The figures from the 5percent sample tabulations are subject to Sampling Variability, which can be estimated roughly from the standard errors shown in tables F, G, and H.
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. Censuses 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 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 F 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 G shows rough standard errors of data in the form of percentages. Linear interpolation in tables F and G 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. Rough estimates of standard errors for rates of children ever born per 1,000 ever married women are presented in table H. 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 F. Rough Approximation to Standard Error of Estimated Number
(Range of 2 chances out of 3)
Estimated number^{1}

Standard error 
50 
30 
100 
40 
250 
60 
500 
90 
1,000 
120 
2,500 
200 
5,000 
280 
10,000 
390 
15,000 
480 
25,000 
620 
50,000 
880 
^{1}To determine the standard errors of data in tables 3 through 18, follow the instructions given later in this section on Sampling Variability.
Table G. Rough Approximation to Standard Error of Estimated Percentage
(Range of 2 chances out of 3)
Estimated percentage 
Base of percentage^{1} 
500 
1,000 
2,500 
10,000 
25,000 
100,000 
2 or 98 
3.3 
2.3 
1.3 
0.8 
0.3 
0.3 
5 or 95 
5.0 
4.0 
2.3 
1.0 
0.5 
0.3 
10 or 90 
7.0 
5.0 
3.0 
1.5 
0.8 
0.5 
25 or 75 
10.0 
6.8 
3.8 
1.8 
1.0 
0.5 
50 
11.0 
7.8 
4.0 
2.0 
1.3 
0.8 
^{1}To determine the standard errors of data in tables 3 through 18, follow the instructions given later In this section on Sampling Variability.
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 H. Table H 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 20 shows a rate of 1,931 children ever born per 1,000 women by age 28 for 702,892 nonwhite women who were born in 1925 to 1929. Table 20 is based on a 5percent sample, and table H shows that for an estimate of 1,931 children ever born per 1,000 women when the universe is 702,892 women, a rough approximation to the standard error is about 7 per 1,000. This means that the chances are about 2 out of 3 that a complete census result would not differ by more than 7 from the estimated rate of 1,931 children per 1,000 women. It also follows that there is only about 1 chance in 100 that a complete count could differ by as much as 18that is, by about 2i times the number estimated from table H.
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 H. Standard Error of Number of Children Ever Born Per 1,000 Women
(Range of 2 chances out of 3)
Number of women^{1}

Number of children ever born per 1,000 women 
500 
1,000 
1,500 
2,000 
2,500 
3,000 
3,500 
4,000 
4,500 
1,000 
90 
141 
174 
220 
276 
307 
348 
389 
438 
2,500 
54 
90 
120 
151 
182 
210 
233 
233 
282 
10,000 
26 
44 
61 
74 
90 
102 
118 
118 
141 
25,000 
18 
31 
41 
49 
59 
67 
72 
72 
87 
100,000 
8 
15 
20 
23 
28 
31 
36 
36 
44 
500,000 
5 
5 
8 
10 
13 
15 
15 
15 
20 
1,000,000 
3 
3 
3 
5 
8 
8 
10 
10 
13 
^{1}To determine the standard errors of data in tables 3 through 18, follow the instructions given later in this section on Sampling Variability.
Special instructions for determining the standard errors of data in tables 3 through 18.
In the preparation of tables 3 through 18, data were tallied separately for each calendar year and then combined into totals for a 5year period. Data for a given woman were tallied for a table cell for as many of the 5 years as she qualified for, which means that a given woman may be represented anywhere from 1 to 5 times. The tables of standard errors (tables P, G, and H) are designed for data in which each woman in the sample is represented only once. They may be used without modification for those types of data in tables 3 through 18 that are of such a nature that the woman could have been counted only once, as explained in subsection A below. Special procedures are necessary, as explained in subsection B, for those data in tables 3 through 18 where a given woman may be represented several times in the 5year period.
A. Data involving single counts of woman
Examples of one count per woman are data on first marriages occurring in a 5year period and data on third births occurring in a 5year period. A given woman can have only one first marriage, only one third child. Another example consists of data for women married less than one yeara given woman can be of that marriage duration only once as of January 1 of some year in a 5year reference period. Wherever the data in tables 3 through 18 are of such a nature that the event could have occurred only once to a woman, the tables of standard errors may be used without modification. This rule applies to absolute numbers of events occurring in a 5year period. It applies also to rates when the base of the rate consists of women who could have been counted only once, as in the case of women married less than 1 year as of January 1 of any year within a 5year period.
B. Data involving multiple counting of women.
As stated above, data were tallied for each calendar year separately and then combined into totals for a 5year period. For example, a woman age 14 on January 1, 1955, was counted at age 14 for that date, again at age 15 for January 1, 1956, and again at each later age on January 1 of 1957 through 1959. During the whole 5year reference period, 1955 to 1959, the woman was counted four times for the broad age group 1417 shown in table 3 and once for the broad age group 1819. In contrast, a woman age on January 1, 1959, qualified only once for age group 1417 in the 5year reference period. Similarly, other age groups of women shown in tables 3 through 18 involved women who were in the broad age group for varying numbers of years during the 5year reference period.
Rough approximations to the average number of times women were counted as being in a broad age group during a 5year reference period can be obtained from arithmetic proportions figured on the assumption that there are equal numbers of women in each singleyear ofage cohort. Data of this type appear in table I, in the column "All women." These rough approximations are useful for approximating the standard errors of data involving women of all marital classes, as explained below. However, many of the data on tables 3 through 18 are for women ever married who were of a specified parity and age as of January 1 of each year within a 5year reference period. Women were counted as many times as they met the specifications. Table I also presents rough approximations to the average number of times women ever married were counted in a broad age group during a 5year reference period. These rough approximations were developed from a model based on 1960 Census data for women ever married by single years of age. Because they are not specific for parity, the rough approximations tend to overstate slightly the average number of times women ever married were counted in tables 3 through 18.
Table I. Average Number of Times Women in a 5Year Period Are Counted, By age at the Beginning of Each Year within the 5Year Period
age of women 
All women 
Evermarried women 
14 years and over 
4.8 
4.8 
14 to 17 years 
2.5 
1.6 
18 and 19 years 
1.7 
1.5 
20 and 21 years 
1.7 
1.6 
22 to 24 years 
2.1 
1.9 
45 years and over 
4.7 
4.7 
5year age groups 
2.8 
2.8 
10year age groups 
3.6 
^{1}3.6 
^{1} Exception: use 2.9 for evermarried women 15 to 24 years old.
When using data from tables 3 through 18 that involve multiple counting of women, the general procedures for figuring the standard errors are as follows:
1. Standard error of an absolute number: Divide the number from tables 3 through 18 by the appropriate factor from table I to obtain an estimate of the unduplicated count of women. Read the standard error of the unduplicated number from table F. Multiply the standard error of the unduplicated number from table F by the same factor from table I to obtain the standard error of the number from tables 3 through 18.
Illustration: Table 4 shows 5,565 white women in 19551959 were age 2021, childless at 7 or more Years since First Marriage. The standard error of the 5,565 is figured first by dividing 5,565 by the factor of 1.6 shown in table I for women ever married age 2021. The result of the first step is an estimate of 3,478 for an unduplicated count of women. Interpolation in table F shows that the standard error of an unduplicated number of 3,478 is approximately 231. Finally, the figure of 231 is multiplied by the same factor of 1.6 from table I, producing 370, the desired standard error of 5,565.
2. Standard error of a percentage where the base of the percentage is from tables 3 through 18: Divide the base of the percentage by the corresponding factor from table I to obtain an estimate of an unduplicated count of women for the base. Determine the standard error of the percentage from table G, using the estimated unduplicated number as the base. The result is the desired standard error of the percentage in tables 3 through 18.
3. Standard error of a fertility rate from tables 3 through 18: The procedure is the same as given above for the standard error of a percentage, except that table H is used instead of table G.