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 C and D below. Table E gives factors to be used to adjust for the size of sample from which the data were tabulated.
For the purpose of estimating standard errors of estimated numbers, the data in this report are considered as comprising two types. Examples of data of type 1 are: The number of families in a class, the number of household heads in a class, the number of wives in a class, and the number of mothers of family head in a class. Such data describe family or household characteristics or population characteristics which generally involve no more than one person in a household. For data of this type, the standard errors may be read from the "Households and families" column of table C.
Examples of data of type 2 are: The number of persons in families in a given family income class, the number of members of husband-wife families, and the number of children in families with employed head. Such data generally involve more than one person in a household. For numbers of this type, rough approximations of the standard error can be obtained from the "Persons" column of table C. The figures in the "Persons" column will tend to understate the standard error of estimates of nonwhite persons. For a closer approximation of the standard error of estimates of nonwhite persons, multiply the standard errors in the "Persons" column of table C by 1.1.
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 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 textbooks.
Table C. Rough Approximation to Standard Error of Estimated Number
(Range of 2 chances out of 3)
Estimated number |
Standard error |
Households and families |
Persons |
50 |
30 |
60 |
100 |
40 |
80 |
250 |
60 |
130 |
500 |
90 |
190 |
1,000 |
120 |
250 |
2,500 |
200 |
400 |
5,000 |
280 |
600 |
10,000 |
390 |
800 |
15,000 |
480 |
1,000 |
25,000 |
620 |
1,300 |
50,000 |
880 |
1,800 |
Table D. 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 |
Note: Tables C and D are applicable to data from the 5-percent population sample. To obtain standard errors for data from the 1-percent and 4-percent samples, see text.
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.
Table E provides a factor by which the standard errors shown in tables C and D should be multiplied to adjust for the reduced sample size for data based on the 1-percent sample, the 4-percent sample, or 1 combination of these subsamples given in tables 17 and 18.
Table E. Factors to Be Applied To Standard Errors
Table |
Tabulation area |
Factor |
1 to 16 |
All |
1.0 |
17 |
All |
2.2 |
18 |
United States |
1.8 |
18 |
Urbanized Areas |
1.6 |
18 |
Other urban |
2.2 |
18 |
Rural nonfarm |
2.2 |
18 |
Rural farm |
2.2 |
18 |
South |
2.0 |
19 to 28 |
All |
1.0 |
Illustrations: Table 8a shows that there are 8,542 nonwhite rural-farm family heads with 4 years of high school. Table C shows that the standard error of an estimate of 8,542 households is about 362. Table E shows that the standard errors in table C can be used without adjustment for size of sample to obtain the estimated standard errors for all data in table 8a. The 362 means that the chances are about 2 out of 3 that the results of a complete census would not differ by more than 362 from the estimated 8,542. It follows that there is only about 1 chance in 100 that a complete census would differ by as much as 905, that is, by about 2 ½ times the standard error.
Similarly, table 8a also shows that there are 22,467 nonwhite rural-farm persons under 18 years old in families in which the head has completed 4 years of high school. Table C shows that the standard error of an estimate of 22,467 persons is about 1,225. Multiplication of this figure by 1.1, which is the adjustment factor for standard errors for numbers of non-white persons, yields an estimated standard error of 1,348.
Table 18 shows that, for the South, there were 38,858 female heads of households with 3 or more automobiles available. Since this is a characteristic of a head of a household, the standard error can be obtained directly from tables C and E. Table E shows that for data from table 18 the standard errors for the South should be multiplied by 2.0. Table C shows a standard error of about 685 for an estimate of 30,858; multiplication of this 685 by 2.0 yields an estimated standard error of about 1,370