The figures from the 5-percent sample tabulations are subject to Sampling Variability, which can be estimated roughly from the standard errors shown in tables B, C, D, and E.
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 B, shows rough standard errors of estimated numbers up to 500,000 for household and population characteristics. For estimated numbers above 500,000, however, the nonsampling errors, e.g., response errors and processing errors, may have an increasingly important effect on the total error. Tables C and D contain rough standard errors of data in the form of percentages. Standard errors of estimated percentages for household characteristics are shown in table C, and those for population characteristics are presented in table D. Table E gives standard errors of estimated numbers of children ever born per 1,000 women ever married. Linear interpolation in tables B, C, D, and E will provide approximate results that are satisfactory for most purposes.
Illustration: Table 1 shows that there were an estimated 463,513 males with socioeconomic status score 80 to 89 between the ages of 55 to 64 years old in the United States in 1960. Table B shows that for an estimated 463,513 persons, the approximate standard error is 3,900. This means that the chances are approximately two out of three that the results of a complete count would not differ by more than 3,900 from a sample estimate. It also follows that there is only about 1 chance in 100 that the results of a complete count would differ by as much as 9,750; that is, by about 2 ½ times the standard error.
Table B. Approximate Standard Errors of Estimated Totals for Household Characteristics and Population Characteristics
(Range of 2 chances out of 3)
Size of estimate |
Standard error for-- |
Household characteristics |
Population characteristics |
1,000 |
100 |
100 |
2,500 |
200 |
200 |
5,000 |
300 |
400 |
10,000 |
400 |
600 |
25,000 |
600 |
900 |
50,000 |
900 |
1,700 |
100,000 |
1,300 |
2,400 |
250,000 |
2,000 |
3,800 |
500,000 |
2,700 |
5,400 |
Table C. Approximate Standard Error of Estimated Percentage for Household Characteristics
(Range of 2 chances out of 3)
Estimated percentage |
Size of base of percentage (thousands) |
10 |
25 |
100 |
250 |
500 |
1,000 |
2 or 98 |
0.8 |
0.3 |
0.2 |
0.1 |
0.1 |
0.1 |
5 or 95 |
1.0 |
0.5 |
0.3 |
0.2 |
0.1 |
0.1 |
10 or 90 |
1.5 |
0.8 |
0.4 |
0.2 |
0.2 |
0.1 |
20 or 80 |
1.7 |
1.0 |
0.5 |
0.3 |
0.2 |
0.2 |
35 or 65 |
1.9 |
1.2 |
0.6 |
0.4 |
0.3 |
0.2 |
50 |
2.0 |
1.3 |
0.6 |
0.4 |
0.3 |
0.2 |
Table D. Approximate Standard Error of Estimated Percentage for Population Characteristics
(Range of 2 chances out of 3)
Estimated percentage |
Size of base of percentage (thousands) |
10 |
25 |
100 |
250 |
500 |
1,000 |
2 or 98 |
1.1 |
0.6 |
0.3 |
0.2 |
0.2 |
0.1 |
5 or 95 |
1.6 |
0.9 |
0.5 |
0.3 |
0.2 |
0.2 |
10 or 90 |
2.2 |
1.4 |
0.7 |
0.5 |
0.3 |
0.2 |
20 or 80 |
3.0 |
2.0 |
1.0 |
0.6 |
0.4 |
0.3 |
35 or 65 |
3.4 |
2.2 |
1.1 |
0.7 |
0.5 |
0.4 |
50 |
3.7 |
2.4 |
1.2 |
0.8 |
0.5 |
0.4 |
Table E. Approximate Standard Error of Estimated Number of Children Ever Born per 1,000 Women Ever Married
(Range of 2 chances out of 3)
Estimated number of women ever married |
Standard error if the number of children ever born per 1,000 women ever married |
500 |
1,000 |
2,000 |
3,000 |
4,000 |
4,500 |
2,500 |
55 |
90 |
150 |
210 |
260 |
280 |
10,000 |
25 |
45 |
75 |
100 |
130 |
140 |
25,000 |
20 |
30 |
50 |
70 |
80 |
90 |
50,000 |
15 |
25 |
40 |
60 |
80 |
90 |
100,000 |
10 |
15 |
30 |
45 |
60 |
65 |
250,000 |
10 |
10 |
20 |
30 |
40 |
40 |
500,000 |
5 |
10 |
15 |
20 |
25 |
30 |
1,000,000 |
5 |
5 |
10 |
15 |
20 |
20 |