Source and Accuracy Statement

Under the estimating methods used in the CPS, all of the results for a given month become available simultaneously and are based on returns from the entire panel of respondents. The estimation procedure involves weighting the data from each sample person by the inverse of the probability of the person being in the sample. This gives a rough measure of the number of actual persons that the sample person represents. Since 1985, most sample persons within the same State have had the same probability of selection. Some selection probabilities may differ within a State due to the sample design or for operational reasons. Field subsampling, for example, which is carried out when areas selected for the sample are found to contain many more households than expected, may cause probabilities of selection to differ for some sample areas within a State. Through a series of estimation steps (outlined below), the selection probabilities are adjusted for noninterviews and survey undercoverage; data from previous months are incorporated into the estimates through the composite estimation procedure.

1. Noninterview adjustment.   The weights for all interviewed households are adjusted to account for occupied sample households for which no information was obtained because of absence, impassable roads, refusals, or unavailability of the respondents for other reasons. This noninterview adjustment is made separately for clusters of similar sample areas that are usually, but not necessarily, contained within a State. Similarity of sample areas is based on Metropolitan Statistical Area (MSA) status and size. Within each cluster, there is a further breakdown by residence. Each MSA cluster is split by "central city" and "balance of the MSA." Each non-MSA cluster is split by "urban" and "rural" residence categories. The proportion of sample households not interviewed varies from 7 to 8 percent, depending on weather, vacation, etc.

2. Ratio estimates.   The distribution of the population selected for the sample may differ somewhat, by chance, from that of the population as a whole in such characteristics as age, race, sex, and State of residence. Because these characteristics are closely correlated with labor force participation and other principal measurements made from the sample, the survey estimates can be substantially improved when weighted appropriately by the known distribution of these population characteristics. This is accomplished through two stages of ratio adjustment, as follows:

a. First-stage ratio estimation.   The purpose of the first-stage ratio adjustment is to reduce the contribution to variance that results from selecting a sample of PSUs rather than drawing sample households from every PSU in the Nation. This adjustment is made to the CPS weights in two race cells: Black and nonBlack; it is applied only to PSUs that are not self-representing and for those States that have a substantial number of Black households. The procedure corrects for differences that existed in each State cell at the time of the 1990 census between 1) the race distribution of the population in sample PSUs and 2) the race distribution of all PSUs. (Both 1 and 2 exclude self-representing PSUs.)

b. Second-stage ratio estimation.   This procedure substantially reduces the variability of estimates and corrects, to some extent, for CPS undercoverage. The CPS sample weights are adjusted to ensure that sample-based estimates of population match independent population controls. Three sets of controls are used:

1) 51 State controls of the civilian noninstitutional population 16 years of age and older,

2) National civilian noninstitutional population controls for 14 Hispanic and 5 non-Hispanic age-sex categories,

3) National civilian noninstitutional population controls for 66 White, 42 Black, and 10 "Other" age-sex categories.

The independent population controls are prepared by projecting forward the resident population as enumerated on April 1, 1990. The projections are derived by updating demographic census data with information from a variety of other data sources that account for births, deaths, and net migration. Estimated numbers of resident Armed Forces personnel and institutionalized persons reduce the resident population to the civilian noninstitutional population. Estimates of net census undercount, determined from the Post Enumeration Survey, are added to the population projections. Prior to January 1994, the projections were based on earlier censuses, and there was no correction for census undercount. A summary of the current procedures used to make population projections is given in "Revisions in the Current Population Survey Effective January 1994," appearing in the February 1994 issue of Employment and Earnings.

3. Composite estimation procedure.   The last step in the preparation of most CPS estimates makes use of a composite estimation procedure. The composite estimate consists of a weighted average of two factors: The two-stage ratio estimate based on the entire sample from the current month and the composite estimate for the previous month, plus an estimate of the month-to-month change based on the six rotation groups common to both months. In addition, a bias adjustment term is added to the weighted average to account for relative bias associated with month-in-sample estimates. This month-in-sample bias is exhibited by unemployment estimates for persons in their first and fifth months in the CPS being generally higher than estimates obtained for the other months.

The composite estimate results in a reduction in the sampling error beyond that which is achieved after the two stages of ratio adjustment. For some items, the reduction is substantial. The resultant gains in reliability are greatest in estimates of month-to-month change, although gains usually are also obtained for estimates of level in a given month, change from year to year, and change over other intervals of time.

The sums of individual items may not always equal the totals shown in the same tables because independent rounding of totals and components to the nearest thousand. Similarly, sums of percent distributions may not always equal 100 percent because of rounding. Differences, however, are insignificant.

An estimate based on a sample survey has two types of error -- sampling error and nonsampling error. The estimated standard errors provided in this appendix are approximations of the true sampling errors. They do incorporate the effect of some nonsampling errors in response and enumeration, but do not account for any systematic biases in the data.

Nonsampling error.   The full extent of nonsampling error is unknown, but special studies have been conducted to quantify some sources of nonsampling error in the CPS. The effect of nonsampling error is small on estimates of relative change, such as month-to-month change; estimates of monthly levels tend to be affected to a greater degree.

Nonsampling errors in surveys can be attributed to many sources, for example, the inability to obtain information about all persons in the sample; differences in the interpretation of questions; inability or unwillingness of respondents to provide correct information; inability of respondents to recall information; errors made in collecting and processing the data; errors made in estimating values for missing data; and failure to represent all sample households and all persons within sample households (undercoverage).

Nonsampling errors occurring in the interview phase of the survey are studied by means of a reinterview program. This program is used to estimate various sources of error as well as to evaluate and control the work of the interviewers. A random sample of each interviewer's work is inspected through reinterview at regular intervals. The results indicate, among other things, that the data published from the CPS are subject to moderate systematic biases. A description of the CPS reinterview program and some results may be found in Appendix G, "Reinterview: Design and Methodology," of "The Current Population Survey: Design and Methodology," Technical Paper 63RV (Washington, U.S. Census Bureau and Bureau of Labor Statistics, March 2002), available on the Internet at www.bls.census.gov/cps/tp/tp63.htm.

The effects of some components of nonsampling error in the CPS data can be examined as a result of the rotation plan used for the sample, because the level of the estimates varies by rotation group. A description appears in Barbara A. Bailar, "The Effects of Rotation Group Bias on Estimates from Panel Surveys," Journal of the American Statistical Association, March 1975, pp. 23-30.

Undercoverage in the CPS results from missed housing units and missed persons within sample households. The CPS covers about 92 percent of the decennial census population (adjusted for census undercount). It is known that the CPS undercoverage varies with age, sex, race, and Hispanic origin. Generally, undercoverage is larger for men than for women and is larger for Blacks, Hispanics, and other races than for Whites. Ratio adjustment to independent age-sex-race-origin population controls, as described previously, partially corrects for the biases due to survey undercoverage. However, biases exist in the estimates to the extent that missed persons in missed households or missed persons in interviewed households have characteristics different from those of interviewed persons in the same age-sex-race-origin group.

Additional information on nonsampling error in the CPS appears in Camilla Brooks and Barbara Bailar, "An Error Profile: Employment as Measured by the Current Population Survey," Statistical Policy Working Paper 3 (Washington, U.S. Department of Commerce, Office of Federal Statistical Policy and Standards, September 1978); Marvin Thompson and Gary Shapiro, "The Current Population Survey: An Overview," Annals of Economic and Social Measurement, Vol. 2, April 1973; and "The Current Population Survey: Design and Methodology," Technical Paper 63RV, referenced above. The last document includes a comprehensive discussion of various sources of errors and describes attempts to measure them in the CPS.

Sampling error.   When a sample, rather than the entire population, is surveyed, estimates differ from the true population values that they represent. This difference, or sampling error, occurs by chance, and its variability is measured by the standard error of the estimate. Sample estimates from a given survey design are unbiased when an average of the estimates from all possible samples would yield, hypothetically, the true population value. In this case, the sample estimate and its standard error can be used to construct approximate confidence intervals, or ranges of values that include the true population value with known probabilities. If the process of selecting a sample from the population were repeated many times, an estimate made from each sample, and a suitable estimate of its standard error calculated for each sample, then:

1. Approximately 68 percent of the intervals from one standard error below the estimate to one standard error above the estimate would include the true population value.

2. 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 true population value.

3. Approximately 95 percent of the intervals from 1.96 standard errors below the estimate to 1.96 standard errors above the estimate would include the true population value.

These confidence interval statements are approximately true for the CPS. Although the estimating methods used in the CPS do not produce unbiased estimates, biases for most estimates are believed to be small. Methods for estimating standard errors reflect not only sampling errors but also some kinds of nonsampling error. Although both the estimates and the estimated standard errors depart from the theoretical ideal, the departures are minor and have little impact on the confidence interval statements. When clarity is needed, an estimated confidence interval is specified to be "approximate," as is the estimated standard error used in the computation.

Tables 1-B through 1-D are provided so that approximate standard errors of estimates can be easily obtained. Tables 1-B and 1-C give approximate standard errors for estimated monthly levels and rates for selected employment status characteristics; the tables also provide approximate standard errors for consecutive month-to-month changes in the estimates. It is impractical to show approximate standard errors for all CPS estimates in Employment and Earnings, so table 1-D provides parameters and factors that allow the user to calculate approximate standard errors for a wide range of estimated levels, rates, and percentages, and also changes over time. The parameters and factors are used in formulas that are commonly called generalized variance functions.

The approximate standard errors provided in Employment and Earnings are based on the sample design and estimation procedures as of 1996, and reflect the population levels and sample size as of that year. Standard errors for years prior to 1996 may be roughly approximated by applying these adjustments to the standard errors presented here. (More accurate standard error estimates for historical CPS data may be found in previous issues of Employment and Earnings.)

Use of tables 1-B and 1-C.   These tables provide a quick reference for standard errors of major characteristics. Table 1-B gives approximate standard errors for estimates of monthly levels and consecutive month-to-month changes in levels for major employment status categories. Table 1-C gives approximate standard errors for estimates of monthly unemployment rates and consecutive month-to-month changes in unemployment rates for some demographic, occupational, and industrial categories. For characteristics not given in tables 1-B and 1-C, refer to table 1-D.

Illustration.   Suppose that, for a given month, the number of women 20 years and over in the civilian labor force is estimated to be 60,000,000. For this characteristic, the approximate standard error of 209,000 is given in table 1-B in the row "Women, 20 years and over; Civilian Labor Force." To calculate an approximate 90-percent confidence interval, multiply the standard error of 209,000 by the factor 1.645 to obtain 344,000. This number is subtracted from and then added to 60,000,000 to obtain an approximate 90-percent confidence interval: 59,656,000 to 60,344,000. Concluding that the true civilian labor force level lies within an interval calculated in this way would be correct for roughly 90 percent of all possible samples that could have been selected for the CPS.

Use of table 1-D.   This table gives a and b parameters that can be used with formulas to calculate approximate monthly standard errors for a wide range of estimated levels, proportions, and rates. Factors are provided to convert monthly measures into approximate standard errors of estimates for other time periods (quarterly and yearly averages) and approximate standard errors for changes over time (consecutive monthly changes, changes in consecutive quarterly and yearly averages, and changes in monthly estimates 1 year apart).

The standard errors for estimated changes in level from one month to the next, one year to the next, etc., depend more on the monthly levels for characteristics than on the size of the changes. Likewise, the standard errors for changes in rates (or percentages) depend more on the monthly rates (or percentages) than on the size of the changes. Accordingly, the factors presented in table 1-D are applied to the monthly standard error approximations for levels, percentages, or rates; the magnitudes of the changes do not come into play. Factors are not given for estimated changes between nonconsecutive months (except for changes of monthly estimates 1 year apart); however, the standard errors may be assumed to be higher than the standard errors for consecutive monthly changes.

Standard errors of estimated levels using table 1-D.   The approximate standard error se(x) of x, an estimated monthly level, can be obtained using the formula below, where a and b are the parameters from table 1-D associated with a particular characteristic.

Illustration. Assume that in a given a month there are an estimated 3 million unemployed men. Obtain the appropriate a and b parameters from table 1-D (Total or White; Men; Unemployed). Use the formula for se(x) to compute an approximate standard error on the estimate of x = 3,000,000.

a = -0.0000348     b = 2927.43

Procedure for using table 1-D factors for levels.   Table 1-D gives factors that can be used to compute approximate standard errors of levels for other time periods or for changes over time. For each characteristic, factors f are given for:

For a given characteristic, the table 1-D factor is used in the following formula, which also uses the a and b parameters from the same line of the table. A three-step procedure for using the formula is given. The f in the formula is frequently called an adjustment factor, because it appears to adjust a monthly standard error se(x). However, the x in the formula is not a monthly level, but an average of several monthly levels (see examples listed under Step 1, below).

where x is an average of monthly levels over a designated period.

Step 1. Average monthly levels appropriately in order to obtain x. Levels for 3 months are averaged for quarterly averages, and those for 12 months are averaged for yearly averages. For changes in consecutive averages, average over the 2 months, 2 quarters, or 2 years involved. For changes in monthly estimates 1 year apart, average the 2 months involved.

Step 2. Calculate an approximate standard error se(x), treating the average x from step 1 as if it were an estimate of level for a single month. Obtain parameters a and b from table 1-D. (Note that, for some characteristics, an approximate standard error of level could instead be obtained from table 1-B and used in place of se(x) in the formula.)

Step 3. Determine the standard error se(x,f) on the average level or on the change in level. Multiply the result from step 2 by the appropriate factor f. The a and b parameters used in step 2 and the factor f used in this step come from the same line in table 1-D.

Illustration of a standard error computation for consecutive month change in level. Continuing the previous example, suppose that in the next month the estimated number of unemployed men increases by 150,000, from 3,000,000 to 3,150,000.

Step 1. The average of the two monthly levels is x = 3,075,000.

Step 2. Apply the a and b parameters from table 1-D (Total or White; Men; Unemployed) to the average x, treating it like an estimate for a single month.

a = -0.0000348     b = 2927.43

Step 3. Obtain f = 1.27 from the same row of table 1-D in the column "Consecutive month-to-month change," and multiply the factor by the result from step 2.

se(150,000) = f*se(3,075,000) = 1.27*93,000 » 118,000

For an approximate 90-percent confidence interval, compute 1.645 * 118,000 » 194,000. Subtract the number from and add the number to 150,000 to obtain an interval of -44,000 to 344,000. This is an approximate 90-percent confidence interval for the true change, and since this interval includes zero, one cannot assert at this level of confidence that any real change has occurred in the unemployment level. The result also can be expressed by saying that the apparent change of 150,000 is not significant at a 90-percent confidence level.

Illustration of a standard error computation for quarterly average level. Suppose that an approximate standard error is desired for a quarterly average of the Black employment level. Suppose that the estimated employment levels for the 3 months making up the quarter are 14,900,000, 15,000,000, and 15,100,000.

Step 1. The average of the three monthly levels is x = 15,000,000.

Step 2. Apply the a and b parameters from table 1-D (Black; Total; Civilian labor force, employed, and not in labor force) to the average x, treating it like an estimate for a single month.

a = -0.0001541    b = 3295.99

se(15,000,000) =

Step 3. Obtain f = .86 from the same row of table 1-D in the column "Quarterly averages," and multiply the factor by the result from step 2.

Illustration of a standard error computation for change in quarterly level. Continuing the example, suppose that, in the next quarter, the estimated average employment level for Blacks is 15,400,000 based on monthly levels of 15,300,000, 15,400,000, and 15,500,000. This is an estimated increase of 400,000 over the previous quarter.

Step 1. The average of the two quarterly levels is x = 15,200,000.

Step 2. Apply the a and b parameters from table 1-D (Black; Total; Civilian labor force, employed, and not in labor force) to the average x, treating it like an estimate for a single month.

a -0.0001541    b = 3295.99

Step 3. Obtain f = .78 from the same row of table 1-D in the column "Change in consecutive quarterly averages," and multiply the factor by the result from step 2.

For an approximate 95-percent confidence interval, compute 1.96 * 94,000 » 184,000. Subtract the number from and add the number to 400,000 to obtain an interval of 216,000 to 584,000. The interval excludes zero. Another way of stating this is to observe that the estimated change of 400,000 clearly exceeds 1.96 standard errors, or 184,000. One can conclude from these data that the change in quarterly averages is significant at a 95-percent confidence level.

Standard errors of estimated rates and percentages using table 1-D. As shown in the formula below, the approximate standard error se(p,y) of an estimated rate or percentage p depends, in part, upon the number of persons y in its base or denominator. Generally, rates and percentages are not published unless the monthly base is greater than 75,000 persons, the quarterly average base is greater than 60,000 persons, or the yearly average base is greater than 35,000 persons. The b parameter is obtained from table 1-D. When the base y and the numerator of p are from different categories within the table, use the b parameter from table 1-D relevant to the numerator of the rate or percentage.

Note that se(p,y) is in percent.

Illustration. For a given month, suppose y = 6,200,000 women 20 to 24 years of age are estimated to be employed. Of this total, 2,000,000 or p = 32 percent, are classified as part-time workers. Obtain the parameter b = 3005.06 from the table 1-D row (Employment; Part-time workers) that is relevant to the numerator of the percentage. Apply the formula to obtain:

percent

For an approximate 95 percent confidence interval, compute 1.96 * 1.0 percent, and round the result to 2 percent. Subtract this from and add this to the estimate of p = 32 percent to obtain an interval of 30 percent to 34 percent.

Procedure for using table 1-D factors for rates and percentages.   Table 1-D factors can be used to compute approximate standard errors on rates and percentages for other time periods or for changes over time. As for levels, there are three steps in the procedure for using the formula.

where p and y are averages of monthly estimates over a designated period.

Note that se(p,y,f) is in percent.

Step 1. Appropriately average estimates of monthly rates or percentages to obtain p, and also average estimates of monthly levels to obtain y. Rates for 3 months are averaged for quarterly averages, and those for 12 months are averaged for yearly averages. For changes in consecutive averages, average over the 2 months, 2 quarters, or 2 years involved. For changes in monthly estimates 1 year apart, average the 2 months involved.

Step 2. Calculate an approximate standard error se(p,y), treating the averages p and y from step 1 as if they were estimates for a single month. Obtain the b parameter from the table 1-D row that describes the numerator of the rate or percentage. (Note that, for some characteristics, an approximate standard error could instead be obtained from table 1-C and used in place of se(p,y) in the formula.)

Step 3. Determine the standard error se(p,y,f) on the average level or on the change in level. Multiply the result from step 2 by the appropriate factor f. The b parameter used in step 2 and the factor f used in this step come from the same line in table 1-D.

Illustration of a standard error computation for consecutive month change in percentage. Continuing the previous example, suppose that, in the next month, 6,300,000 women 20 to 24 years of age are reported employed, and that 2,150,000 or 34 percent, are part-time workers.

Step 1. The month-to-month change is 2 percent = 34 percent - 32 percent. The average of the two monthly percentages of 32 percent and 34 percent is needed (p = 33 percent), as is the average of the two bases of 6,200,000 and 6,300,000 (y = 6,250,000).

Step 2. Apply the b = 3005.06 parameter from table 1-D (Employment; Part-time workers) to the averaged p and y, treating the averages like estimates for a single month.

percent

Step 3. Obtain f = .65 from the same row of table 1-D in the column "Consecutive month-to-month change," and multiply the factor by the result from step 2.

For an approximate 95-percent confidence interval, compute 1.96 * .65 percent, and round the result to 1.3 percent. Subtract this from and add this to the 2-percent estimate of change to obtain an interval of 0.7 percent to 3.3 percent. Since this interval excludes zero, it can be concluded at a 95-percent confidence level that the change is significant.

Table 1-C. Approximate standard errors for unemployment rates by major characteristics (in percent)

Table 1-D. Parameters and factors for computation of approximate standard errors for estimates of monthly levels

Table 1-D. Parameters and factors for computation of approximate standard errors for estimates of monthly levels - Continued

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