Estimates in this report come from data obtained in June 1998 in the Current Population Survey (CPS). The U.S. Census Bureau conducts the survey every month, although this report uses only June data for its estimates. The June 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. Field representatives ask questions concerning labor force participation about each member 15 years old and over in every sample household.

June 1998 Supplement. In addition to the basic CPS questions, field representatives asked supplementary questions in June 1998 about fertility of women 15 to 44 years old.

Sample Design. The CPS sample includes coverage in all 50 states and the District of Columbia. The Census Bureau continually updates the sample to account for new residential construction. The Census Bureau divides the United States into 2,007 geographic areas. In most states, a geographic area consists of a county or several contiguous counties. In some areas of New England and Hawaii, the Census Bureau uses minor civil divisions instead of counties. We select a total of 754 geographic areas for sample. About 50,000 occupied households are eligible for interview every month. Field representatives 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.

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 Census Bureau completely implemented the most recent changes in July 1995.

CPS Estimation Procedure. This survey's estimation procedure adjusts weighted sample results to independent estimates of the civilian noninstitutional population of the United States by age, sex, race, Hispanic/non-Hispanic origin, and state of residence. The independent estimates are based on:

• 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.

ACCURACY OF THE ESTIMATES

Since the CPS estimates come from a sample, they may differ from figures from a complete census using the same questionnaires, instructions, and enumerators. A sample survey estimate has two possible types of errors: sampling and nonsampling. The accuracy of an estimate depends on both types of errors, but the full extent of the nonsampling error is unknown. 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 Variability. We can attribute nonsampling errors to several sources including the following:

• Inability to obtain information about all cases in the sample.
• 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 the data.
• Errors made in processing the data.
• Errors made in estimating values for missing data.
• Failure to represent all units with the sample (undercoverage).

CPS undercoverage results from missed housing units and missed people within sample households. Compared with the level of the 1990 Decennial Census, overall CPS undercoverage is about 8 percent. 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 people in missed households or missed people in interviewed households have different characteristics from those of interviewed people in the same age-sex-race-origin-state group.

A common measure of survey coverage is the coverage ratio, the estimated population before the post-stratification ratio estimate 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, but these are a typical set of coverage ratios.

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, U.S. Census Bureau, U.S. Department of Commerce.

Comparability of Data. Data obtained from the CPS and other sources are not entirely comparable. This results from differences in field representative training and experience and in differing survey processes. This is an example of nonsampling variability not reflected in the standard errors. Use caution 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 Bureau of Labor Statistics redesigned the questionnaire 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 Census Bureau modified the March supplemental income questions for adaptation to computer-assisted interviewing, but did not change definitions and concepts. Because of these and other changes, one should use caution when comparing estimates from data collected in 1994 or later years with estimates from earlier years.

Data users should also use caution when comparing estimates in this report (which reflect 1990 census-based population controls) with estimates for 1993 and earlier years (which reflect 1980 census-based population controls). This change in population controls had relatively little impact on summary measures such as means, medians and percentage distributions. It did have a significant impact on levels. For example, 1990-based population controls caused 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.

Since the Census Bureau did not use independent population control totals for people of Hispanic origin before 1983, compare Hispanic estimates over time cautiously.

Based on results of each decennial census, the Census Bureau gradually introduces a new sample design for CPS. During this phase-in period, the Census Bureau collects CPS data from sample designs based on different censuses. While most CPS estimates have been 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. For more information, see Appendix C, Current Population Reports, Series P60-193, Money Income in the United States: 1995 (With Separate Data on Valuation of Noncash Benefits).

Note When Using Small Estimates. The Census Bureau shows summary measures (such as medians and percentage distributions) only when the base is 75,000 or greater. Because of the large standard errors involved, summary measures would probably not reveal useful information when computed on a smaller base. However, we display estimated numbers even though the relative standard errors of these numbers are larger than those for corresponding percentages. These smaller estimates permit combinations of the categories to suit data users' needs. Take care in the interpretation of small differences. For instance, even a small amount of nonsampling error can cause a borderline difference to appear significant or not, thus distorting a seemingly valid hypothesis test.

Sampling Variability. Sampling variability is variation that occurred by chance because a sample was surveyed rather than the entire population. Standard errors, as calculated by methods described in "Standard Errors and Their Use," are primarily measures of sampling variability, although they may include some nonsampling errors.

Standard Errors and Their Use. Data users must use a number of approximations to derive, at a moderate cost, standard errors applicable to all the estimates in this report. Instead of providing an individual standard error for each estimate, we have provided parameters to calculate standard errors for each type of characteristic.

Table B provides standard error parameters for labor force data. Table C provides standard error parameters for persons, families, households, householders, and unrelated individuals. Table D provides standard error parameters for fertility ratios. Tables E and F provide fertility and labor force standard error parameters for previous years.

The sample estimate and its standard error enable one to construct a confidence interval, 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.

Data users may also use standard errors to perform hypothesis testing. This is a procedure for distinguishing between population parameters using sample estimates. One common type of hypothesis appearing in this report is that two population parameters are different. An example of this would be comparing the fertility ratio of White women to the fertility ratio of Black women 15 to 44 years old.

One can perform tests at various levels of significance. The significance level of a test is the probability of concluding that the characteristics are different when, in fact, they are the same. All statements of comparison in the text were tested at the 0.10 level of significance or better. This means that the absolute value of the estimated difference between characteristics is 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. One can obtain the approximate standard error, s_x, of an estimated number shown in this report by using the formula

(1)

Here x is the size of the estimate and a and b are the parameters in Tables B and C 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.

Illustration.

Suppose there were 609,000 unemployed women 35-44 years of age in the civilian labor force. Use the appropriate parameters from Table B to get

The 90-percent confidence interval is calculated as 609,000 ± 1.645x42,000.

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 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 B or C indicated by the numerator.

One can obtain the approximate standard error, s_x,p, of an estimated percentage by using the formula

(2)

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 or C associated with the characteristic in the numerator of the percentage.

Illustration.

Suppose that 47.6 percent of the 5,099,000 never-married Black women 15-44 years old in 1998 had ever had a child. Use the appropriate parameter from Table C and formula (2) to get

The standard error is calculated as

The 90-percent confidence interval for the percentage of never-married Black women 15-44 years old who had ever had a child is calculated as 47.6 ± 1.645x1.05.

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

(3)

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 3,671,000 women in 1998 between 15-44 years of age who had a child in the previous year, 2,155,000 or 58.7 percent were in the labor force, and of the 3,696,000 women in 1995 between 15-44 years of age who had a child in the previous year, 2,034,000 or 55.0 percent were in the labor force. Use the appropriate parameters from Table E 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 3.7 ± 1.645x1.8. Since this interval does not contain zero, we can conclude, at the 10-percent level of significance, that the percentage of women between 15-44 years of age who had a child in 1998 who were in the labor force is different from the 1995 percentage of women 15-44 with infants who were in the labor force.

Standard error of a fertility ratio. The standard error of a fertility ratio is a function of the number of children ever born per 1,000 women and the number of women in a given category. The formula for the standard error of a fertility ratio is

(4)

where a, b and c are the parameters from Table D, x is the number of children ever born or expected per 1,000 women and y is the number of women, in thousands. This formula should be used when calculating standard errors for data involving two or more events per woman, i.e., two or more children ever born. For data involving only one event, convert the ratio to a percentage and use formula (2) and the parameters in Table C to calculate the standard errors.

Illustration.

Suppose that 9,995,000 ever-married women 40-44 years old had 2,002 children ever born per 1,000 women. Use formula (4) and the parameters in Table D to get

The standard error is calculated as

The 90-percent confidence interval is from 1,954 to 2,050 children ever born per 1,000 women (i.e., 2,002 ± 1.645x29). 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 Error of a Ratio. Certain estimates may be calculated as the ratio of two numbers. The standard error of a ratio, x/y, may be computed using

(5)

The standard error of the numerator, s_x, and that of the denominator, s_y, may be calculated using formulas described earlier. In formula (5), 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 persons 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 mean number of children per family with children.

For all other types of ratios, r is assumed to be zero. If r is actually positive (negative), then this procedure will provide an overestimate (underestimate) of the standard error of the ratio. Examples of this type are the average number of children per family and the poverty rate.

NOTE: For estimates expressed as the ratio of x per 100 y or x per 1,000 y, multiply formula (5) by 100 or 1,000, respectively, to obtain the standard error.

Illustration.

Suppose the ratio of ever-married women 15-44 years old, x, to never-married women 15-44 years old, y, is 1.50. Use the appropriate parameters from Table C and equations (1) and (5) to get

Using formula (5) with r = 0, the estimate of the standard error is

The 90-percent confidence interval is calculated as 1.50 ± 1.645x0.03.

NOTE:

Multiply the parameters in Tables B, C and D by the factors in Tables G and H to get region, state and nonmetropolitan parameters for labor force and fertility estimates.

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.

Note:

For foreign-born characteristics for Total and White, multiply the parameters by 1.3. No adjustment is necessary for foreign born characteristics for Blacks, APIs and Hispanics.

Note:

For foreign-born characteristics for Total and White, multiply the parameters by 1.3. No adjustment is necessary for foreign born characteristics for Blacks, APIs and Hispanics.

Note:

Multiply the parameters by 1.3 to get foreign born parameters for Total and White. No adjustment is necessary for foreign born Blacks, APIs and Hispanics.

Survey Year	Fertility - a parameter				Fertility - b parameter				Percent in Labor Force b parameter			Factor for fertility ratios2
	Total/ White	Black	Hispanic	API	Total/ White	Black	Hispanic	API	Total/ White	Black	Hispanic
1998	-0.000037	-0.000254	-0.000422	-0.000444	2,241	2,241	4,100	2,241	2,530	2,637	3,896	1.00
1995	-0.000035	-0.000244	-0.000587	-0.000699	2,072	2,072	3,791	2,072	2,205	2,299	3,395	0.92
1994	-0.000035	-0.000244	-0.000587	-0.000699	2,072	2,072	3,791	2,072	2,601	2,736	3,395	0.92
1990 to 1992	-0.000038	-0.000279	-0.000280	-0.000908	2,030	2,030	3,422	2,030	2,485	2,485	2,485	0.91
1988	-0.000038	-0.000277	-0.000326	(NA)	2,259	2,259	2,259	(NA)	2,048	2,048	2,048	1.01
1985 to 1987	-0.000037	-0.000233	-0.000262	(NA)	1,903	1,903	1,903	(NA)	1,725	1,725	1,725	0.85
1982 to 1984	-0.000036	-0.000261	-0.000079	(NA)	1,903	1,903	4,137	(NA)	1,725	1,725	1,546	0.85
1977 to 1981	-0.000032	-0.000233	-0.000071	(NA)	1,698	1,698	3,696	(NA)	1,541	1,541	1,381	0.76
1967 to 1976	-0.000031	-0.000227	-0.000069	(NA)	1,656	1,656	3,604	(NA)	1,503	1,503	1,347	0.74

¹Fertility includes number of women by number of children ever born, percent childless, women who have had a child in the last year.

²Multiply the fertility ratio parameters in Table D by the factor to get parameters for previous years.

Source: U.S. Census Bureau, Population Division,
Fertility & Family Statistics Branch
Questions? / 1-866-758-1060
Created: October 24, 2000

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