COMPUTATION OF RATES AND OTHER MEASURES Population bases The rates shown in this report were computed on the basis of population statistics prepared by the U.S. Bureau of the Census. Rates for 1940, 1950, 1960, 1970, 1980, and 1990 are based on the population enumerated as of April 1 in the censuses of those years. Rates for all other years are based on the estimated midyear (July 1) population for the respective years. Birth rates for the United States, individual States, and metropolitan areas are based on the total resident populations of the respective areas. Except as noted these populations exclude the Armed Forces abroad but include the Armed Forces stationed in each area. The resident population of the birth- and death-registration States for 1900-32 and for the United States for 1900-94 is shown in table 4-1. In addition, the population including Armed Forces abroad is shown for the United States. Table B shows the sources for these populations. In both the 1980 and 1990 censuses, a substantial number of persons did not specify a racial group that could be classified as any of the White, Black, American Indian, Eskimo, Aleut, Asian, or Pacific Islander categories on the census form (16). In 1980 the number of persons of "other" race was 6,758,319; in 1990, it was 9,804,847. In both censuses, the large majority of these persons were of Hispanic origin (based on response to a separate question on the form), and many wrote in their Hispanic origin, or Hispanic origin type (for example, Mexican, Puerto Rican) as their race. In both 1980 and 1990, persons of unspecified race were allocated to one of the four tabulated racial groups (white, black, American Indian, Asian or Pacific Islander), based on their response to the Hispanic origin question. These four race categories conform with OMB Directive 15 which mandates that race data must contain at least these 4 categories. These categories are also more consistent with the race categories in vital statistics. In 1980 the allocation of unspecified race was carried out using cross-tabulations of age, sex, race, type of Hispanic origin, and county of residence. Persons of Hispanic origin and unspecified race were allocated to either white or black, based on their Hispanic origin type. Persons of "other" race and Mexican origin were categorically assumed to be white, while persons in other Hispanic categories were distributed to white and black pro rata within the county-age-sex group. For "other-not-specified" persons who were not Hispanic, race was allocated to white, black, or Asian and Pacific Islander, based on proportions gleaned from sample data. The 20-percent sample (respondents who were enumerated on the longer census form) provided a highly detailed coding of race, which allowed identification of otherwise unidentifiable responses with a specified race category. Allocation proportions were thus established at the State level, which were used to distribute the non-Hispanic persons of "other" race in the 100-percent tabulations. In 1990 the race modification procedure was carried out using individual census records. Persons whose race could not be specified were assigned to a racial category using a pool of "race donors," which was derived from persons of specified race and the identical response to the Hispanic origin question within the auspices of the same Census District cmpnat94.doc- Page 1 Table B. Sources for resident population and population including Armed Forces abroad: Birth- and death-registration States, 1900-1932, and United States, 1900-1994. ----------------------------------------------------------------------------- Year | Source --------------|-------------------------------------------------------------- 1994----------| U.S. Bureau of the Census, United States population | estimates, by age, sex, race, and Hispanic origin: 1990- | 1994. Census file PPL-21. Washington: U.S. Department of | Commerce. 1995 1993----------| U.S. Bureau of the Census, United States population | estimates, by age, sex, race, and Hispanic origin: 1993. | Census file RESO793. Washington: U.S. Department of | Commerce. 1995 1992----------| U.S. Bureau of the Census. United States population | estimates, by age, sex, race, and Hispanic origin: 1992. | Census file RESPO792. Washington: U.S. Department of | Commerce. 1994 1991----------| U.S. Bureau of the Census, Unpublished data consistent | with Current Population Reports, Series P-25, No.1095, | Feb. 1993. 1990----------| U.S. Bureau of the Census, Unpublished data from the 1990 | census. 1990 CPH-L-74 and unpublished data consistent with | Current Population Reports, Series P-25, No. 1095, Nov. 1992 1989----------| U.S. Bureau of the Census, Current Population Reports, | Series P-25, No. 1057, Mar. 1990. 1988----------| U.S. Bureau of the Census, Current Population Reports, | Series P-25, No. 1045, Jan. 1990. 1986-87-------| U.S. Bureau of the Census, Current Population Reports, | Series P-25, No. 1022, Mar. 1988. 1985----------| U.S. Bureau of the Census, Current Population Reports, | Series P-25, No. 1000, Feb. 1987. 1984----------| U.S. Bureau of the Census, Current Population Reports, | Series P-25, No. 985, Apr. 1986. 1983----------| U.S. Bureau of the Census, Current Population Reports, | Series P-25, No. 965, Mar. 1985. 1982----------| U.S. Bureau of the Census, Current Population Reports, | Series P-25, No. 949, May 1984. 1981----------| U.S. Bureau of the Census, Current Population Reports, | Series P-25, No. 929, May 1983. 1980----------| U.S. Bureau of the Census, U.S. Census of Population: | 1980, Number of Inhabitants, PC80-1-A1, United States | Summary, 1983. 1971-79-------| U.S. Bureau of the Census, Current Population Reports, | Series P-25, No. 917, July 1982. 1970----------| U.S. Bureau of the Census, U.S. Census of Population: | 1970, Number of Inhabitants, Final Report PC(1)-A1, | United States Summary, 1971. 1961-69-------| U.S. Bureau of the Census, Current Population Reports, | Series P-25, No. 519, Apr. 1974. 1960----------| U.S. Bureau of the Census, U.S. Census of Population: | 1960, Number of Inhabitants, PC(1)-A1, United States | Summary, 1964. 1951-59-------| U.S. Bureau of the Census, Current Population Reports, | Series P-25, No. 310, June 30, 1965. 1940-50-------| U.S. Bureau of the Census, Current Population Reports, | Series P-25, No. 499, May 1973 cmpnat94.doc- Page 2 Table B (cont'd). Sources for resident population and population including Armed Forces abroad: Birth- and death-registration States, 1900-1932, and United States, 1900-1994. ----------------------------------------------------------------------------- Year | Source --------------|-------------------------------------------------------------- 1930-39-------| U.S. Bureau of the Census, Current Population Reports, | Series P-25, No. 499, May 1973, and National Office of | Vital Statistics, Vital Statistics Rates in the United | States, 1900-1940, 1947 1920-29-------| National Office of Vital Statistics, Vital Statistics | Rates in the United States, 1900-1940, 1947 1917-19-------| Same as for 1930-39. 1900-16-------| Same as for 1920-29. ______________|______________________________________________________________ Office. As in 1980, the underlying assumption was that the Hispanic origin response was the major criterion for allocating race. Unlike 1980, persons of Hispanic origin, including Mexican, could be assigned to any racial group, rather than white or black only, and the non-Hispanic component of "other" race was allocated primarily on the basis of geography (District Office), rather than detailed characteristic. The means by which respondent's age was determined were fundamentally different in the two censuses; therefore, the problems that necessitated the modification were different. In 1980 respondents reported year of birth and quarter of birth (within year) on the census form. When census results were tabulated, persons born in the first quarter of the year (before April 1) had age equal to 1980 minus year of birth, while persons born in the last three quarters had age equal to 1979 minus year of birth. In 1990 the quarter year of birth was not reported on the census form, so that direct determination of age from year of birth was impossible. In 1990 census publications age is based on respondents' direct reports of age at last birthday. This definition proved inadequate for postcensal estimates, because it was apparent that many respondents had reported their age at time of either completion of the census form or interview by an enumerator, which could occur several months after the April 1 reference data. As a result, age was biased upward. Modification was based on a respecification of age, for most individual respondents, by year of birth, with allocation to first quarter (persons aged 1990 minus year of birth) and last three quarters (aged 1989 minus year of birth) based on a historical series of registered births by month. This process partially restored the 1980 logic for assignment of age. It was not considered necessary to correct for age overstatement and heaping in 1990, because the availability of age and year of birth on the census form provided elimination of spurious year-of-birth reports in the census data before modification occurred. Populations for 1994--The population of the United States by age, sex, race, and Hispanic origin are shown in the Census Bureau report, United States population estimates by age, sex, race, and Hispanic origin: 1990 to 1994. U.S. Bureau of the Census. PPL-21. Washington: U.S. Department of Commerce. 1995. Populations for 1993--The population of the United States by age, sex, race, and Hispanic origin are tabulated from Census file RESO793. Washington: U.S. Department of Commerce. 1995. cmpnat94.doc- Page 3 Populations for 1992--The population of the United States by age, sex, race, and Hispanic origin are tabulated from Census file RESPO792. Washington: U.S. Department of Commerce. 1994. Populations for 1991--The population of the United States by age, race, and sex are shown in Current Population Reports, Series P-25, Number 1095. Monthly population figures were published in Current Population Reports, Series P-25, Number 1097. Populations for 1990--The population of the United States by age, race, and sex, and the population for each State are shown in Current Population Reports, Series P-25, Number 1095. The figures have been modified as described above. Monthly population figures were published in Current Population Reports, Series P-25, Number 1094. Population estimates for 1981-89--Birth rates for 1981-89 (except those for cohorts of women) have been revised, based on revised population estimates that are consistent with the 1990 census levels, and thus may differ from rates published in volumes of Vital Statistics of the United States for these years. The 1990 census counted approximately 1.5 million fewer persons than had earlier been estimated for April 1, 1990. The revised estimates for the United States by age, race, and sex were published by the U.S. Bureau of the Census in Current Population Reports, Series P-25, Number 1095. Population estimates by month are based on data published in Current Population Reports, Series P-25, Number 1094 and unpublished data. Unpublished revised estimates for States were obtained from the U.S. Bureau of the Census. Populations for 1980--The population of the United States by age, race, and sex, and the population for each State are shown in tables 4-2 and 4-3 of volume I, Vital Statistics of the United States, 1980. The figures by race have been modified as described above. Monthly population figures were published in Current Population Reports, Series P-25, Number 899. Population estimates for 1971-79--Birth rates for 1971-79 (except those for cohorts of women) have been revised, based on revised population estimates that are consistent with the 1980 census levels, and thus may differ from rates published in volumes of Vital Statistics of the United States for these years. The 1980 census counted approximately 5.5 million more persons than had earlier been estimated for April 1, 1980 (17). The revised estimates for the United States by age, race, and sex were published by the U.S. Bureau of the Census in Current Population Reports, Series P-25, Number 917. Population estimates by month are based on data published in Current Population Reports, Series P-25, Number 899. Unpublished revised estimates for States were obtained from the U.S. Bureau of the Census. Population estimates for 1961-69--Birth rates for 1961-69 are based on revised estimates of the population and thus may differ slightly from rates published before 1976. The revised estimates used in computing these rates were published in Current Population Reports, Series P-25, Number 519. The rates for 1961-64 are based on revised estimates of the population published in Current Population Reports, Series P-25, Numbers 321 and 324 and may differ slightly from rates published in those years. Population estimates for 1951-59--Final intercensal estimates of the population by age, race, and sex and total population by State for 1951-59 are shown in tables 4-4 and 4-5 of volume I, Vital Statistics of the United States, 1966. Beginning with 1963 these final estimates have been used to compute birth rates for 1951-59 in all issues of Vital Statistics of the United States. cmpnat94.doc- Page 4 Net census undercounts and overcounts The U.S. Bureau of the Census has conducted extensive research to evaluate the coverage of the U.S. population (including undercount, overcount, and misstatement of age, race, and sex) in the last five decennial censuses--1950, 1960, 1970, 1980, and 1990. These studies provide estimates of the national population that was not enumerated or overenumerated in the respective censuses, by age, race, and sex (17-19). The report for 1990 (20) includes estimates of net underenumeration and overenumeration for age, sex, and racial subgroups of the national population, modified for race consistency with previous population counts as described in the section "Population bases." These studies indicate that there is differential coverage in the censuses among the population subgroups; that is, some age, race, and sex groups are more completely enumerated than others. To the extent that these estimates of overcounts or undercounts are valid, that they are substantial, and that they vary among subgroups and geographic areas, census miscounts can have consequences for vital statistics measures (18). However, the effects of undercounts in the census are reduced to the extent that there is underregistration of births. If these two factors are of equal magnitude, rates based on unadjusted populations are more accurate than those based on adjusted populations because the births have not been adjusted for underregistration. The impact of net census miscounts on vital statistics measures includes the effects on levels of the rates and effects on differentials among groups. If adjustments were made for persons who were not counted in the census of population, the size of the denominators would generally increase and the rates would be smaller than without an adjustment. Adjusted rates for 1990 can be computed by multiplying the reported rates by ratios of the 1990 census-level population adjusted for the estimated net census miscounts, which are shown in table C. A ratio of less than 1.0 indicates a net census undercount and would result in a corresponding decrease in the rate. A ratio in excess of 1.0 indicates a net census overcount and would result in a corresponding increase in the rate. Enumeration of white females in the childbearing ages was at least 97 percent complete for all ages. Among black women, the undercount ranged up to 5 percent. Generally, females in the childbearing ages were more completely enumerated than males for similar race-age groups. If vital statistics measures were calculated with adjustments for net census miscounts for each of these subgroups, the resulting rates would have been differentially changed from their original levels; that is, rates for those groups with the greatest estimated overcounts or undercounts would show the greatest relative changes due to these adjustments. Thus the racial differential in fertility between the white and the "All other" population can be affected by such adjustments. Cohort fertility tables The various fertility measures shown for cohorts of women are computed from births adjusted for underregistration and population estimates corrected for underenumeration and misstatement of age. Data published after 1974 use cmpnat94.doc- Page 5 revised population estimates prepared by the U.S. Bureau of the Census and have been expanded to include data for the two major racial groups. Heuser has prepared a detailed description of the methods used in deriving these measures as well as more detailed data for earlier years (21). Parity distribution--The percent distribution of women by parity (number of children ever born alive to mother) is derived from cumulative birth rates by order of birth. The percent of zero-parity women is found by subtracting the cumulative first birth rate from 1,000 and dividing by 10. The proportions of women at parities one through six are found from the following formula: (cum. rate, order N)-(cum. rate, order N+1) Percent at N parity =3D ------------------------------------------- 10 The percent of women at seventh higher parities is found by dividing the cumulative rate for seventh-order births by 10. Birth probabilities--birth probabilities indicate the likelihood that a woman of a certain parity and age at the beginning of the year will have a child during the year. Birth probabilities differ from central birth rates in that the denominator for birth probabilities is specific for parity as well as for age. Age-sex-adjusted birth rates The age-sex-adjusted birth rates are computed by the direct method. The age distribution of women aged 10-49 years as enumerated in 1940 and the total population of the United States for that year are used as the standard populations. The age-sex-adjusted birth rates show differences in the level of fertility independent of differences in the age and sex composition of the population. It is important not to confuse these adjusted rates with the crude rates shown in other tables. Total fertility rate The total fertility rate is the sum of the birth rates by age of mother (in 5-year age groups) multiplied by 5. It is an age-adjusted rate because it is based on the assumption that there are the same number of women in each age group. The rate of 2,036 in 1994, for example, means that if a hypothetical group of 1,000 women were to have the same birth rates in each age group that were observed in the actual childbearing population in 1994, they would have a total of 2,036 children by the time they reached the end of the reproductive period (taken here to be age 50 years), assuming that all of the women survived to that age. Intrinsic vital rates The intrinsic vital rates are calculated from a stable population. A stable population is that hypothetical population, closed to external migration, that would become fixed in age-sex structure after repeated applications of a constant set of age-sex specific birth and death rates. For the mathematical derivation of intrinsic vital rates, see pages 4-13 and 4-14 cmpnat94.doc- Page 6 in the Technical Appendix of volume I, Vital Statistics of the United States, 1962. The technique of calculating intrinsic vital rates is described by Barclay (22). Seasonal adjustment of rates The seasonally adjusted birth and fertility rates are computed from the X-11 variant of Census Method II (23). This method of seasonal adjustment used since 1964 differs slightly from the U.S. Bureau of Labor Statistics (BLS) Seasonal Factor Method, which was used for Vital Statistics of the United States, 1964. The fundamental technique is the same in that it is an adaptation of the ratio-to-moving-average method. Before 1964 the method of seasonal adjustment was based on the X-9 variant and other variants of Census Method II. A comparison of the Census Method II with the BLS Seasonal Factor Method shows the differences in the seasonal patterns of births to be negligible. Computation of percents, medians, and means Percent distributions, medians, and means are computed using only events for which the characteristic is reported. The "Not stated" category is subtracted from the total before computation of these measures. The asterisk (*) indicates that the numerator and/or denominator number is less than 20. cmpnat94.doc- Page 7 Table C. Ratio of census-level resident population to resident population adjusted for estimated net census undercount by age, sex, and race: United States, April 1, 1990 ______________________________________________________________________________ | Total | White | |_______________________________|_______________________________| Age | Both | Male | Female | Both | Male | Female | | Sexes | | | Sexes | | | _____________|_________|__________|__________|__________|__________|________ | All ages | 0.9815 | 0.9721 | 0.9906 | 0.9802 | 0.9728 | 0.9873 | 10-14 years | 0.9882 | 0.9891 | 0.9873 | 0.9830 | 0.9841 | 0.9818 | 15-19 years | 1.0166 | 1.0198 | 1.0133 | 1.0094 | 1.0128 | 1.0059 | 20-24 years | 1.0002 | 0.9987 | 1.0017 | 0.9975 | 0.9985 | 0.9966 | 25-29 years | 0.9591 | 0.9439 | 0.9748 | 0.9558 | 0.9441 | 0.9681 | 30-34 years | 0.9687 | 0.9487 | 0.9892 | 0.9669 | 0.9518 | 0.9828 | 35-39 years | 0.9790 | 0.9628 | 0.9954 | 0.9764 | 0.9643 | 0.9888 | 40-44 years | 0.9901 | 0.9758 | 1.0044 | 0.9875 | 0.9764 | 0.9988 | 45-49 years | 0.9775 | 0.9633 | 0.9916 | 0.9762 | 0.9648 | 0.9877 | 50-54 years | ... | 0.9623 | ... | ... | 0.9651 | ... | 55 years | | | | | | | and older | ... | 0.9758 | ... | ... | 0.9783 | ... | 15-44 years | ... | ... | 0.9954 | ... | | 0.9890 | 15-54 years | ... | 0.9710 | ... | ... | 0.9710 | ... | _____________|_________|__________|__________|__________|__________|_________| cmpnat94.doc- Page 8 Table C (cont'd). Ratio of census-level resident population to resident population adjusted for estimated net census undercount by age, sex, and race: United States, April 1, 1990 ______________________________________________________ | Black | |_______________________________| Age | Both | Male | Female | | Sexes | | | _____________________|_________|__________|__________| All ages | 0.9432 | 0.9151 | 0.9699 | 10-14 years | 0.9591 | 0.9586 | 0.9595 | 15-19 years | 0.9988 | 1.0016 | 0.9959 | 20-24 years | 0.9593 | 0.9432 | 0.9753 | 25-29 years | 0.9123 | 0.8732 | 0.9510 | 30-34 years | 0.9129 | 0.8599 | 0.9651 | 35-39 years | 0.9303 | 0.8808 | 0.9778 | 40-44 years | 0.9410 | 0.8943 | 0.9850 | 45-49 years | 0.9302 | 0.8807 | 0.9762 | 50-54 years | ... | 0.8802 | ... | 55 years and older | ... | 0.9294 | ... | | | | | 15-44 years | ... | ... | 0.9739 | 15-54 years | ... | 0.9046 | ... | _____________________|_________|__________|__________| cmpnat94.doc- Page 9