Coverage. The concept of coverage in the survey sampling process is the extent to which the total population that could be selected for sample Acovers@ the survey = s target population. CPS undercoverage results from missed housing units and missed people 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 the bias due to undercoverage. However, biases exist in the estimates to the extent that missed people in missed households or missed people in interviewed households have different characteristics from those of interviewed persons in the same age-sex-race-ancestry-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 1 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 (subpopulation) 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

Technical Paper 63, The Current Population Survey: Design and Methodology, Bureau of the Census, U.S. Department of Commerce, 2000.

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 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 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 the percentage of Whites with a college education to the percentage of Blacks with a college education.

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 texts for alternative criteria.

Estimating standard errors. To estimate the standard error of a CPS estimate, the Census Bureau uses replicated variance estimation methods. 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 due to nonsampling error. (Bias is the average of the differences, over all possible samples, between the sample estimates and the desired value.)

Generalized Variance Parameters. Consider all of the possible estimates of characteristics of the population that are of interest to data users. Now consider all of the subpopulations such as racial groups, age ranges, etc. Finally, consider every possible comparison or ratio combination. The list would be completely unmanageable. Similarly, a list of standard errors to go with every estimate would be unmanageable.

Through experimentation, we have found that certain groups of estimates have similar relationships between their variances and expected values. We provide a generalized method for calculating standard errors for any of the characteristics of the population of interest. The generalized method uses generalized variance parameters for groups of estimates. These parameters are in Table 2, for basic CPS monthly labor force estimates, and Tables 3 through 9, for November supplement data.

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 2 through 9 associated with the particular type of characteristic. When calculating standard errors for numbers from cross-tabulations involving different characteristics, use the factor or set of parameters for the characteristic which will give the largest standard error.

In November 2000, there were 2,957,000 unemployed men in the civilian labor force. Use the appropriate parameters from Table 2 and formula (1) to get:

The standard error is calculated as

The 90-percent confidence interval is calculated as 2,957,000 "1.645 H91,000

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 2 through 9 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 people, 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 2 through 9 associated with the characteristic in the numerator of the percentage.

In November 2000, out of 13,590,000 people with an elementary school education, 24.7 percent reported voting. Use the appropriate parameter from Table 3 and formula (2) to get:

The standard error is calculated as

the 90-percent confidence interval of the percentage of people with an elementary school education who reported voting is calculated as 24.7 " 1.645 H 0.7

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.

Out of 6,810,000 men who had an elementary school education, 1,690,000 or 24.8 percent had voted, and of the 6,779,000 women who had an elementary school education, 1,670,000 or 24.6 percent had voted. Use the appropriate parameters from Table 2 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 0.2 " 1.645 H 1.3. Since this interval does include zero, we cannot conclude, at the 10 percent significance level, that the percentage of women with an elementary school education who voted is different from the percentage of men with an elementary school education who voted.

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

A number of changes were made in data collection and estimation procedures beginning with the January 1994 CPS. The major change was the use of a new questionnaire. The questionnaire was redesigned to measure the official labor force concepts more precisely, to expand the amount of data available, to implement several definitional changes, and to adapt to a computer-assisted interviewing environment. The March supplemental income questions were also modified for adaptation to computer-assisted interviewing, although there were no changes in definitions and concepts. Due to these and other changes, one should use caution when comparing estimates from data collected before 1994 with estimates from data collected in 1994 and later.

Caution should also be used when comparing data from this microdata file, which reflects 1990 census-based population controls, with microdata files from March 1993 and earlier years, which reflect 1980 census-based population controls. Although this 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 1990 based population controls results in about a 1 percent increase in the civilian noninstitutional population and in the number of families and households. Thus, estimates of levels for data collected in 1994 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 subpopulation groups than for the total population.

Caution should also be used when comparing Hispanic estimates over time. No independent population control totals for people of Hispanic ancestry were used before 1985.

Based on the results of each decennial census, the Census Bureau gradually introduces a new sample design for the CPS. During this phase-in period, CPS data are collected from sample designs based on different censuses. While most CPS estimates were unaffected by this mixed sample, geographic estimates are subject to greater error and variability. Users should exercise caution when comparing estimates across years for metropolitan/ nonmetropolitan categories.

Note when using small estimates. Because of the large standard errors involved, summary measures probably do not reveal useful information when computed on a base smaller than 75,000.

Take care in the interpretation of small differences. Even a small amount of nonsampling error can cause a borderline difference to appear significant or not, thus distorting a seemingly valid hypothesis test.

Technical Assistance. If you require assistance or additional information, please contact the Demographic Statistical Methods Division via e-mail at DSMD_S&A@census.gov.

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