Documentation: Census 1960 (US, County & State)
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Publisher: U.S. Census Bureau
Document: Women by Number of Children Ever Born (Volume II, Part III - Subject Reports)
citation:
U.S. Bureau of the Census. U.S. Census of Population: 1960. Subject Reports, Women by Number of Children Ever Born. Final Report PC(2)-3A. U.S. Government Printing Office, Washington, D.C. 1964.
Women by Number of Children Ever Born (Volume II, Part III - Subject Reports)
Sample Design and Sampling Variability
Sample Design
For persons in housing units at the time of the 1960 Census, the sampling unit was the housing unit and all its occupants; for persons in group quarters, it was the person. On the first visit to an address, the enumerator assigned a sample key letter (A, B, C, or D) to each housing unit sequentially in the order in which he first visited the units, whether or not he completed an interview. Each enumerator was given a random key letter to start his assignment, and the order of canvassing was indicated in advance, although these Instructions allowed some latitude in the order of visiting addresses. Each housing unit to which the key letter "A" was assigned was designated as a sample unit, and all persons enumerated in the unit were included in the sample. In every group quarters, the sample consisted of every fourth person in the order listed. Most of the 1960 statistics in this report are based on a subsample of one-fifth of the original 25-percent sample schedules; some, however, are based on the full 25-percent sample (tables 10, 11, 46, 50) and a few on a 4-percent sample 2 (tables 43 and 44). The 5-percent subsample was selected on the computer, using a stratified systematic Sample Design. The strata were made up as follows: for persons in regular housing units there were 36 strata, i.e., 9 household size groups by 2 tenure groups by 2 color groups; for persons in group quarters, there were 2 strata, i.e., the 2 color groups.

Although the sampling procedure did not automatically insure an exact 5-percent sample of persons, the Sample Design was unbiased if carried through according to instructions. Generally, for large areas, the deviation from the estimated sample size was found to be quite small. Biases may have arisen, however, when the enumerator failed to follow his listing and sampling instructions exactly.

Table B compares rates of Children Ever Born per 1,000 women, based on the several sample sizes used in this report. Differences in this table reflect primarily sampling error. This is relatively small and should have little influence on the interpretation of the data.

Table B. Comparison of Numbers of Women Ever Married and Rates of Children Ever Born Per 1,000 Women Ever Married From Three Sample Sizes, By Age and Color, For the United States: 1960


Age of women White Nonwhite
Women ever married Children Ever Born per 1,000 women ever married Women ever married Children Ever Born per 1,000 women ever married
25-percent sample 5-percent sample 4-percent sample 25-percent sample 5-percent sample 4-percent sample 25-percent sample 5-percent sample 4-percent sample 25-percent sample 5-percent sample 4-percent sample
15 to 19 years 927,390 527,745 929,939 729 725 727 132,467 132,762 133,700 1,234 1,237 1,264
20 to 24 years 3,501,515 3,490,391 3,494,524 1,370 1,370 1,367 450,800 444,037 444,343 1,992 1,999 1,996
25 to 29 years 4,367,223 4,363,765 4,372,854 2,171 2,171 2,171 587,767 592,345 593,412 2,766 2,771 27,762
30 to 34 years 5,027,100 5,023,379 5,025,735 2,559 2,564 2,566 661,407 657,809 657,347 3,138 3,155 3,159
35 to 39 years 5,372,979 5,396,254 5,402,871 2,629 2,625 2,624 656,033 652,506 654,318 3,147 3,138 3,143
40 to 44 years 4,978,718 4,959,398 4,954,399 2,516 2,515 2,514 579,845 578,256 579,857 2,977 2,984 2,973
45 to 49 years 4,650,767 4,666,602 4,675,741 2,354 2,354 2,353 532,228 533,824 532,588 2,824 2,818 2,818
50 years and over 18,431,259 18,385,438 18,380,425 2,751 2,753 2,754 1,760,450 1,767,948 1,769,094 3,188 3,197 3,195
50 to 54 years 4,115,625 4,106,661 … 2,313 2,317 … 440,823 445,945 … 2,747 2,742 …
55 to 59 years 3,652,921 3,646, 375 … 2,451 2,450 … 395,297 397,087 … 2,889 2,904 …
60 to 64 years 3,148,811 3,139,670 … 2,679 2,676 … 293,398 292,131 … 3,093 3,109 …
65 and over 7,513,902 7,492,732 … 3,166 3,172 … 630,932 632,785 … 3,726 3,741 …



Ratio Estimation
The statistics based on the 5-percent sample of the 1960 Census returns are estimates that have been developed through the use of a Ratio Estimation procedure. This procedure was carried out for each of the following 44 groups of persons in each of the sample-weighting areas.3 The sample weighting areas were defined as those areas within a State consisting of Central Cities of Urbanized Areas, the remaining portion of Urbanized Areas not in central cities, urban places not in Urbanized Areas, or rural areas.

Footnote:
1For a detailed description of the Sample Design and the Ratio Estimation procedure for the 25-percent sample, see 1960 Census of Population, Volume I, Characteristics of the Population, Part 1, United States Summary.
2The 4-percent sample represents households in the 20-percent housing sample that fell into the 5-percent population sample. Statistics shown for this sample were produced by inflating (?) from the 5-percent population sample by a uniform factor of 1.25.
3 Estimates of characteristics from the sample for a given area are produced using the formula:

PIC

Where x' is the estimate of the characteristic for the area obtained through the use of the Ratio Estimation procedure,


xi is the count of sample persons with the characteristic for the area in one (i) of the 44 groups,
yi is the count of all sample persona for "the area in the same one of the 44 groups, and
Yi is the count of persons in the complete count for the area in the same one of the 44 groups.

Group Sex, Color, and Age Relationship and tenure
  Male white:  
1 Under 5  
2 5 to 13  
3 14 to 24 Head of owner household
4 14 to 24 Head of renter household
5 14 to 24 Not head of household
6-8 25 to 44 Same groups as age group 14 to 24
9-11 45 and over Same groups as age group 14 to 24
  Male nonwhite:  
12-22 Same groups as male white  
  Female white:  
23-33 Same groups as male white  
  Female nonwhite:  
34-44 Same groups as male white  


For each of the 44 groups, the ratio of the complete count to the sample count of the population in the group was determined. Each specific sample person in the group was assigned an integral weight so that the sum of the weights would equal the complete count for the group. For example, if the ratio for a group was 20.1, one-tenth of the persons (selected at random) within the group were assigned a weight of 21, and the remaining nine-tenths a weight of 20. The use of such a combination of integral weights rather than a single fractional weight was adopted to avoid the complications involved in rounding in the final tables. In order to increase the reliability, where there were fewer than 275 persons in the complete count in a group, or where the resulting weight was over 80, groups were combined in a specific order to satisfy both of these two conditions.

These ratio estimates reduce the component of sampling error arising from the variation in the size of household and achieve some of the gains of stratification in the selection of the sample, with the strata being the groups for which separate ratio estimates are computed. The net effect is a reduction in the sampling error and bias of most statistics below what would be obtained by weighting the results of the 5- percent sample by a uniform factor of twenty. The reduction in sampling error will be trivial for some items and substantial for others. A by-product of this estimation procedure, in general, is that estimates for this sample are generally consistent with the complete count with respect to the total population and for the subdivisions used as groups in the estimation procedure. A more complete discussion of the technical aspects of these ratio estimates will be presented in another report.
Sampling Variability
The figures from the sample tabulations are subject to Sampling Variability, which can be estimated roughly from the standard errors shown in tables C, D, and E below. These tables14 do not reflect the effect of response variance, processing variance, or bias a- rising in the collection, processing and estimation steps. Estimates of the magnitude of some of these factors in the total error are being evaluated and will be published at a later date. The chances are about two out of three that the difference due to Sampling Variability between an estimate and the figure that would have been obtained from a complete count of the population is less than the standard error. The chances are about 19 out of 20 that the difference is less than twice the standard error and about 99 out of 100 that it is less than times the standard error. The amount by which the estimated standard error must be multiplied to obtain other odds deemed more appropriate can be found in most statistical textbooks.

Table C shows rough standard errors of estimated numbers up to 50,000. The relative sampling errors of larger estimated numbers are somewhat smaller than for 50,000. For estimated numbers above 50,000, however, the nonsampling errors, e.g., response errors and processing errors, may have an increasingly important effect on the total error. Table D shows rough standard errors of data in the form of percentages. Linear interpolation in tables C and D will provide approximate results that are satisfactory for most purposes.

The Sampling Variability of the number of Children Ever Born per 1,000 women depends on the variability of the distribution on which the rate is based, the size of the sample, the Sample Design (for example, the use of households as the sampling unit) and the use of ratio estimates. Estimates of standard errors for rates of Children Ever Born per 1,000 ever-married women are presented in table E. The estimates are approximations that involved a number of simplifying assumptions such as the use of regression equations. If a closer approximation to the standard error of the rate of Children Ever Born is needed, it can be calculated using the following equation:


Table C. Rough Approximation to Standard Error of Estimated Number
(Range of 2 chances out of 3)
Estimated number Standard error
25-percent sample 5-percent sample 4-percent sample
50 15 30 30
100 20 40 40
250 30 60 70
500 40 90 100
1,000 50 120 130
2,500 80 200 220
5,000 110 280 310
10,000 160 390 430
15,000 190 480 530
25,000 250 620 680
50,000 350 880 970


Table D. Rough Approximation to Standard Error of Estimated Precentage
(Range of 2 chances out of 3)
Estimated percentage Base of percentage
500 1,000 2,500 10,000 25,000 100,000
25-percent sample  
2 or 98 1.3 0.9 0.5 0.3 0.1 0.1
5 or 95 2.0 1.4 0.9 0.4 0.2 0.1
10 or 90 2.8 2.0 1.2 0.6 0.3 0.2
25 or 75 3.8 2.7 1.5 0.7 0.4 0.2
50 4.4 3.1 1.6 0.8 0.5 0.3
5-percent sample  
2 or 98 … 2.3 1.3 0.8 0.3 0.3
5 or 95 … 4.0 2.3 1.0 0.5 0.3
10 or 90 … 5.0 3.0 1.5 0.8 0.5
25 or 75 … 6.8 3.8 1.8 1.0 0.5
50 … 7.8 4.0 2.0 1.3 0.8
4-percent sample  
2 or 98 … 2.5 1.4 0.9 0.3 0.3
5 or 95 … 4.4 2.5 1.1 0.6 0.3
10 or 90 … 5.5 3.3 1.6 0.9 0.6
25 or 75 … 7.5 4.2 2.0 1.1 0.6
50 … 8.6 4.4 2.2 1.4 0.9


Table E. Standard Error of Number of Children Ever (Range of 2 chances out of 3)
Sample size and number of women ever married Number of Children Ever Born per 1,000 women ever married
500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500
25-percent sample  
500 40 61 80 98 114 132 147 164 180
1,000 35 55 68 86 108 120 136 152 171
2,500 21 35 47 59 71 82 91 101 110
10,000 10 17 24 29 35 40 46 50 55
25,000 7 12 16 19 23 26 28 32 34
100,000 3 6 8 9 11 12 14 16 17
500,000 2 2 3 4 5 6 6 7 8
1,000,000 1 1 2 2 3 3 4 4 5
5-percent sample  
1,000 90 141 174 220 276 307 348 389 438
2,500 54 90 120 151 182 210 233 259 282
10,000 26 44 61 74 90 102 118 128 141
25,000 18 31 41 49 59 67 72 82 87
100,000 8 15 20 23 28 31 36 41 44
500,000 5 5 8 10 13 15 15 18 20
1,000,000 3 3 5 5 8 8 10 10 13
4-percent sample  
1,000 101 158 195 246 309 344 390 436 491
2,500 60 101 134 169 204 235 261 290 316
10,000 29 49 68 83 101 114 132 143 158
25,000 20 35 46 55 66 75 81 92 97
100,000 9 17 22 26 31 35 40 46 49
500,000 6 6 9 11 15 17 17 20 22
1,000,000 3 3 6 6 9 9 11 11 15


The use of the equation will provide a closer approximation to the standard error of a rate of children ever born than the use of table E. Table E was prepared using this formula and also a regression function relating the distribution of women with 0, 1, 2, etc., children to the total number of Children Ever Born. In any specific case, this regression function is only an approximation.

Illustration: Table 31 shows a rate of 2,892 Children Ever Born per 1,000 women for 48,109 white women 25 to 29 years old whose husbands are employed as farm laborers and foremen. Table 31 is based on a 5-percent sample, and table E shows that for an estimate of 2,892 Children Ever Born per 1,000 women ever married, based on the 5-percent sample for 48,109 women, a rough approximation to the standard error is about 54. This means that the chances are about 2 out of 3 that a complete census result would not differ by more than 54 from the estimated rate of 2,892 children per 1,000 women. It also follows that there is only about 1 chance in 100 that a complete count would differ by as much as 135, that is, by about 2 ½ times the number estimated from table E.

For a further discussion of the Sampling Variability and of the method for obtaining standard errors of differences between two estimates, see Volume I, Characteristics of the Population.