1959	330	33,400	1,200	33,400	1,200

1 The ASEC was referred to as the Annual Demographic Survey (ADS) until 2002.

2 The Census Bureau redesigned the CPS following the Census 2000. During phase-in of the new design, housing units from the new and old designs were in the sample.

3 The Census Bureau redesigned the CPS following the 1980 Decennial Census of Population and Housing.

4 The Census Bureau redesigned the CPS following the 1970 Decennial Census of Population and Housing.

The 2013 Annual Social and Economic Supplement. In addition to the basic CPS questions, interviewers asked supplementary questions for the ASEC. They asked these questions of the civilian noninstitutional population and also of military personnel who live in households with at least one other civilian adult. The additional questions covered the following topics:

• Household and family characteristics

• Marital status

• Geographic mobility

• Foreign-born population

• Income from the previous calendar year

• Poverty

• Work status/occupation

• Health insurance coverage

• Program participation

• Educational attainment

Including the basic CPS sample, approximately 98,100 housing units were in sample for the ASEC. About 83,200 housing units were determined to be eligible for interview, and about 75,500 interviews were obtained (see Table 1).

The additional sample for the ASEC provides more reliable data for Hispanic households, non-Hispanic minority households, and non-Hispanic White households with children 18 years or younger. These households were identified for sample from previous months and the following April. For more information about the households eligible for the ASEC, please refer to reference [2].

1Estimation Procedure. This survey’s estimation procedure adjusts weighted sample results to agree with independently derived population estimates of the civilian noninstitutionalized population of the United States and each state (including the District of Columbia). These population estimates, used as controls for the CPS, are prepared monthly to agree with the most current set of population estimates that are released as part of the Census Bureau’s population estimates and projections program.

The population controls for the nation are distributed by demographic characteristics in two ways:

• Age, sex, and race (White alone, Black alone, and all other groups combined).

• Age, sex, and Hispanic origin.

The population controls for the states are distributed by race (Black alone and all other race groups combined), age (0-15, 16-44, and 45 and over), and sex.

The independent estimates by age, sex, race, and Hispanic origin, and for states by selected age groups and broad race categories, are developed using the basic demographic accounting formula whereby the population from the 2010 Decennial Census data is updated using data on the components of population change (births, deaths, and net international migration) with net internal migration as an additional component in the state population estimates.

The net international migration component 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.

1ACCURACY OF THE ESTIMATES

A sample survey estimate has two types of error: sampling and nonsampling. The accuracy of an estimate depends on both types of error. The nature of the sampling error is known given the survey design; the full extent of the nonsampling error is unknown.

Sampling Error. Since the CPS estimates come from a sample, they may differ from figures from an enumeration of the entire population using the same questionnaires, instructions, and enumerators. For a given estimator, the difference between an estimate based on a sample and the estimate that would result if the sample were to include the entire population is known as sampling error. Standard errors, as calculated by methods described in “Standard Errors and Their Use,” are primarily measures of the magnitude of sampling error. However, they may include some nonsampling error.

Nonsampling Error. For a given estimator, the difference between the estimate that would result if the sample were to include the entire population and the true population value being estimated is known as nonsampling error. There are several sources of nonsampling error that may occur during the development or execution of the survey. It can occur because of circumstances created by the interviewer, the respondent, the survey instrument, or the way the data are collected and processed. For example, errors could occur because:

• The interviewer records the wrong answer, the respondent provides incorrect information, the respondent estimates the requested information, or an unclear survey question is misunderstood by the respondent (measurement error).

• Some individuals who should have been included in the survey frame were missed (coverage error).

• Responses are not collected from all those in the sample or the respondent is unwilling to provide information (nonresponse error).

• Values are estimated imprecisely for missing data (imputation error).

• Forms may be lost, data may be incorrectly keyed, coded, or recoded, etc. (processing error).

To minimize these errors, the Census Bureau applies quality control procedures during all stages of the production process including the design of the survey, the wording of questions, the review of the work of interviewers and coders, and the statistical review of reports.

Two types of nonsampling error that can be examined to a limited extent are nonresponse and undercoverage.

Nonresponse. The effect of nonresponse cannot be measured directly, but one indication of its potential effect is the nonresponse rate. For the cases eligible for the 2013 ASEC, the basic CPS household-level nonresponse rate was 10.72 percent. The household-level nonresponse rate for the ASEC was an additional 10.8 percent. These two non-response rates lead to a combined supplement nonresponse rate of 20.4 percent.

Sufficient Partial Interview. A sufficient partial interview is an incomplete interview in which the household or person answered enough of the questionnaire for the supplement sponsor to consider the interview complete. The remaining supplement questions may have been edited or imputed to fill in missing values. Insufficient partial interviews are considered to be nonrespondents. Refer to the supplement overview attachment in the technical documentation for the specific questions deemed critical by the sponsor as necessary to be answered in order to be considered a sufficient partial interview.

1Coverage. 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 March 2013 is estimated to be about 15.0 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.

1The 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.

1A 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 March 2013 CPS coverage ratios by age and sex for certain race and Hispanic groups. The CPS coverage ratios can exhibit some variability from month to month.

Table 2. CPS Coverage Ratios: March 2013
	Total			White only		Black only		Residual race		Hispanic
Age group	All people	Male	Female	Male	Female	Male	Female	Male	Female	Male	Female
0-15	0.85	0.84	0.86	0.87	0.89	0.75	0.76	0.75	0.76	0.81	0.83
16-19	0.84	0.84	0.85	0.85	0.87	0.83	0.81	0.70	0.73	0.79	0.83
20-24	0.74	0.73	0.74	0.76	0.78	0.61	0.61	0.63	0.69	0.71	0.75
25-34	0.81	0.80	0.82	0.82	0.85	0.66	0.72	0.73	0.72	0.75	0.79
35-44	0.87	0.84	0.89	0.87	0.92	0.74	0.83	0.76	0.79	0.77	0.87
45-54	0.88	0.87	0.88	0.88	0.90	0.79	0.80	0.79	0.82	0.80	0.85
55-64	0.90	0.89	0.90	0.90	0.91	0.79	0.87	0.86	0.87	0.81	0.84
65+	0.90	0.91	0.89	0.91	0.90	0.97	0.89	0.81	0.85	0.82	0.82
15+	0.86	0.85	0.86	0.87	0.89	0.76	0.79	0.76	0.78	0.77	0.82
0+	0.85	0.85	0.86	0.87	0.89	0.76	0.79	0.75	0.78	0.78	0.83

Notes: (1) The Residual race group includes cases indicating a single race other than White or Black,

and cases indicating two or more races.

2. Hispanics may be any race. For a more detailed discussion on the use of parameters for

race and ethnicity, please see the “Generalized Variance Parameters” section.

1Comparability of Data. Data obtained from the CPS and other sources are not entirely comparable. This results from differences in interviewer training and experience and in differing survey processes. This is an example of nonsampling variability not reflected in the standard errors. Therefore, caution should be used when comparing results from different sources.

Data users should be careful when comparing the data from this microdata file, which reflects Census 2010-based controls, with microdata files from January 2003 through December 2011, which reflect 2000 census-based controls. Ideally, the same population controls should be used when comparing any estimates. In reality, the use of the same population controls is not practical when comparing trend data over a period of 10 to 20 years. Thus, when it is necessary to combine or compare data based on different controls or different designs, data users should be aware that changes in weighting controls or weighting procedures can create small differences between estimates. See the discussion following for information on comparing estimates derived from different controls or different sample designs.

Microdata files from previous years reflect the latest available census-based controls. Although the most recent change in population controls had relatively little impact on summary measures such as averages, medians, and percentage distributions, it did have a significant impact on levels. For example, use of Census 2010-based controls results in about a 0.2 percent increase from the 2000 census-based controls in the civilian noninstitutionalized population and in the number of families and households. Thus, estimates of levels for data collected in 2012 and later years will differ from those for earlier years by more than what could be attributed to actual changes in the population. These differences could be disproportionately greater for certain population subgroups than for the total population.

Users should also exercise caution because of changes caused by the phase-in of the Census 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 was 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.

1A 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].

Estimation of Median Incomes. The Census Bureau has changed the methodology for computing median income over time. The Census Bureau has computed medians using either Pareto interpolation or linear interpolation. Currently, we are using linear interpolation to estimate all medians. Pareto interpolation assumes a decreasing density of population within an income interval, whereas linear interpolation assumes a constant density of population within an income interval. The Census Bureau calculated estimates of median income and associated standard errors for 1979 through 1987 using Pareto interpolation if the estimate was larger than $20,000 for people or $40,000 for families and households. This is because the width of the income interval containing the estimate is greater than $2,500.

We calculated estimates of median income and associated standard errors for 1976, 1977, and 1978 using Pareto interpolation if the estimate was larger than $12,000 for people or $18,000 for families and households. This is because the width of the income interval containing the estimate is greater than $1,000. All other estimates of median income and associated standard errors for 1976 through 2012 (2013 ASEC) and almost all of the estimates of median income and associated standard errors for 1975 and earlier were calculated using linear interpolation.

Thus, use caution when comparing median incomes above $12,000 for people or $18,000 for families and households for different years. Median incomes below those levels are more comparable from year to year since they have always been calculated using linear interpolation. For an indication of the comparability of medians calculated using Pareto interpolation with medians calculated using linear interpolation, see reference [5].

1Standard Errors and Their Use. 1The 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.

1A 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.

1Standard errors may also be used to perform hypothesis testing, a procedure for distinguishing between population parameters using sample estimates. The most common type of hypothesis is that the population parameters are different. An example of this would be comparing the percentage of men who were part-time workers to the percentage of women who were part-time workers.

1Tests 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.

1The Census Bureau uses 90-percent confidence intervals and 0.10 levels of significance to determine statistical validity. Consult standard statistical textbooks for alternative criteria.

1Estimating Standard Errors. The Census Bureau uses replication methods to estimate the standard errors of CPS estimates. These methods primarily measure the magnitude of sampling error. However, they do measure some effects of nonsampling error as well. They do not measure systematic biases in the data associated with nonsampling error. Bias is the average over all possible samples of the differences between the sample estimates and the true value.

There are two ways to calculate standard errors for the CPS ASEC 2013 microdata file. They are:

• Direct estimates created from replicate weighting methods;

• Generalized variance estimates created from generalized variance function parameters a and b.

While replicate weighting methods provide the most accurate variance estimates, this approach requires more computing resources and more expertise on the part of the user. The Generalized Variance Function (GVF) parameters provide a method of balancing accuracy with resource usage as well as a smoothing effect on standard error estimates across time. For more information on calculating direct estimates, see reference [6]. For more information on generalized variance estimates refer to the “Generalized Variance Parameters” section.

1Generalized 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.

1Experience 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 2013 ASEC supplement. Also, tables are provided that allow the calculation of parameters for prior years and parameters for states and regions. Table 6 provides factors to derive prior year parameters. Tables 7 and 8 contain correlation coefficients for comparing estimates from consecutive years. Tables 9 and 10 provide factors and population controls to derive state and regional parameters.

The basic CPS questionnaire records the race and ethnicity of each respondent. With respect to race, a respondent can be White, Black, Asian, American Indian and Alaskan Native (AIAN), Native Hawaiian and Other Pacific Islander (NHOPI), or combinations of two or more of the preceding. A respondent’s ethnicity can be Hispanic or non-Hispanic, regardless of race.

The generalized variance parameters to use in computing standard errors are dependent upon the race/ethnicity group of interest. Table 3 summarizes the relationship between the race/ethnicity group of interest and the generalized variance parameters to use in standard error calculations.

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
White alone, White AOIC, or White non-Hispanic population	Total or White
Black alone, Black AOIC, or Black non-Hispanic population	Black
Asian alone, Asian AOIC, or Asian non-Hispanic population	Asian, AIAN, NHOPI
AIAN alone, AIAN AOIC, or AIAN non-Hispanic population
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	Black
Two or more races – all other characteristics	Asian, AIAN, NHOPI

Notes: (1) AIAN is American Indian and Alaska Native and NHOPI is Native Hawaiian and Other Pacific Islander.

2. AOIC is an abbreviation for alone or in combination. The AOIC population for a race group of interest includes people reporting only the race group of interest (alone) and people reporting multiple race categories including the race group of interest (in combination).

3. Hispanics may be any race.

4. Two or more races refers to the group of cases self-classified as having two or more races.

Standard Errors of Estimated Numbers. The approximate standard error, s_x, of an estimated number from this microdata file can be obtained by using the formula:

(1)

1Here 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 5,340,000 unemployed females in the civilian labor force. Use Formula (1) and the appropriate parameters from Table 4 to get

Illustration 1
Number of unemployed females in the civilian labor force (x)	5,340,000
a parameter (a)	-0.000031
b parameter (b)	2,782
Standard error	118,000
90-percent confidence interval	5,146,000 to 5,534,000

The standard error is calculated as

1and the 90-percent confidence interval is calculated as 5,340,000 ± 1.645 × 118,000.

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.

Illustration 2

Suppose there were 59,204,000 married-couple family households. Use Formula (1) and the appropriate parameters from Table 5 to get

Illustration 2
Number of married-couple family households (x)	59,204,000
a parameter (a)	-0.000004
b parameter (b)	1,052
Standard error	220,000
90-percent confidence interval	58,842,000 to 59,566,000

The standard error is calculated as

1and the 90-percent confidence interval is calculated as 59,204,000 ± 1.645 × 220,000.

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.

1Standard Errors of Estimated Percentages. The reliability of an estimated percentage, computed using sample data for both numerator and denominator, depends on both the size of the percentage and its base. Estimated percentages are relatively more reliable than the corresponding estimates of the numerators of the percentages, particularly if the percentages are 50 percent or more. When the numerator and denominator of the percentage are in different categories, use the parameter from Table 4 or 5 as indicated by the numerator.

1The approximate standard error, s_y,p, of an estimated percen­tage can be obtained by using the formula:

(2)

1Here y is the total number of people, families, households, or unrelated individuals in the base or denominator of the percentage, p is the percentage 100*x/y (0 ≤ p ≤ 100), and b is the parameter in Table 4 or 5 associated with the characteristic in the numerator of the percentage.

Illustration 3

Suppose there were 207,170,000 out of 236,929,000 adults (aged 18 and older), or 87.4 percent, who graduated from high school. Use Formula (2) and the appropriate parameter from Table 5 to get

Illustration 3
Percentage of adults who are high school graduates (p)	87.4
Base (y)	236,929,000
b parameter (b)	1,206
Standard error	0.07
90-percent confidence interval	87.3 to 87.5

The standard error is calculated as

1The 90-percent confidence interval of the percentage of adults who graduated from high school is calculated as 87.4 ± 1.645 × 0.07.

1Standard Errors of Estimated Differences. The standard error of the difference between two sample estimates is approximately equal to

(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. Tables 7 and 8 contain the correlation coefficient, r, for CPS year-to-year comparisons. The correlations were derived for income, poverty, and health insurance estimates, but they can be used for other types of estimates where the year-to-year correlation between identical households is high. For making other comparisons, assume that r equals zero. Making this assumption will result in accurate estimates of standard errors for the difference between two estimates 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 4

Suppose there were 21,187,000 men over age 24 who were never married and 10,846,000 men over age 24 who were divorced. The apparent difference is 10,341,000. Use Formulas (1) and (3) with r = 0 and the appropriate parameters from Table 5 to get

Illustration 4
	Never married (x1)	Divorced (x2)	Difference
Number of males over age 24	21,187,000	10,846,000	10,341,000
a parameter (a)	-0.000009	-0.000009	-
b parameter (b)	2,652	2,652	-
Standard error	228,000	166,000	282,000
90-percent confidence interval	20,812,000 to 21,562,000	10,573,000 to 11,119,000	9,877,000 to 10,805,000

The standard error of the difference is calculated as

1The 90-percent confidence interval around the difference is calculated as 10,341,000 ± 1.645 × 282,000. Since this interval does not include zero, we can conclude with 90 percent confidence that the number of never married men over age 24 was higher than the number of divorced men over age 24.

Illustration 5

Suppose that the percentage of people without health insurance coverage for 2012 was 15.4 percent out of 311,116,000 people, and the percentage of people without health insurance coverage for 2011 was 15.7 percent out of 308,827,000 people. The apparent difference is 0.3 percent. Use Formulas (2) and (3) and the appropriate parameter, factor, and correlation coefficient from Tables 5, 6, and 7 to get

Illustration 5
	2011 (x1)	2012 (x2)	Difference
Percentage of people without health insurance (p)	15.7	15.4	0.3
Base	308,827,000	311,116,000	-
b parameter (b)	2,652*	2,652	-
Correlation coefficient (r)	-	-	0.30
Standard error	0.11	0.11	0.13
90-percent confidence interval	15.5 to 15.9	15.2 to 15.6	0.1 to 0.5

*This parameter is calculated by multiplying the year factor for 2010 from Table 6, 1.0, by the current b parameter.

The standard error of the difference is calculated as

1and the 90-percent confidence interval around the difference is calculated as 0.3 ± 1.645 × 0.13. Since this interval does not include zero, we can conclude with 90 percent confidence that the percentage of people without health insurance in 2011 is statistically different than the percentage of people without health insurance in 2012.

Standard Errors of Estimated Ratios. Certain estimates may be calculated as the ratio of two numbers. Compute the standard error of a ratio, x/y, using

(4)

The standard error of the numerator, s_x, and that of the denominator, s_y, may be calculated using formulas described earlier. In Formula (4), r represents the correlation between the numerator and the denominator of the estimate.

For one type of ratio, the denominator is a count of families or households and the numerator is a count of people in those families or households with a certain characteristic. If there is at least one person with the characteristic in every family or household, use 0.7 as an estimate of 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 and the family poverty rate. 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 (4) by 100 or 1,000, respectively, to obtain the standard error.

Illustration 6

Suppose there were 12,857,000 males working part-time and 21,186,000 females working part-time. The ratio of males working part-time to females working part-time would be 0.607, or 60.7 percent. Use Formulas (1) and (4) with r = 0 and the appropriate parameters from Table 4 to get

Illustration 6
	Males (x)	Females (y)	Ratio
Number who work part- time	12,857,000	21,186,000	0.607
a parameter (a)	-0.000032	-0.000031	-
b parameter (b)	2,971	2,782	-
Standard error	181,000	212,000	0.011
90-percent confidence interval	12,559,000 to 13,155,000	20,837,000 to 21,535,000	0.590 to 0.624

The standard error is calculated as

and the 90-percent confidence interval is calculated as 0.607 ± 1.645 × 0.011.

Illustration 7

Suppose that the number of families below the poverty level was 9,520,000 and the total number of families was 80,944,000. The ratio of families below the poverty level to the total number of families would be 0.118 or 11.8 percent. Use the appropriate parameters from Table 5 and Formulas (1) and (4) with r = 0 to get

Illustration 7
	In poverty (x)	Total (y)	Ratio (in percent)
Number of families	9,520,000	80,944,000	11.8
a parameter (a)	0.000052	-0.000004	-
b parameter (b)	1,243	1,052	-
Standard error	129,000	243,000	0.16
90-percent confidence Interval	9,308,000 to 9,732,000	80,544,000 to 81,344,000	11.5 to 12.1

The standard error is calculated as

and the 90-percent confidence interval of the percentage is calculated as 11.8 ± 1.645 × 0.16.

Standard Errors of Estimated Medians. The sampling variability of an estimated median depends on the form of the distribution and the size of the base. One can approximate the reliability of an estimated median by determining a confidence interval about it. (See “Standard Errors and Their Use” for a general discussion of confidence intervals.)

Estimate the 68-percent confidence limits of a median based on sample data using the following procedure:

1. Using Formula (2) and the base of the distribution, calculate the standard error of 50 percent.

2. Add to and subtract from 50 percent the standard error determined in step 1. These two numbers are the percentage limits corresponding to the 68-percent confidence interval about the estimated median.

3. Using the distribution of the characteristic, determine upper and lower limits of the

68-percent confidence interval by calculating values corresponding to the two points established in step 2.

Note: The percentage limits found in step 2 may or may not fall in the same characteristic distribution interval.

Use the following formula to calculate the upper and lower limits:

(5)

where

X_p = estimated upper and lower bounds for the confidence interval

(0 ≤ p ≤ 1). For purposes of calculating the confidence interval, p takes on the values determined in step 2. Note that X_p estimates the median when p = 0.50.

N = for distribution of numbers: the total number of units (people,

households, etc.) for the characteristic in the distribution.

= for distribution of percentages: the value 100.

p = the values obtained in Step 2.

A₁, A₂ = the lower and upper bounds, respectively, of the interval

containing X_p.

N₁, N₂ = for distribution of numbers: the estimated number of units

(people, households, etc.) with values of the characteristic less than or equal to A₁ and A₂, respectively.

= for distribution of percentages: the estimated percentage of units (people, households, etc.) having values of the characteristic less than or equal to A₁ and A₂, respectively.

4. Divide the difference between the two points determined in step 3 by 2 to obtain the standard error of the median.

Note: Median incomes and their standard errors calculated as below may differ from those in published tables and reports showing income, since narrower income intervals were used in those calculations.

1Illustration 8

Suppose there were 122,459,000 households in 2013, and their income was distributed in the following way:

Illustration 8
Income level	Number of households	Cumulative number of households	Cumulative percent of households
Under $5,000	4,204,000	4,204,000	3.43%
$5,000 to $9,999	4,729,000	8,933,000	7.29%
$10,000 to $14,999	6,983,000	15,916,000	13.00%
$15,000 to $24,999	14,288,000	30,204,000	24.66%
$25,000 to $34,999	13,094,000	43,298,000	35.36%
$35,000 to $49,999	16,633,000	59,931,000	48.94%
$50,000 to $74,999	21,419,000	81,350,000	66.43%
$75,000 to $99,999	14,284,000	95,634,000	78.09%
$100,000 and over	26,825,000	122,459,000	100.00%

1. Using Formula (2) with b = 1,140, the standard error of 50 percent on a base of 122,459,000 is about 0.15 percent.

2. To obtain a 68-percent confidence interval on an estimated median, add to and subtract from 50 percent the standard error found in step 1. This yields percentage limits of 49.85 and 50.15.

3. The lower and upper limits for the interval in which the percentage limits falls are $35,000 and $50,000, respectively.

Then the estimated numbers of households with an income less than or equal to $35,000 and $50,000 are 43,298,000 and 59,931,000, respectively.

Using Formula (5), the lower limit for the confidence interval of the median is found to be about

Similarly, the upper limit is found to be about

Thus, a 68-percent confidence interval for the median income for households is from

$51,005 to $51,337.

4. The standard error of the median is, therefore,

Standard Errors of Averages for Grouped Data. 1The formula used to estimate the standard error of an average for grouped data is

(6)

In this formula, y is the size of the base of the distribution and b is the parameter from Table 4 or 5. The variance, S², is given by the following formula:

(7)

where , the average of the distribution, is estimated by

(8)

where

c = the number of groups; i indicates a specific group, thus taking on values 1 through c.

p_i = estimated proportion of households, families, or people whose values for the characteristic being considered fall in group i.

= (Z_Li + Z_Ui)/2 where Z_Li and Z_Ui are the lower and upper interval boundaries, respectively, for group i. is assumed to be the most representative value for the characteristic of households, families, or people in group i. If group c is open-ended, i.e., no upper interval boundary exists, use a group approximate average value of

(9)

Illustration 9

Suppose that there were 9,520,000 families in poverty and that the distribution of the income deficit (the difference between their family income and poverty threshold) for all families in poverty was

Income deficit	Number of families in poverty	Percentage of families in poverty (pi)	Average income deficit
Under $1000	633,000	6.6	500
$1000 to $2,499	926,000	9.7	2,250
$2,500 to $4,999	1,470,000	15.4	5,000
$5,000 to $7,499	1,281,000	13.5	8,750
$7,500 to $9,999	1,040,000	10.9	12,500
$10,000 to $12,499	959,000	10.1	16,250
$12,500 to $14,999	873,000	9.2	20,000
$15,000 and over	2,339,000	24.6	22,500
Total	9,521,000*	100.0

*There may be a difference due to rounding

Using Formula (8),

and Formula (7),

Use the appropriate parameter from Table 5 and Formula (6) to get

Illustration 9
Average income deficit for families in poverty	$12,581
Variance (S2)	61,451,000
Base (y)	9,520,000
b parameter (b)	1,243
Standard error	$90
90-percent confidence interval	$12,433 to $12,729

The standard error is calculated as

and the 90-percent confidence interval is calculated as $12,581 ± 1.645 × $90.

Standard Errors of Estimated Per Capita Deficits. Certain average values in reports associated with the ASEC data represent the per capita deficit for households of a certain class. The average per capita deficit is approximately equal to

(10)

where

h = number of households in the class.

m = average deficit for households in the class.

p = number of people in households in the class.

x = average per capita deficit of people in households in the class.

To approximate standard errors for these averages, use the formula

(11)

In Formula (11), r represents the correlation between p and h.

For one type of average, the class represents households containing a fixed number of people. For example, h could be the number of 3-person households. In this case, there is an exact correlation between the number of people in households and the number of households. Therefore, r = 1 for such households. For other types of averages, the class represents households of other demographic types, for example, households in distinct regions, households in which the householder is of a certain age group, and owner-occupied and tenant-occupied households. In this and other cases in which the correlation between p and h is not perfect, use 0.7 as an estimate of r.

Illustration 10

Suppose there were 33,198,000 people living in families in poverty, and 9,520,000 families in poverty, with an average deficit income for families in poverty of $12,581 with a standard error of $90 (from Illustration 9). Use Formulas (1), (10), and (11) and the appropriate parameters from Table 5 and r = 0.7 to get

Illustration 10
	Number (h)	Number of people (p)	Average income deficit (m)	Average per capita deficit (x)
Value for families in poverty	9,520,000	33,198,000	$12,581	$3,608
a parameter (a)	+0.000052	-0.000017	-	-
b parameter (b)	1,243	5,282	-	-
Correlation (r)	-	-	-	0.7
Standard Error	129,000	396,000	$90	$44
90-percent confidence interval	9,308,000 to 9,732,000	32,547,000 to 33,849,000	$12,433 to $12,729	$3,536 to $3,680

The estimate of the average per capita deficit is calculated as

and the standard error is calculated as

The 90-percent confidence interval is calculated as $3,608  1.645  $44.

Accuracy of State Estimates. 1The redesign of the CPS following the 1980 census provided an opportunity to increase efficiency and accuracy of state data. All strata are now defined within state boundaries. The sample is allocated among the states to produce state and national estimates with the required accuracy while keeping total sample size to a minimum. Improved accuracy of state data was achieved with about the same sample size as in the 1970 design.

Since the CPS is designed to produce both state and national estimates, the proportion of the total population sampled and the sampling rates differ among the states. In general, the smaller the population of the state the larger the sampling proportion. For example, in Vermont approximately 1 in every 250 households is sampled each month. In New York the sample is about 1 in every 2,000 households. Nevertheless, the size of the sample in New York is four times larger than in Vermont because New York has a larger population.

Note: The Census Bureau recommends the use of 3-year averages to compare estimates across states and 2-year averages to evaluate changes in state estimates over time. See “Standard Errors of Data for Combined Years” and “Standard Errors of Differences of 2-

Year Averages.” The Census Bureau also recommends the American Community Survey microdata file as the preferred source for income and poverty state data in years 2006 (2005 estimates) to the present.

Standard Errors for State Estimates. The standard error for a state may be obtained by determining new state-level a and b parameters and then using these adjusted parameters in the standard error formulas mentioned previously. To determine a new state-level b parameter (b_state), multiply the b parameter from Table 4 or 5 by the state factor from Table 9. To determine a new state-level a parameter (a_state), use the following:

(1) If the a parameter from Table 4 or 5 is positive, multiply it by the state factor from Table 9.

(2) If the a parameter in Table 4 or 5 is negative, calculate the new state-level a parameter as follows:

(12)

where POP_state is the state population found in Table 9.

Illustration 11

Suppose there were 15,061,000 people living in New York state who were born in the United States. Use Formulas (1) and (12) and the appropriate parameter, factor, and population from Tables 5 and 9 to get

Illustration 11
Number of people in NY who were born in the U.S. (x)	15,061,000
b parameter (b)	2,652
New York state factor	1.17
State population	19,377,966
State a parameter (astate)	-0.000160
State b parameter (bstate)	3,103
Standard error	102,000

Obtain the state-level b parameter by multiplying the b parameter, 2,652, by the state factor, 1.17. This gives b_state = 2,652 × 1.17 = 3,103. Obtain the needed state-level a parameter by

The standard error of the estimate of the number of people in New York state who were born in the United States can then be found by using Formula (1) and the new state-level a and b parameters, -0.000160 and 3,103, respectively. The standard error is given by

Standard Errors of Regional Estimates. To compute standard errors for regional estimates, follow the steps for computing standard errors for state estimates found in “Standard Errors for State Estimates” using the regional factors and populations found in Table 10.

Illustration 12

Suppose there were 19,106,000 of 115,957,000 people, or 16.5 percent, living in poverty in the South. Use Formulas (2) and (12) and the appropriate parameter, factor, and population from Tables 5 and 10 to get

Illustration 12
Poverty rate in the South (p)	16.5
Base (y)	115,957,000
b parameter (b)	5,282
South regional factor	1.08
Regional b parameter (bregion)	5,705
Standard error	0.26
90-percent confidence interval	16.1 to 16.9

Obtain the region-level b parameter by multiplying the b parameter, 5,282, by the South regional factor, 1.08. This gives b_region = 5,282 × 1.08 = 5,705.

The standard error of the estimate of the poverty rate for people living in the South can then be found by using Formula (2) and the new region-level b parameter, 5,705. The standard error is given by

and the 90-percent confidence interval of the poverty rate for people living in the South is calculated as 16.5  1.645  0.26.

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

Use the following formula to determine a new state group factor:

(13)

where POP_i and state factor_i are the population and factor for state i from Table 9. To obtain a new state group b parameter (b_{state group}), multiply the b parameter from Table 4 or 5 by the state factor obtained by Formula (13). To determine a new state group a parameter (a_{state group}), use the following:

(1) If the a parameter from Table 4 or 5 is positive, multiply it by the state group factor determined by Formula (13).

(2) If the a parameter in Table 4 or 5 is negative, calculate the new state group a parameter as follows:

(14)

Illustration 13

Suppose the state group factor for the state group Illinois-Indiana-Michigan was required. The appropriate factor would be

Standard Errors of Data for Combined Years. Sometimes estimates for multiple years are combined to improve precision. For example, suppose is an average derived from n consecutive years’ data, i.e., , where the x_i are the estimates for the individual years. Use the formulas described previously to estimate the standard error, , of each year’s estimate. Then the standard error of is

(15)

where

(16)

and are the standard errors of the estimates x_i. Tables 7 and 8 contain the correlation coefficients, r, for the correlation between consecutive years i and i+1. Correlation between nonconsecutive years is zero. The correlations were derived for income and poverty estimates, but they can be used for other types of estimates where the year-to-year correlation between identical households is high.

The Census Bureau recommends the use of 3-year average estimates for certain small population subgroups⁴ (see also “Accuracy of State Estimates.”) Two-year moving averages are recommended for these small population subgroups for comparisons across adjacent years (see “Standard Errors of Differences of 2-Year Averages.”)

Illustration 14

Suppose the 2010-2012 3-year average percentage of the AIAN population without health insurance was 27.5. Suppose the percentages and bases for 2010, 2011, and 2012 were 27.2, 27.4, and 28.0 percent and 3,093,000, 3,216,000, and 3,475,000 respectively. Use the appropriate parameters, factors, and correlation coefficients from Tables 5, 6, and 7 and Formulas (2), (15), and (16) to get

Illustration 14
	2010	2011	2012	2010-2012 avg
Percentage of AIAN without health insurance (p)	27.2	27.4	28.0	27.5
Base (y)	3,093,000	3,216,000	3,475,000	-
b parameter (b)	3,809*	3,809*	3,809	-
Correlation (r)	-	-	-	0.30, 0.30
Standard error	1.56	1.53	1.49	1.04
90-percent confidence interval	24.6 to 29.8	24.9 to 29.9	25.5 to 30.5	25.8 to 29.2

*These parameters are calculated by multiplying the year factors from Table 6 by the current parameter.

The standard error of the 3-year average is calculated as

where

The 90-percent confidence interval for the 3-year average percentage of the AIAN population without health insurance is 27.5  1.645  1.04.

Standard Errors of Differences of 2-Year Averages. Comparing two non-overlapping 2-year averages also improves precision for comparisons across years. Use the formulas described previously to estimate the standard error, s_xi, of each year’s estimate, x_i, and the standard error, , of each average, . Then the standard error of the difference of the two non-overlapping 2-year averages, , is

(17)

Illustration 15

Suppose that you want to calculate the standard error of the difference between the 2009, 2010 and 2011, 2012 averages of the percent of people in California without health insurance. Use the following information along with Tables 5, 6, 9 and Formula (2) to get

	20091	2010	2011	2012
Percentage of people in CA without health insurance (p)	19.3	19.4	19.7	17.9
Base (y)	36,794,000	37,292,000	37,634,000	37,985,000
b parameter (b)	2,6522	2,6522	2,6522	2,652
California state factor	1.25	1.25	1.25	1.25
State b parameter (bstate)	3,315	3,315	3,315	3,315
Standard error3	0.37	0.37	0.37	0.36

¹The data for 2009 were revised to reflect the results of enhancements to the editing process. See <http://www.census.gov/hhes/www/hlthins/data/revhlth/index.html>

²These parameters are calculated by multiplying the year factors from Table 6 by the current parameter.

³See “Standard Errors of State Estimates” for instructions and illustrations on calculating state standard errors.

Use this information, Formulas (15), (16), and (17), and the appropriate correlation coefficient from Table 7 to get

Illustration 15
	2009, 2010	2010, 2011	2011, 2012	avg(2011, 2012) -avg(2009, 2010)
Average percent of people in CA without health insurance ( )	19.4	-	18.8	-0.6
Correlation coefficient (r)	0.30	0.30	0.30	-
Standard error	0.30*	-	0.29*	0.39
90-percent confidence interval	18.9 to 19.9	-	18.3 to 19.3	-1.2 to 0.0

*See “Standard Errors of Data for Combined Years” for instructions and illustrations on calculating these standard errors.

The standard error of the difference of the two 2-year averages is calculated as

and the 90-percent confidence interval around the difference of the 2-year averages is calculated as -0.6  1.645  0.39. Since this interval does not include zero, we can conclude with 90 percent confidence that the 2011-2012 average percent of people in California without health insurance was lower than the 2009-2010 average percent of people in California without health insurance.

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.

Table 4. Parameters for Computation of Standard Errors for Labor Force Characteristics: March 2013
Characteristic	a	b
Total or White
Civilian labor force, employed	-0.000016	3,068
Not in labor force	-0.000009	1,833
Unemployed	-0.000016	3,096
Civilian labor force, employed, not in labor force, and unemployed
Men	-0.000032	2,971
Women	-0.000031	2,782
Both sexes, 16 to 19 years	-0.000022	3,096
Black
Civilian labor force, employed, not in labor force, and unemployed	-0.000151	3,455
Men	-0.000311	3,357
Women	-0.000252	3,062
Both sexes, 16 to 19 years	-0.001632	3,455
Hispanic, may be of any race
Civilian labor force, employed, not in labor force, and unemployed	-0.000141	3,455
Men	-0.000253	3,357
Women	-0.000266	3,062
Both sexes, 16 to 19 years	-0.001528	3,455
Asian, American Indian and Alaska Native, Native Hawaiian and Other Pacific Islander
Civilian labor force, employed, not in labor force, and unemployed	-0.000346	3,198
Men	-0.000729	3,198
Women	-0.000659	3,198
Both sexes, 16 to 19 years	-0.004146	3,198

NOTES: (1) These parameters are to be applied to basic CPS monthly labor force estimates.

2. The Total or White, Black, and Asian, AIAN, NHOPI parameters are to be used for both alone and in combination race group estimates.

3. For nonmetropolitan characteristics, multiply the a and b parameters by 1.5. If the characteristic of interest is total state population, not subtotaled by race or ethnicity, the a and b parameters are zero.

4. For foreign-born and noncitizen characteristics for Total and White, the a and b parameters should be multiplied by 1.3. No adjustment is necessary for foreign-born and noncitizen characteristics for Black, Hispanic, and Asian, AIAN, NHOPI parameters.

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

Table 5. Parameters for Computation of Standard Errors for People and Families: 2013 ASEC
Characteristics	Total or White		Black		Asian, AIAN, & NHOPI		Hispanic
	a	b	a	b	a	b	a	b
PEOPLE
Educational attainment	-0.000005	1,206	-0.000026	1,364	-0.000051	1,101	-0.000021	922
Employment	-0.000013	3,068	-0.000068	3,455	-0.000154	3,198	-0.000093	3,455
People by family income	-0.000010	2,494	-0.000054	2,855	-0.000132	2,855	-0.000067	2,855
Income characteristics
Total	-0.000005	1,249	-0.000027	1,430	-0.000066	1,430	-0.000033	1,430
Male	-0.000010	1,249	-0.000059	1,430	-0.000139	1,430	-0.000066	1,430
Female	-0.000010	1,249	-0.000051	1,430	-0.000126	1,430	-0.000067	1,430
Age
15 to 24	-0.000029	1,249	-0.000125	1,430	-0.000295	1,430	-0.000103	1,430
25 to 44	-0.000015	1,249	-0.000075	1,430	-0.000169	1,430	-0.000089	1,430
45 to 64	-0.000015	1,249	-0.000090	1,430	-0.000238	1,430	-0.000148	1,430
65 and over	-0.000029	1,249	-0.000234	1,430	-0.000609	1,430	-0.000445	1,430
Health insurance	-0.000009	2,652	-0.000056	3,809	-0.000134	3,809	-0.000072	3,809
Marital status, household and family
Some household members	-0.000009	2,652	-0.000056	3,809	-0.000134	3,809	-0.000072	3,809
All household members	-0.000010	3,222	-0.000082	5,617	-0.000197	5,617	-0.000106	5,617
Mobility (movers)
Educational attainment, labor force, Marital status, HH, family, and income	-0.000005	1,460	-0.000021	1,460	-0.000051	1,460	-0.000027	1,460
US, county, state, region, or MSA	-0.000013	3,965	-0.000058	3,965	-0.000139	3,965	-0.000075	3,965
Below poverty
Total	-0.000017	5,282	-0.000077	5,282	-0.000185	5,282	-0.000099	5,282
Male	-0.000035	5,282	-0.000163	5,282	-0.000384	5,282	-0.000197	5,282
Female	-0.000033	5,282	-0.000146	5,282	-0.000359	5,282	-0.000200	5,282
Age
Under 15	-0.000066	4,072	-0.000241	4,072	-0.000529	4,072	-0.000256	4,072
Under 18	-0.000050	4,072	-0.000187	4,072	-0.000432	4,072	-0.000208	4,072
15 and over	-0.000021	5,282	-0.000101	5,282	-0.000244	5,282	-0.000123	5,282
15 to 24	-0.000046	1,998	-0.000174	1,998	-0.000412	1,998	-0.000144	1,998
25 to 44	-0.000025	1,998	-0.000104	1,998	-0.000236	1,998	-0.000124	1,998
45 to 64	-0.000024	1,998	-0.000126	1,998	-0.000333	1,998	-0.000206	1,998
65 and over	-0.000047	1,998	-0.000327	1,998	-0.000851	1,998	-0.000621	1,998
Unemployment	-0.000013	3,096	-0.000068	3,455	-0.000154	3,198	-0.000093	3,455
FAMILIES, HOUSEHOLDS, OR UNRELATED INDIVIDUALS
Income	-0.000005	1,140	-0.000024	1,245	-0.000057	1,245	-0.000029	1,245
Marital status, HH and family, educational
attainment, population by age/sex	-0.000004	1,052	-0.000018	952	-0.000044	952	-0.000022	952
Poverty	0.000052	1,243	0.000052	1,243	0.000052	1,243	0.000052	1,243

NOTES: (1) These parameters are to be applied to the 2013 Annual Social and Economic Supplement data.

(2) AIAN, NHOPI are American Indian and Alaska Native, Native Hawaiian and Other Pacific Islander, respectively.

(3) Hispanics may be any race. For a more detailed discussion on the use of parameters for race and ethnicity, please see the “Generalized Variance Parameters” section.

(4) The Total or White, Black, and Asian, AIAN, NHOPI parameters are to be used for both alone and in-combination race group estimates.

(5) For nonmetropolitan characteristics, multiply the a and b parameters by 1.5. If the characteristic of interest is total state population, not subtotaled by race or ancestry, the a and b parameters are zero.

(6) For foreign-born and noncitizen characteristics for Total and White, the a and b parameters should be multiplied by 1.3. No adjustment is necessary for foreign-born and noncitizen characteristics for Black, Asian, AIAN, NHOPI, and Hispanic.

(7) For the group self-classified as having two or more races, use the Asian, AIAN, NHOPI parameters for all characteristics except employment, unemployment, and educational attainment, in which case use Black parameters.

(8) To obtain parameters prior to 2012, multiply the parameter from this table by the appropriate year factor in Table 6.

Table 6. CPS Year Factors: ASEC 1947 to 2012
Data Collection Period	Total or White	Black		Hispanic
	a and b	a and b	a*	a and b
2003 – 2012	1.00	1.00	1.00	1.00
2001 (expanded) – 2002	1.00	1.00	1.53	1.00
1996 – 2001 (basic)	1.97	1.97	3.00	1.97
1990 – 1995	1.82	1.82	2.78	1.82
1989	2.02	2.02	3.09	2.12
1985 – 1988	1.70	1.70	2.60	1.70
1982 – 1984	1.70	1.70	2.60	2.38
1973 – 1981	1.52	1.52	2.32	2.13
1967 – 1972	1.52	1.52	2.32	3.58
1957 – 1966	2.28	2.28	3.48	5.38
1947 – 1956	3.42	3.42	5.22	8.07

NOTES: (1) Blacks have separate factors for the a and b parameter factors due to the new race

definitions and how they affected the population control totals.

(2) Use the asterisked factor to get a parameters for all estimates of the Black population

except those for Black families, households, and unrelated individuals in poverty.

(3) For races not listed, use the factor for Total or White.

(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.

Table 7. CPS Year-to-Year Correlation Coefficients for Income and Health Insurance Characteristics: 1961 to 2013
Characteristics	1961-2001 (basic) or 2001 (expanded)-2013		2000 (basic)- 2001 (expanded)
	People	Families	People	Families
Total	0.30	0.35	0.19	0.22
White	0.30	0.35	0.20	0.23
Black	0.30	0.35	0.15	0.18
Other	0.30	0.35	0.15	0.17
Hispanic	0.45	0.55	0.36	0.28

NOTES: (1) Correlation coefficients are not available for income data before 1961.

(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.

(3) These correlation coefficients are for comparisons of consecutive years. For comparisons of

nonconsecutive years, assume the correlation is zero.

(4) For households and unrelated individuals, use the correlation coefficient for families

Table 8. CPS Year-to-Year Correlation Coefficients for Poverty Characteristics: 1971 to 2013
Characteristics	1973-84, 1985-2001 (basic) or 2001 (expanded)-2013		2000 (basic)- 2001 (expanded)		1984-1985		1972-1973		1971-1972
	People	Families	People	Families	People	Families	People	Families	People	Families
Total	0.45	0.35	0.29	0.22	0.39	0.30	0.15	0.14	0.31	0.28
White	0.35	0.30	0.23	0.20	0.30	0.26	0.14	0.13	0.28	0.25
Black	0.45	0.35	0.23	0.18	0.39	0.30	0.17	0.16	0.35	0.32
Other	0.45	0.35	0.22	0.17	0.30	0.30	0.17	0.16	0.35	0.32
Hispanic	0.65	0.55	0.52	0.40	0.56	0.47	0.17	0.16	0.35	0.32

NOTES: (1) Correlation coefficients are not available for income data before 1961.

(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.

(3) These correlation coefficients are for comparisons of consecutive years. For comparisons of

nonconsecutive years, assume the correlation is zero.

(4) For households and unrelated individuals, use the correlation coefficient for families

Table 9. Factors and Populations for State Standard Errors and Parameters: 2013 ASEC
State	Factor	Population	State	Factor	Population
Alabama	1.05	4,756,374	Montana	0.24	993,600
Alaska	0.18	706,639	Nebraska	0.46	1,835,650
Arizona	1.23	6,488,907	Nevada	0.67	2,741,759
Arkansas	0.68	2,904,963	New Hampshire	0.34	1,306,685
California	1.25	37,731,658	New Jersey	1.12	8,781,807
Colorado	1.20	5,131,065	New Mexico	0.58	2,050,323
Connecticut	0.88	3,543,300	New York	1.17	19,377,966
Delaware	0.22	906,400	North Carolina	1.11	9,584,727
District of Columbia	0.18	631,790	North Dakota	0.16	693,972
Florida	1.12	19,143,761	Ohio	1.09	11,379,156
Georgia	1.08	9,754,357	Oklahoma	0.91	3,751,524
Hawaii	0.29	1,343,938	Oregon	1.01	3,877,412
Idaho	0.36	1,581,082	Pennsylvania	1.09	12,588,108
Illinois	1.13	12,704,599	Rhode Island	0.30	1,035,005
Indiana	1.08	6,455,003	South Carolina	1.06	4,645,655
Iowa	0.77	3,040,191	South Dakota	0.17	821,708
Kansas	0.73	2,833,766	Tennessee	1.08	6,384,216
Kentucky	1.05	4,292,802	Texas	1.28	25,813,088
Louisiana	1.05	4,511,809	Utah	0.54	2,852,914
Maine	0.39	1,315,125	Vermont	0.18	619,131
Maryland	1.13	5,817,198	Virginia	1.08	8,014,454
Massachusetts	1.06	6,594,007	Washington	1.15	6,832,790
Michigan	1.09	9,779,602	West Virginia	0.39	1,827,036
Minnesota	1.07	5,341,788	Wisconsin	1.10	5,664,400
Mississippi	0.71	2,919,583	Wyoming	0.15	571,888
Missouri	1.11	5,922,781

NOTES: (1) The state population counts in this table are for the 0+ population.

(2) For foreign-born and noncitizen characteristics for Total and White, the a and b parameters should be multiplied by 1.3. No adjustment is necessary for foreign-born and noncitizen characteristics for Black, Asian, AIAN, NHOPI, and Hispanic.

Table 10. Factors and Populations for Regional Standard Errors and Parameters: 2013 ASEC
Region	Factor	Population
Midwest	1.03	66,472,616
Northeast	1.05	55,161,134
South	1.08	115,659,737
West	1.10	72,903,975

NOTES: (1) The state population counts in this table are for the 0+ population.

(2) For foreign-born and noncitizen characteristics for Total and White, the a and b parameters should be multiplied by 1.3. No adjustment is necessary for foreign-born and noncitizen characteristics for Black, Asian, AIAN, NHOPI, and Hispanic.

References

[1] Bureau of Labor Statistics. 2004. Employment and Earnings. “Redesign of the Sample for the Current Population Survey.” Volume 51 Number 11, May 2004. Washington, DC: Government Printing Office. pp 4-6.

[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/tp66.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)

[4] U.S. Census Bureau. 1993. Money Income of Households, Families, and Persons in the United States: 1992. Current Population Reports, P60-184. Washington, DC: Government Printing Office. (http://www2.census.gov/prod2/popscan/p60-184.pdf)

[5] U.S. Census Bureau. 1978. Money Income in 1976 of Families and Persons in the United States. Current Population Reports, P60-114. Washington, DC: Government Printing Office. (http://www2.census.gov/prod2/popscan/p60-114.pdf)

[6] U.S. Census Bureau, July 15, 2009, “Estimating ASEC Variances with Replicate Weights Part I: Instructions for Using the ASEC Public Use Replicate Weight File to Create ASEC Variance Estimates.” (http://www.bls.census.gov/cps_ftp.html#cpsmarch )

1 For detailed information on the 2000 sample redesign, please see reference [1].

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

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

4 Estimates of characteristics of the American Indian and Alaska Native (AIAN) and Native Hawaiian and Other Pacific Islander (NHOPI) populations based on a single-year sample would be unreliable due to the small size of the sample that can be drawn from either population. Accordingly, such estimates are based on multiyear averages.