Documentation: Census 1960 (US, County & State)
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Publisher: U.S. Census Bureau
Document: Women by Children Under 5 Years Old (Volume II, Part III - Subject Reports)
citation:
U.S. Bureau of the Census. U.S. Census of Population: 1960. Subject Reports, Women by Children Under 5 Years Old. Final Report PC(2)-3C. U.S. Government Printing Office, Washington, D.C. 1968.
Women by Children Under 5 Years Old (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; 5 some, however, are based on a V-percent sample (tables 61+ and 65). 6 The sub-sample 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. 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 C compares ratios of own children under 5 per 1,000 women, as presented in this report, based on the 5-Percent sample, with corresponding statistics based on the 25-percent sample presented in Volume I of the 1960 Census of Population. Differences in this table reflect primarily sampling error.

Table C. Comparisons of Numbers of Women and Ratios of own children Under 5 Years Old per 1,000 Women from 25-Percent and 5-Percent Samples, By age, color, and Marital Status, For the United States: 1960

age of woman White Nonwhite
Total women Women ever married Children under 5 years old Total women Women ever married Children under 5 years old
Per 1,000 women Per 1,000 women ever married Per 1,000 women Per 1,000 women ever married
25-percent sample 5-percent sample 25-percent sample 5-percent sample 25-percent sample 5-percent sample 25-percent sample 5-percent sample 25-percent sample 5-percent sample 25-percent sample 5-percent sample 25-percent sample 5-percent sample 25-percent sample 5-percent sample
15 to 19 years 5,772,421 5,770,262 927,390 927,745 94 94 585 584 816,181 817,908 132,467 132,762 141 144 868 888
20 to 24 years 4,822,377 4,817,117 3,501,515 3,490,391 826 826 1,138 1,140 697,560 689,395 450,800 444,037 861 863 1,333 1,340
25 to 29 years 4,839,982 4,833,803 4,367,223 4,363,765 1,070 1,074 1,186 1,190 697,122 703,625 587,767 592,345 1,004 1,002 1,191 1,191
30 to 34 years 5,379,640 5,372,270 5,027,100 5,023,379 726 730 777 781 731,782 727,655 661,407 657,809 748 762 827 843
35 to 39 years 5,708,902 5,733,474 5,372,979 5,396,254 416 417 442 443 709,634 705,445 656,033 652,506 498 504 539 545
40 to 44 years 5,298,273 5,279,545 4,978,718 4,959,437 171 175 182 186 619,532 618,028 579,845 578,236 249 252 266 270
45 to 49 years 4,988,493 4,993,406 4,658,767 4,666,582 38 41 41 44 565,450 566,163 532,226 533,804 84 92 89 98


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: 7

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  


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 urbanizes areas, or rural areas.

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 control a potential bias in the estimates, 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 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 byproduct 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.
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 D, E, and F.
These tables do not reflect the effect of response variance, processing variance, or bias arising in the collection, processing, and estimation steps. Estimates of the magnitude of some of these factors in the total error are being evaluated and are being published in reports in Series ER 60, Evaluation and Research Program of the U.S. Census of Population and Housing: 1960. 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 2i 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 D 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 E shows rough standard errors of data in the form of percentages. Linear interpolation in tables D and E will provide approximate results that are satisfactory for most purposes.

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


Table E. Rough Approximation to Standard Error of Estimated Percentage
(Range of 2 chances out of 3)

Estimated percentage Base of percentage
1,000 2,500 10,000 25,000 100,000
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


The Sampling Variability of the number of own children under 5 years old 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 ratios of children per 1,000 women are presented in table F. 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:


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 F. Table F 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 10 shows that there were 22,466 nonwhite women 19 years old in the Northeast Region and that these women had a ratio of 336 children under 5 years old per 1,000 women. Table 10 is based on a 5-percent sample, and table F shows that for an estimate of 336 children under 5 years old per 1,000 women, based on a 5-percent sample for 22,466 women, a rough approximation to the standard error is about 20. This means that the chances are about 2 out of 3 that a complete census result would not differ by more than 20 from the estimated ratio of 336 children under 5 years old 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 50, that is, by about 2 ½ times the number estimated from table F.
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.

Table F. Standard Errors of Fertility Ratios, For 5-Percent and 4-Percent Samples

Sample size and number of women Number of own children under 5 per 1,000 women
25 50 100 200 300 400 600 800 1,000
5-percent sample  
1,000 25 35 51 74 89 99 120 129 137
2,500 16 22 32 47 56 63 76 82 87
10,000 8 11 16 24 28 31 38 41 43
25,000 5 7 10 15 18 20 24 26 27
100,000 2 3 5 7 9 10 12 13 14
500,000 1 2 2 3 4 4 5 6 6
1,000,000 1 1 2 2 3 3 4 4 4
4-percent sample  
1,000 27 39 57 83 99 110 133 144 153
2,500 17 24 36 52 63 70 84 91 97
10,000 9 12 18 26 31 35 42 46 48
25,000 5 8 11 17 20 22 27 29 31
100,000 3 4 6 8 10 11 13 14 15
500,000 1 2 3 4 4 5 6 6 7
1,000,000 1 1 2 3 3 3 4 5 5