The figures from the 5percent sample tabulations are subject to sampling variability, which can be estimated roughly from the standard errors shown in tables B and C. Somewhat more precise estimates of sampling error may be obtained by using the factors shown in table D in conjunction with table C for percentages and table B for absolute numbers. 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 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 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.
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 
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 D provides a factor by which the standard errors shown in table 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 D the factor applying to the characteristic. Multiply the standard error given for the size of the estimate as shown in table B by this factor from table D. 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 C by the factor from table D.
Illustration: Table 1 shows that there are 31,135 ruralfarm males in the total labor reserve (last worked 1950 to 1960) in the age group 18 and 19 years old. Table D shows that for data on age, by sex (by farm, nonfarm), the appropriate standard error in table B should be multiplied by a factor of 1.8. Table B shows that a rough approximation to the standard error for an estimate of 31,135 is 684. The factor of 1.8 times 684 is 1,231, which means that the chances are approximately 2 out of 3 that the results of a complete census will not differ by more than 1,231 from this estimated 31,135. It also follows that there is only about 1 chance in 100 that a complete census result would differ by as much as 3,078, that is, by about 2 ½ times the number estimated from tables B and D.
Table D. Factor to Be Applied To Standard Errors
Characteristics^{1}

Factor 
Age, by sex (by rural farm, nonfarm) 
1.8 
Color or race (by rural farm, nonfarm) 
1.8 
Nativity and parentage 
1.4 
Household relationship 
0.8 
School enrollment, by age 
0.8 
Residence in 1955 
1.8 
<sup
>1
sup
>All characteristics not appearing in this table have a factor of 1.0 to be applied to the standard errors.