2Estimates of characteristics from the sample for a given area are produced using the formula:
where x
1 is the estimate of the characteristic for the area obtained through the use of the ratio estimation procedure,
x
i is the count of sample persons with the characteristic for the area in one (i) of the 44 groups,
y
i is the count of all sample persons for the area in the same one of the 44 groups, and
Y
i is the count of persons in the complete count for the area in the same one of the 44 groups.
3These estimates of sampling variability are based on partial information on variances calculated from a sample of "the 1960 Census results. Further estimates are being calculated and will be made available at a later date.
Table C. Rough Approximation to Standard Error of Estimated Number (25-Percent Sample)
(Range of 2 chances out of 3)
| Estimated number |
Standard error |
| 50 |
20 |
| 100 |
30 |
| 250 |
40 |
| 500 |
60 |
| 1,000 |
70 |
| 2,500 |
110 |
| 5,000 |
150 |
| 10,000 |
220 |
| 15,000 |
270 |
| 25,000 |
350 |
| 50,000 |
490 |
Table D. Rough Approximation to Standard Error of Estimated Percentage (25-Percent Sample)
(Range of 2 chances out of 3)
| Estimated number |
Base of percentage |
| 500 |
1,000 |
2,500 |
10,000 |
25,000 |
100,000 |
| 2 or 98 |
1.8 |
1.3 |
0.7 |
0.4 |
0.1 |
0.1 |
| 5 or 95 |
2.8 |
2.0 |
1.3 |
0.6 |
0.3 |
0.1 |
| 10 or 90 |
3.9 |
2.8 |
1.7 |
0.8 |
0.4 |
0.3 |
| 25 or 75 |
5.3 |
3.8 |
2.1 |
1.0 |
0.6 |
0.3 |
| 50 |
6.2 |
4.3 |
2.2 |
1.1 |
0.7 |
0.4 |
Table C 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 D shows rough standard errors of data in the form of percentages. Linear interpolation in tables C and D 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
1960 Census of Population, Volume I,
Characteristics of the Population, Part 1,
United States Summary.
Illustration: Table 1 shows that there are 33,158 white persons of Spanish surname living in Arizona but born in Mexico. Table C shows that the standard error for an estimate of 33,158 is about 396, which means that the chances are approximately 2 out of 3 that the results of a complete census would not differ by more than 396 from this estimated 33,158. It also follows that there is only about 1 chance in 100 that a complete census result would differ by as much as 990, that is, by about 2 ½ times the number estimated from table C.
