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 and C below. These tables
^{3} 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 Â½ 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 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 C shows rough standard errors of data in the form of percentages. Linear interpolation in tables B and C 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 of the 7-year-old persons enrolled in the second year of elementary school in the United States 29,540 are native white of Northern or Western European stock. Table B shows that for an estimate of 29,540 the approximate standard error is 667, which means that the chances are approximately 2 out of 3 that the results of a complete census would not differ by more than 667 from this estimated 29,540. It also follows that there is only about 1 chance in 100 that a complete census result would differ by as much as 1,668, that is, by about 2 Â½ times the number estimated from table B.
Table B. 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 C. 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 |
^{1}Estimates of characteristics from the sample for a given area are produced using the formula
Where x 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.
^{2}For the definitions of urbanized area and urban place, see 1960 Census of Population, Volume I, Characteristics of Population, Part 1, United States Summary.
^{3} These 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.