The analysisofremarriagestatisticsinthisreport is based primarilyon frequenciespublishedinVital statistics of the United Stutes, volume 111.1969. Data forearlieryearsusedforcomparisonwere takenfrom appropriateannualvolumes of thispublication.Each annual volume includesa completediscussionof the technicalaspectsof the marriage data itcontains.
Sources of Data
Marriage statisticsfor the UnitedStatesand for the marriage-registrationarea are limitedto events occurringduringthe year and registeredwithinthe specifiedarea.TabulationsforStatesand otherareas are by placeof occurrence.Eventsoccurring tonon-residentsare included;marriagesof members oftbe Armed Forces or otherU.S.nationals thatoccurout-sideof the UnitedStatesare excluded.UnitedStates refersto the 50 Statesand the DistrictofColumbia.
Alaska has been includedintheU.S.tabulationssince 1959 and Hawaiisince1960.Figuresforcharacteris-ticsof marriages are based on datatabulatedfrom probabilitysamplesofrecordsselectedintheNational Centerfor HealthStatisticsfrom copiesofmarriage forms sent in by Statesparticipatingin the MM.
!n1969theMRA included39 StatesandtheDistrict of Columbia.The Virginislandsand PuertoRicoare
a part of The MRA
the MRA but are excludedfrom thisreport.
includesStateswithcentralfilesof mar-riage certificatesand sufficientlycompleteand ac-curatereportingofdemographicitemson theirrecord towarrantcollection,processing,andpublicationinthe officialU.S.annualreports.MarriagesintheMRA rep-resentabout 77 percentof thenationaltotalin1969.
Marriage Sample
Records from the MRA were sampledatfivedif-ferentrateswhich dependedon the annualtotalsfor eachStateas indicatedinthetablebelow.
Estimating Procedures
Frequenciesbasedon the marriage sampleswere estimatedintwo steps.
1.
Marriage sample - sampling rates and sample size:
Each samplecasewas assigneda weightwhich was the reciprocaloftheprobability (orsam-plingrate)used to select the case. Thus if a marriage record was selected from a State with a probability of 1/10, the record had a weight of 10.
Marriage-registrationarea, 1969
Stratum and area
Stratum 1: Alaska, Delaware, Vermont, and Wyoming Stratum 2: District of Columbia, Hawaii, Maine,
Montana, New Hampshire, Rhode Island, South Dakota, and Utah
Stratmn 3: Connecticut,Idaho, Iowa, Kansas, Louisiana, Mississf.ppi,Nebraska, Oregon and West Virginia
Stratum 4: Alabama, Florida, Indiana, Kentucky, Maryland, Massachusetts,Missouri, New Jersey, North Carolina, Tennesse, Virginia, and Wisconsin
Stratum 5: California,Georgia, Illinois, Mf.chigan, New York, Ohio, and Pennsylvania
Sampling rate
All records
1/2
1/5
Number of sample records
15,891
37,258
38,154
59,295 39,321
I
2. Frequencies were estimated by summing the weights of the records instead of tabulating the number of sample cases. Thus each frequency distribution such as age at marriage of remar-rying. brides is a tabulation of the total of weighted sample cases included in each age cat-egory.
Rates for census years are based on the population enumerated as of April 1. All other rates are based on estimates of the population present in the area as of July 1, including Armed Forces stationed in the area but excluding Armed Forces abroad. The estimates were prepared by the U.S. Bureau of the Census.
“Not Stafedl” Cases
!INot stated! ! cases arise chiefly frOITI ~ck of
re-sponses to items on reporting forms and from variations in, items requested on forms usedin the MRA. The num-bers of not stated cases for each MRA State and char-acteristic may be found in Vital SWiatics of the United States, Volume III, of the appropriate year. In table D of this .qeport the “not stated” cases for previous mar-ital status were distributed before computing the percent distribution.
Remarriage Estimates for United States
Estimates of the number of remarriages in the United States for each year, 1965 to 1%9, were pre-pared using the percent of all marriages that were re-marriages in the MRA. The MRA consisted of 39 States and the District of Columbia in 1968 and 1%9, and 38 States and the District of Columbia in 1965, 1966, and 1967. The addition of Missouri in 1968 affected the per-cent of remarriages very slightly. The percent of re-marriages obtained for each year was multiplied times the unrounded marriage total for the United States in that year. Rates were computed from these estimated numbers per 1,000 divorced and widowed persons in the United States. The estimated total remarriages shown in table A are rounded to the nearest 1,000.
Sampling Errors
Estimates computed from sample data vary some-what about the value that would be obtained from a com-plete census of the same population. The standard error is a measure of this sampling variability. On the average, estimates will differ from the corresponding census valpe by less than a standard error about 68 percent of.
the time. Approximate standard errors of estimates shown in this report may be obtained from tables I and 11of this appendix.
Table 1. Standard errors of estimated marriage frequencies: Marriage-registration area, 1969
[Marriages ro.n&d to the nearest 500]
Percent of
Number of marriages
1,660,500
16,500 or 1,644,000 33,000 or 1,627,500 50,000 or 1,610,500 66,500 or 1,594,000 83,000 or 1,577,500 116,000 or 1,544,500 166,000 or 1,494,500 249,000 or 1,411,500 332,000 or 1,328,500 415,000 Or 1,245,500 498,000 or 1,162,500 664,000 or 996,500 830,250
Since the magnitude of a sampling error of an esti-mated rate depends orsboth the frequency and the popula-tion on which the rate is computed, two or more identical rates may have different sampling errors. Marriage fre-quericies and estimates for the unmarried resident pop-ulation by age, marital status, and sex for the MRA used in computing rates included in this report appear in Vitii statistics of the United Statet?, Volume 111,of the specified years.
k is useful to note that the population data often may be extracted from rates and frequencies. If f is an estimated frequency and ~ is the corresponding rate, then the size of the Pc@ation involved is f/r.
Rates which appear in this report may be one of three types, each of which involves a different method for computing the corresponding error.
1. The” standard error of an estimated proportion of a known total can be computed by dividing the standard error for the estimated frequency by the known total.
As an illustration, table D shows that an estimated 23.1 percent of all brides married in 1%9 in the MM had been previously married.
The corresponding number of marriages of the previously married is 383,576. Table I indicates that the sampling error of the number 383,576 must lie ~omewher~. Eaween the sampling error for 20 percent and 25-percent, or between 1,837
Table II. Standard errors of estimated marriage rates (per 1,000 population) by number of marria es and size of base population, and standard errors of the population: Marriage-registration area, 19 98
Percent lf total mrriages in the
.b 25 50
Population in 1, 000s Number of marriages
T
100 200 300 500 L, 000 ?, 500 5,000 10,000 15,000Standard errors of
the population --- 5,000 7,000
+
27,000 36,000 20,000
and 1,989. By interpolating, a sampling error of .9X = standard error of x
1,931 is obt~ned, which &yvidedby-the ;otal num-ber of MRA marriages (1,660,500) yields .0012 or 0.1 percent. By adding and subtracting 0.1 from 23.1 we obtain the interval 23.0 to 23.2.
The chances are about 68 out of 100 that the ac-tual percentage falls within this interval.
Sy = standard error of y
For example, if we desire the standard error of the proportion of remarriages in which the bride was divorced (77.5 percent) then from table D:
To obtain a more exact sampling error for a given marriage frequency the formula used for computing table I can be applied:
Sx G 4,592+ (a)
Where pis the percentage of interest and q =1-p
x = 297,230 y = 383,576
From table I, we can interpolate to get
.$x & 1,754 SY + 1,931
Applying formula (b), SP + .0024. The standard error of the percent is .24.
Applying this formula to the above example, the sampling error of 383,576 marriages is found to be 1,935, a slightly more accurate figure than 1,931. However, the sampling error of the per-cent would still be 0.1.
3. The sampling error of a ratio can be approxi-mated when the numerator and the denomina-tor are estimates of different parameters based on probability samples using the following formula:
>
sXlq= —.1Y
J
S:+:2S:()
Y2. Proportions with an estimated base, and with
counts in the numerator also included in the (c)
denominator, have standard error:
Where x = the estimated frequency of a particular char-acteristic of the population
(b)
of interest
Y = the estimated size of the population at risk s, = the standard error of x
Sv = the standard error of y
Where p = XIY is the proportion
It should be noted that formula (C)gives the sam-pling error of a proportion. To obtain a sampling error of a rate per 1,000, SX,ymust be multiplied by 1,000.
The sampling errors of many such rates are given in table II. For example, the sampling error of the remarriage rate for previously di-vorced men in the MR4 can be approximated.
This rate in 1969 was 220.8 (table 2) and the base population was 1,213,000. The total number of remarriages for this population is (1,213,000) (220.8/1,000) = 267,830. From table II an ap-proximate sampling error for tbe rate can be obtained by using the numbers closest to the numbers in the example. The number of mar-riages used in the table would be 249,000, and the population would be 1,000,000. F,or these two numbers an approximate sampling error of 6.9 is obtained from the table.
A more exact sampling error can be com-puted using formula (c) given above.
x = 267,830 y = 1,213,000
Calculated from formula (a) for marriage fre-quencies
Sx A 1,688
Interpolating from the row of standard errors of the population given in table II
Sv & 28,278
The resulting Sx,yis .0053. The standard error of the rate per 1,000 is 5.3.
Statistical Significance
To determine if two proportions P, and P2 (or
two percentages of rates converted into proportions) are
significantly different statistically, the following ex-pression can be used:
P, - P2
.-(d)
If this quotient is greater than 2, the probability is less than .05 that the difference between the two proportions is due to chance. For example, the remarriage rate for brides 25 to 29 years is 291.6 and the remarriage rate for brides 30 to 34 is 2!36.3 (table 4). Formula (d) can be used to test whether these two rates are significantly different statistically.
Converting the rates to proportions
P,=.2916 P2 =.2063
C)btaining the frequencies for these age groups from the annual volume for 1969
~, =71,148 X2 = 4%296
Dividing the frequencies by the proportions to obtain the population bases
y, = 243,992 Y2 = 238,953
Interpolating from tables I and H to obtain standard errors of frequencies
5X, & 928 SX2 k 777
Svl & 14,320 Sy, a 14,169
Applying formula (c)
Spl =.0175 SP2=.0127
The quotient obtained by applying formula (d) is 3.947.
Therefore, the two rates can be assumed to be signifi-cantly different statistically.
000
-2 U. S. GOVERNMENT PI?DJTRJGOFFICE :1974 543-8 S0/38
VITAL AND HEALTH STATISTICS PUBLICATION SERt ES Originally Public Health Service Publication No. 1000
Series 1. programs and collection procedures. —Reports which describe the general programs of the National Center for Health Statistics and its offices and divisions, data collection methods used, definitions, and other material necessary for understanding the data.
Series 2. Data emluation and methods research. —Studies of new statistical methodology including: experi-mental tests of new survey methods, studies of vital statistics collection methods, new analytical techniques, objective evaluations of reliability of collected data, contributions to statistical theory.
Series 3. Analytical studies.—Reports presenting analytical or interpretive studies basedon vital and health statistics, carrying the analysis further than the expository types of reports in the other series.
Series 4. Documents and committee repo~ts. —Final reports of major committees concerned wit$ vital and health statistics, and documents such as recommended model vital registration laws and revised birth and death certificates,
Series 10. Dab from the Health Intevview Swvev.— Statistics on illness, accidental injuries, disability, use of hpspital, medical, dental, and other services, and other health-related topics, based on data collected in a continuing national household interview survey.
Series 11. Data from the Health Examination Swvey.—Data from direct examination, testing, and measure-ment of national samples of the civilian, noninstitutional population provide the basis for two types of reports: (1) estimates of the medically defined prevalence of specific diseases in the United Statea and the distributions of the population with respect to physical, physiological, and psycho-logical characteristics; and (2) analysis of relationships among the various measurements without reference to an explicit finite universe of persons.
Series 12. Data from the Ins titutional Population Surveys. —Statistics relating to the health characteristics of persons in institutions, and their medical, nursing, and personal care received, based on national samples of establishments providing these services and samples of the residents or patients.
Series 13. Datu fi’om the Hospital Discharge Swvey. –Statistics relating to discliarged patients in short-stay hospitals, based on a sample of patient records in a national sample of hospitals.
Series 14, Data on health resources: manpower and facilities. —Statistics on the numbers, geographic distri-bution, and characteristics of health resources including physicians, dentists, nurses, other health occupations, hospitals, nursing homes, and outpatient facilities.
Series 20. Data on movtality. —Various statistics on mortality other than as included in regular annual or montnl y reports —special analyses by cause of death, age, and other demographic variables, also geographic and time series analyses.
Sevies 21. Data on natality, marriage, and divorce. —Various statistics on nata~ity, marriage, and divorce other than as included in regular annual or monthly reports-special analyses by demographic variables, also geographic and time series analyses, studies of fertility.
Series 22. Data porn the National Natality and Movtality Suvveys. —Statistics on chai-acteristics of births and deaths not available from the vital records, based on sample surveys stemming from these records, including such topics as mortality by socioeconomic class, hospital experience in the last year of life, medical care during pregnancy, health insurance coverage, etc.
For a list of titles of reports published in these series, write to: Office of Information
U.S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE PUBLIC HEALTH SERVICE
Health Resources Administration
5600 Fishers Lane POSTAGE AND FEES PAID
o
*
Rockvillc, Maryland 20852
U.S. DEPARTMENT OF HEW
US.MAIL
OFFICIAL BUSINESS HEW 390
Penah y for Private Use $300
THIRD CLASS BLK. RT.