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 A and B. These tables
^{4} 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 A. 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 B. 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. |
25 or 75 |
10.0 |
6.8 |
3.8 |
1.8 |
1.0 |
0 |
50 |
11.0 |
7.8 |
4.0 |
2.0 |
1.3 |
0.8 |
Table A 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 B shows rough standard errors of data in the form of percentages. Linear interpolation in tables A and B will provide approximate 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 1.960 Census of Population, Volume I, Characteristics of the Population, Part 1, United States Summary.
Illustration: Table 3 for the South shows that there are 17,000 craftsmen, foremen, and kindred workers, age 35 to 44 years, who completed 4 years of high school and who are in the income class $3,000 to $3,999. Table A shows that for an estimate of 17,000 the approximate standard error is 508, which means that the chances are approximately 2 out of 3 that the results of a complete census would not differ by more than 508 from this estimated 17,000. It also follows that there is only 1 chance in 100 that a complete census result would differ by as much as 1,270, that is, by about 2 ½ times the number estimated from table A.