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 
5percent sample 
4percent 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 
5percent 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 
4percent 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 5percent sample, and table F shows that for an estimate of 336 children under 5 years old per 1,000 women, based on a 5percent 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 Â½ 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 5Percent and 4Percent 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 
5percent 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 
4percent 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 