The figures from the 25-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 do not reflect all the effect of response 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 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 |
25 |
| 100 |
35 |
| 250 |
50 |
| 500 |
65 |
| 1,000 |
80 |
| 2,500 |
130 |
| 5,000 |
180 |
| 10,000 |
260 |
| 15,000 |
305 |
| 25,000 |
400 |
| 50,000 |
560 |
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 |
2.1 |
1.4 |
0.8 |
0.5 |
0.2 |
0.2 |
| 5 or 95 |
3.2 |
2.2 |
1.4 |
0.6 |
0.3 |
0.2 |
| 10 or 90 |
4.5 |
3.2 |
1.9 |
1.0 |
0.5 |
0.3 |
| 25 or 75 |
6.1 |
4.3 |
2.4 |
1.1 |
0.6 |
0.3 |
| 50 |
7.0 |
5.0 |
2.6 |
1.3 |
0.8 |
0.5 |
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 contains rough standard errors of data in the form of percentages, and although percentages are not published in this text, table B may be useful. Linear interpolation in tables A and B will provide approximate results that are satisfactory for most purposes.
The standard errors estimated from tables A and B are not directly applicable to differences between two sample estimates. For a difference between two estimates, the standard error is approximately the square root of the sum of the squares of the standard error of each estimate considered separately. The estimated differences shown in table 5 are based on the sample estimates in table 4. The approximate standard error of the differences in table 5 can be determined from the above formula using the standard error of the corresponding estimates from table 4. (see illustration).
Illustration
Table 4- shows that there were an estimated 6,398 persons whose residence in 1960 was in economic subregion 7, hut whose residence in 1955 was in economic subregion 1. Table 4 shows that for an estimated 6,398 persons, the approximate standarderror is 202. Table 4 also shows that there were an estimated 4,543 persons whose residence in 1960 was in economic subregion 1, but whose residence in 1955 was in economic subregion 7. Table A shows that for an estimated 4,543 persons, the approximate standard error is 171. Table 5 shows that there were an estimated 1,855 persons in net migration between economic subregions 1 and7
. Therefore, the approximate standard error for this estimated 1,855 persons in net migration is
, or 265. This means that the chances are approximately two out of three that the results of a complete count would not differ by as much as 265 from a sample estimate. It also follows that there is only about one chance in 100 that the results of a complete count would differ by as much as 663, that is, by about 2 ½ times the standard error.
