Source and Accuracy Statement for the February 2000 CPS Microdata File for Displaced Workers and Employee Tenure

SOURCE OF DATA

The data for this microdata file come from the February 2000 Current Population Survey (CPS). The February survey uses two sets of questions, the basic CPS and the supplement.

Basic CPS. The basic CPS collects primarily labor force data about the civilian noninstitutional population. Interviewers ask questions concerning labor force participation about each member 15 years old and over in every sample household.

February 2000 supplement. In February 2000, in addition to the basic CPS, interviewers asked supplementary questions on displaced workers, job tenure, and occupational mobility.

Sample Design. The present CPS sample was selected from the 1990 Decennial Census files with coverage in all 50 states and the District of Columbia. The sample is continually updated to account for new residential construction. To obtain the sample, the United States was divided into 2,007 geographic areas. In most states, a geographic area consisted of a county or several contiguous counties. In some areas of New England and Hawaii, minor civil divisions are used instead of counties. These 2,007 geographic areas were then grouped into 754 strata, and one geographic area was selected from each stratum. About 50,000 occupied households are eligible for interview every month out of these 754 areas. Interviewers are unable to obtain interviews at about 3,200 of these units. This occurs when the occupants are not found at home after repeated calls or are unavailable for some other reason.

Sample Redesign. Since the introduction of the CPS, the Census Bureau has redesigned the CPS sample several times. These redesigns have improved the quality and accuracy of the data and have satisfied changing data needs. The most recent changes were completely implemented in July 1995.

Estimation procedure. This survey's estimation procedure adjusts weighted sample results to agree with independent estimates of the civilian noninstitutional population of the United States by age, sex, race, Hispanic/non-Hispanic origin, and state of residence. This adjusted estimate is called the post-stratification ratio estimate. The independent estimates are calculated based on information from four primary sources:

• The 1990 Decennial Census of Population and Housing.
• An adjustment for undercoverage in the 1990 census.
• Statistics on births, deaths, immigration, and emigration.
• Statistics on the size of the Armed Forces.

The independent population estimates include some, but not all, undocumented immigrants.

ACCURACY OF THE ESTIMATES

A sample survey estimate has two possible 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 give the survey design. The full extent of the nonsampling error, however, is unknown.

Sampling error. As with all surveys, CPS estimates come from a sample of the population. Therefore, they can differ from similar figures that could be collected from the whole population (a census). That difference is known as sampling error.

Consequently, one should be particularly careful when interpreting results based on a relatively small number of cases or on small differences between estimates. The standard errors for CPS estimates primarily indicate the magnitude of sampling error. They also partially measure the effect of some nonsampling errors in responses and enumeration, but do not measure systematic biases in the data. (Bias is the average over all possible samples of the differences between the sample estimates and the desired value.)

Nonsampling error. All other sources of error in the survey estimates are collectively called nonsampling error. Sources of nonsampling errors include the following:

• Inability to get information about all sample cases (nonresponse)
• Definitional difficulties
• Differences in the interpretation of questions
• Respondents' inability or unwillingness to provide correct information
• Respondents' inability to recall information
• Errors made in data collection such as recording and coding data
• Errors made in processing the data
• Errors made in estimating values for missing data
• Failure to represent all units with the sample (undercoverage).

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 February 2000 basic CPS, the nonresponse rate was 6.7%. The nonresponse rate for the displaced workers supplement was an additional 5.9%, for a total supplement nonresponse rate of 12.2%.

Undercoverage. 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. CPS undercoverage results from missed housing units and missed persons within sample households. Overall CPS undercoverage is estimated to be about 8 percent. CPS undercoverage varies with age, sex, and race. Generally, undercoverage is larger for males than for females and larger for Blacks and other races combined than for Whites. As described previously, ratio estimation to independent age-sex-race-Hispanic population controls partially corrects for bias due to undercoverage. However, biases exist in the estimates to the extent that missed persons in missed households or missed persons in interviewed households have different characteristics from those of interviewed persons in the same age-sex-race-origin-state group.

A common measure of survey coverage is the coverage ratio, the estimated population before post-stratification divided by the independent population control. Table A shows CPS coverage ratios for age-sex-race groups for a typical month. The CPS coverage ratios can exhibit some variability from month to month. Other Census Bureau household surveys experience similar coverage.

A nonsampling error warning. Since the full extent of the nonsampling error is unknown, one should be particularly careful when interpreting results based on small differences between estimates. Even a small amount of nonsampling error can cause a borderline difference to appear significant or not, thus distorting a seemingly valid hypothesis test. Caution should also be used when interpreting results based on a relatively small number of cases. Summary measures probably do not reveal useful information when computed on a base smaller than 75,000. For additional information on nonsampling error including the possible impact on CPS data when known, refer to Statistical Policy Working Paper 3, An Error Profile: Employment as Measured by the Current Population Survey, Office of Federal Statistical Policy and Standards, U.S. Department of Commerce, 1978 and Technical Paper 63, The Current Population Survey: Design and Methodology, Bureau of the Census, U.S. Department of Commerce.

Standard errors and their use. The sample estimate and its standard error enable one to construct a confidence interval. A confidence interval is a range that would include the average result of all possible samples with a known probability. For example, if all possible samples were surveyed under essentially the same general conditions and using the same sample design, and if an estimate and its standard error were calculated from each sample, then approximately 90 percent of the intervals from 1.645 standard errors below the estimate to 1.645 standard errors above the estimate would include the average result of all possible samples.

A particular confidence interval may or may not contain the average estimate derived from all possible samples. However, one can say with specified confidence that the interval includes the average estimate calculated from all possible samples.

Standard errors may also be used to perform hypothesis testing. This is 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 males who left a job involuntarily to females who left a job involuntarily.

Tests may be performed at various levels of significance. A significance level is the probability of concluding that the characteristics are different when, in fact, they are the same. For example, to conclude that two parameters are different at the 0.10 level of significance, the absolute value of the estimated difference between characteristics must be greater than or equal to 1.645 times the standard error of the difference.

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

For information on calculating standard errors for labor force data from the CPS which involve quarterly or yearly averages, changes in consecutive quarterly or yearly averages, consecutive month-to-month changes in estimates, and consecutive year-to-year changes in monthly estimates, see "Explanatory Notes and Estimates of Error: Household Data" in the corresponding Employment and Earnings published by the Bureau of Labor Statistics.

Standard errors of estimated numbers. The approximate standard error, s_x, of an estimated number from this microdata file can be obtained using this formula:

Here x is the size of the estimate and a and b are the parameters in Table B 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 which will give the largest standard error.

Illustration

Suppose there were 2,862,000 unemployed men in the civilian labor force. Use the appropriate parameters from Table B and formula (1) to get

The standard error is calculated as

The 90- percent confidence interval is calculated as 2,862,000 ± 1.645´91,000.

A conclusion that the average estimate derived from all possible samples lies within a range computed in this way would be correct for roughly 90 percent of all possible samples.

Standard errors of estimated percentages. The reliability of an estimated percentage, computed using sample data from 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 B indicated by the numerator.

The approximate standard error, s_x,p, of an estimated percentage can be obtained by use of the formula

Here x is the total number of persons, families, households, or unrelated individuals in the base of the percentage, p is the percentage (0 £ p £ 100), and b is the parameter in Table B associated with the characteristic in the numerator of the percentage.

Suppose of 7,561,000 displaced workers, 3,267,000, or 43.2 percent, lost their jobs when a plant or company closed down or moved. Use the appropriate parameter from Table B and formula (2) to get

The standard error is calculated as

The 90 percent confidence interval of the percentage of displaced workers who lost their jobs when a plant or company closed down or moved is calculated as 43.2 ± 1.645´1.0.

Standard error of a difference. The standard error of the difference between two sample estimates is approximately equal to

where s_x and s_y are the standard errors of the estimates, x and y. The estimates can be numbers, percentages, ratios, etc. This will represent the actual standard error quite accurately for the difference between 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

Suppose that of 6,594,000 employed men between 20-24 years of age, 193,000 or 2.9 percent were part-time workers, and of the 6,042,000 employed women between 20-24 years of age, 254,000 or 4.2 percent were part-time workers. Use the appropriate parameters from Table B and formulas (2) and (3) to get

The standard error of the difference is calculated as

The 90-percent confidence interval around the difference is calculated as 1.3 ± 1.645´0.5. Since this interval includes zero, we cannot conclude with 90-percent confidence that the percentage of part-time women workers between 20-24 years of age is greater than the percentage of part-time men workers between 20-24 years of age.

Standard Error of a Median. 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 the section on 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. Determine, using formula (2), the standard error of the estimate of 50 percent from the distribution.

2. Add to and subtract from 50 percent the standard error determined in step 1.

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.

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

where

X_pN = 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_pN estimates the median when p = 0.50.

N = for distribution of numbers: the total number of units (persons, households, etc.) for the characteristic in the distribution.

= for distribution of percentages: the value 1.0.

p = the values obtained in step 2.

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

N₁, N₂ = for distribution of numbers: the estimated number of units (persons, households, etc.) with values of the characteristic greater than or equal to A₁ and A₂, respectively.

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

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

Illustration

Suppose that the estimated median years on the lost job for all displaced workers is 3.3 years and suppose the following table gives the distribution of years.

(1) Using b = 2,985 from Table B and formula (2), the standard error of 50 percent on a base of 6,655,000 is around 1.1 percent.

(2) To obtain a 68-percent confidence interval for a median, add to and subtract from 50 percent, the standard error found in step (1). This yields limits of 48.9 and 51.1 percent.

(3) It can be seen that 27.8 percent of the displaced workers had less than 1 year on their lost job, and 66.8 percent had less than 5 years on their lost job. By linear interpolation the lower and upper limits of the 68-percent confidence interval for the median are calculated as

(4) The standard error of the median is, therefore,

Table B. Parameters for Computation of Standard Errors for Labor Force Characteristics - 2000
Characteristic	a	b
Labor Force and Not In Labor Force Data Other than Agricultural Employment and Unemployment
Total 1	-0.000018	2,985
- Men 1	-0.000033	2,764
- Women	-0.000030	2,530
- Both sexes, 16 to 19 years	-0.000172	2,545
White 1	-0.000020	2,985
- Men	-0.000037	2,767
- Women	-0.000034	2,527
- Both sexes, 16 to 19 years	-0.000204	2,550
Black	-0.000125	3,139
- Men	-0.000302	2,931
- Women	-0.000183	2,637
- Both sexes, 16 to 19 years	-0.001295	2,949
Hispanic origin	-0.000206	3,896
Not In Labor Force (use only for Total, Total Men, and White)	+0.000006	829
Agricultural Employment - Total or White	+0.000782	3,049
- - Men	+0.000858	2,825
- - Women or Both sexes, 16 to 19 years	-0.000025	2,582
- Black	-0.000135	3,155
- Hispanic origin - - Total or Women	+0.011857	2,895
- - Men or Both sexes, 16 to 19 years	+0.015736	1,703
Unemployment - Total or White	-0.000018	2,957
- Black	-0.000212	3,150
- Hispanic origin	-0.000102	3,576

1 For not in labor force characteristics, use the Not In Labor Force parameters.

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