The figures from the 25percent sample tabulations are subject to sampling variability, which can be estimated roughly from the standard errors shown in tables A and B. Somewhat more precise estimates of sampling error may be obtained by using ,the factors shown in table C in conjunction with table B for percentages and table A for absolute numbers. These tables
^{2} 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 text books.
Table A. Rough Approximation to Standard Error of Estimated Number
(Range of 2 chances out of 3)
Estimated number 
Standard error 
50 
15 
100 
20 
250 
30 
500 
40 
1,000 
50 
2,500 
80 
5,000 
110 
10,000 
160 
15,000 
190 
25,000 
250 
50,000 
350 
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 
1.3 
0.9 
0.5 
0.3 
0.1 
0.1 
5 or 95 
2.0 
1.4 
0.9 
0.4 
0.2 
0.1 
10 or 90 
2.8 
2.0 
1.2 
0.6 
0.3 
0.2 
25 or 75 
3.8 
2.7 
1.5 
0.7 
0.4 
0.2 
50 
4.4 
3.1 
1.6 
0.8 
0.5 
0.3 
Table A shows rough approximations to 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
1960 Census of Population, Volume I,
Characteristics of the Population, Part 1,
United States Summary.
Table C provides a factor by which the standard errors shown in table A or B should be multiplied to adjust for the combined effect of the sample design and the estimation procedure. To estimate a somewhat more precise standard error for a given characteristic, locate in table C the factor applying to the characteristic. Multiply the standard error given for the size of the estimate as shown in table A by this factor from table C. The result of this multiplication is the approximate standard error. Similarly, to obtain a somewhat more precise estimate of the standard error of a percentage, multiply the standard error as shown in table B by the factor from table C.
Illustration: Table 1 shows that there were 26,942 native persons 75 years old and over who lived in their State of birth in 1960, but not in 1955. For data shown as the crossclassification of place of birth by place of residence in 1955 and 1960, table C shows that the factor to be applied to the standard error is 1.4. Table A shows that for an estimate of 26,942, the approximate standard error is 258. This number, multiplied by the factor of 1.4 from table C, gives 361, which means that the chances are approximately 2 out of 3 that the results of a complete count would not differ by more than 361 from this estimated 26,942. It also follows that there is only about one chance in 100 that a complete census result would differ by as much as 902, that is, by about 2 ½ times the number estimated from tables A and C.
Table C. Factor to Be Applied To Standard Errors
Characteristic 
Factor 
Place of residence: 

In 1960 
0.8 
By place of birth 
1.0 
By place of residence In 1955 
1.2 
By years of school completed 
1.0 
In 1955 
1.6 
By place of birth 
1.4 
Migration (by color) 
1.6 
Years of school completed 
1.0 
Place of birth, nativity 
1.2 
By place of residence in 1955 and 1960 
1.4 