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 D and E below. These tables
^{5} 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 will be published at a later date. The chances are about 2 out of 3 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 2 ½ 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 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 appreciate results that are satisfactory for most purposes.
For a discussion of the Sampling Variability of medians and means and of the method for obtaining standard errors of differences between two estimates, see 1960 Census of Population. Volume I, Characteristics of the Population, Part 1, United States Summary.
Illustration: Table 1 shows that for husband-wife families with head between 25 and 64 years of age there are a total of 66,742 three- and four-person families with 2 earners or more where the head is not an earner. Of this number 6,453 (or 9.7 percent) have family income in the range $6,000 to $6,999. Table D shows that the standard error of the 6,453 is about 313. This means that the chances are approximately two out of three that the results of a complete census would not differ by more than 313 from the estimated 6,453. It also follows that, there is only about 1 chance in 100 that a complete census would differ by as much as 783, i.e., by about 2 ½ times the number estimated from table D. Table E shows that the standard error of a 97 percent figure based on 66,742 is about 0.6 percent. This means that the chances are approximately two out of three that the results of a complete census would not differ by more than 0.6 percent from the estimated 9-7 percent. It also follows that there is only about 1 chance in 100 that a complete census would differ by as much as 1,5 percent, i.e., by about 2 ½ times the number estimated in table E.
Table D. Rough Approximation to Standard Error of Estimated Number
(Range of 2 chances out of 3)
Estimated number |
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 |
Table E. Rough Approximation to Standard Error of Estimated Percentage
(Range of 2 chances out of 3)
Estimated percentage |
Base of percentage |
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 |