Documentation: Census 1960 Tracts Only Set
you are here: choose a survey survey document chapter
Publisher: U.S. Census Bureau
Document: Persons by Family Characteristics (Volume II, Part IV - Subject Reports)
citation:
U.S. Bureau of the Census. U.S. Census of Population: 1960. Subject Reports, Persons by Family Characteristics. Final Report PC(2)-4B U.S. Government Printing Office, Washington, D.C. 1964.
Persons by Family Characteristics (Volume II, Part IV - Subject Reports)
Sample Design and Sampling Variability
Sample Design
For persons in housing units at the time of the 1960 Census, the sampling unit was the housing unit and all its occupants; for persons in group quarters, it was the person. On the first visit to an address, the enumerator assigned a sample key letter (A, B, C, or D) to each housing unit sequentially in the order in which he first visited the units, whether or not he completed an interview. Each enumerator was given a random key letter to start his assignment, and the order of canvassing was indicated in advance, although these instructions allowed some latitude in the order of visiting addresses. Each housing unit to which the key letter "A" was assigned was designated as a sample unit, and all persons enumerated in the unit were included in the sample. In every group quarters, the sample consisted of every fourth person in the order listed.

The 1960 statistics in tables 1 to 16 and 19 to 28 of this report are based on a subsample of one-fifth of the original 25-percent sample schedules. The 5-percent sample was selected on the computer, using a stratified systematic Sample Design. The strata were made up as follows: For persons in regular housing units there were 36 strata, i.e., 9 household size groups by 2 tenure groups by 2 color groups; for persons in group quarters, there were 2 strata, i.e., the 2 color groups.
A 1-percent sample was used for the data in table 17. The 1-percent sample and a 4-percent sample were used for the data in table 18. These samples represent, respectively, those households in the 5-percent and 20-percent housing samples that fell in the 5-percent population sample.

Although the sampling procedure used for the 5-percent population sample did not automatically insure an exact 5-percent sample of persons, the Sample Design was unbiased if carried through according to instructions. Generally, for large areas, the deviation from the estimated sample size was found to be quite small. Biases may have arisen, however, when the enumerator failed to follow his listing and sampling instructions exactly.

Ratio Estimation
The statistics based on the 5-percent sample of the 1960 Census returns are estimates that have been developed through the use of a Ratio Estimation procedure, This procedure was carried out for each of the following 44 groups of persons in each of the sample weighting areas:2

Group Sex, color, and age Relationship and tenure
  Male white:  
1 Under 5  
2 5 to 13  
3 14 to 24 Head of owner household
4 14 to 24 Head of renter household
5 14 to 24 Not head of household
6-8 25 to 44 Same groups as age group 14 to 24
9-11 45 and over Same groups as age group 14 to 24
  Male nonwhite:  
12-22 Same groups as male white  
  Female white:  
23-33 Same groups as male white  
  Female nonwhite:  
34-44 Same groups as male white  


The sample weighting areas -were defined as those areas within a State consisting of central cities of Urbanized Areas, the remaining portion of urbanized areas not in central cities, urban places not in Urbanized Areas, or rural areas.3

For each of the 44 groups, the ratio of the complete count to the sample count of the population in the group was determined. Each specific sample person in the group was assigned an integral weight so that the sum of the weights would equal the complete count for the group. For example, if the ratio for a group was 20.1, one-tenth of the persons (selected at random) within the group were assigned a weight of 21, and the remaining nine-tenths a weight of 20. The use of such a combination of integral weights rather than a single fractional weight was adopted to avoid the complications involved in rounding in the final tables. (The weights for the 1-percent and the 4-percent samples were produced by inflating weights from the 5-percent sample by uniform factors of 5 and 1.25, respectively.) In order to increase the reliability, where there were fewer than 275 persons in the complete count in a group, or where the resulting 5-percent sample weight was over 80, groups were combined in a specific order to satisfy both of these two conditions.

These ratio estimates reduce the component of sampling error arising from the variation In the size of household and achieve some of the gains of stratification in the selection of the sample, with the strata being the groups for which separate ratio estimates are computed. The net effect is a reduction in the sampling error and bias of most statistics below what would be obtained by weighting the results of the 5-percent sample by a uniform factor of 20. The reduction in sampling error will be trivial for some Items and substantial for others. A by-product of this estimation procedure, In general, is that estimates for the 5-percent sample are generally consistent with the complete count with respect to the total population and for the subdivisions used as groups in the estimation procedure. Since the 1-percent and 4-percent samples were not subjected to Ratio Estimation procedures, data based on these samples are not always consistent with the complete count. A more complete discussion of the technical aspects of these ratio estimates will be presented in another report.

Footnotes:
2Estimates 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,
xi is the count of sample persons with the characteristic for the area in one (i) of the 44 groups,
yi is the count of all sample persons for the area in the same one of the 44 groups, and
Yi is the count of persons in the complete count for the area in the same one of the 44 groups.
3For the definitions of Urbanized Area and urban place, see 1960 Census of Population, Volume I, Characteristics of the Population, Part I, United States Summary.

Sampling Variability
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

Footnote:
4The estimates of sampling variability are based on calculations from a preliminary sample of the 1960 Census results. Further estimates are being calculated and will be available at a later date.