Documentation: Census 1960 (US, County & State)
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Publisher: U.S. Census Bureau
Document: Mobility for States and State Economic Areas (Volume II, Part II - Subject Reports)
citation:
U.S. Bureau of the Census. U.S. Census of Population: 1960. Subject Reports, Mobility for States and State Economic Areas. Final Report PC(2)-2B. U.S. Government Printing Office, Washington, D.C. 1963.
Mobility for States and State Economic Areas (Volume II, Part II - 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. Although most of the 1960 statistics in this report are based on the full 25-percent sample, some are based on a subsample of one-fifth of the original 25-pereent sample schedules. The sub- 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.

Although the sampling procedure did not automatically insure an exact 25-percent or 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.

Table A compares the distribution by mobility status of the population 5 years old and over based on the 5-percent sample with corresponding statistics based on the 25-percent sample. Differences between the distributions reflect primarily sampling error with the exception of the categories "same county" and "different county, same State." In preparing the record for the 5-percent sample, all movers from one borough to another within New York City were classified as movers within the "same county," whereas the 25-percent record classified persons who moved across borough lines as movers between counties within the "same State." From the 5-percent sample records, statistics for the categories "same county" and "different county, same State" cannot be obtained for New York City on a basis directly comparable with statistics for the 25-percent sample records. Hence, the 5-percent sample shows approximately 450,000 more movers within the same county, and the number of migrants between counties in the same State is approximately 450,000 less than the number shown in the 25-percent sample. This difference in treatment should have little influence on the percent distribution of characteristics of movers and migrants for the United States as a whole.

Table A. Comparison of the 25-Percent and 5-Percent Sample Data on Mobility of the Population 5 Years Old and Over in 1960, For the United States: 1960

Mobility status 25-percent sample 5-percent sample Percent distribution Ratio of 25-percent sample number to 5-precent sample number
Ratio of 25-percent 5-percent sample
Total, 5 years old and over 159,003,811 158,991,057 100.0 100.0 1.000
Same house 79,331,018 79,383,929 49.9 49.9 .999
Different house in the United States 75,185,801 75,132,406 47.3 47.3 1.001
    Same county 47,387,169 47,812,950 29.8 30.1 .991
    Different county 27,798,632 27,319,456 17.5 17.2 1.018
        Same State 13,627,145 13,177,139 8.6 8.3 1.036
        Different State 13,657,145 14,142,317 8.9 8.9 .999
Abroad 14,141,487 1,997,813 1.3 1.3 1.003
Place of prior residence not reported 2,484,170 2,476,909 1.6 1.6 1.003


Ratio Estimation
The statistics based on the 25-percent and 5- percent samples of the 1960 Census returns are estimates that have been developed through the use of a ratio estimation procedure. (For a discussion of the ratio estimation procedure used in the full 25-percent sample, see the Volume I report for the United States.) For the 5-percent sample, this procedure was carried out for each of the following 44 groups of persons in each of the sample weighting areas:33


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.

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. In order to increase the reliability, where there were fewer than 275 persons in the complete count in a group, or where the resulting 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 this 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. A more complete discussion of the technical aspects of these ratio estimates will be presented in another report.

Footnotes:
3Estimates 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 persona 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.

Sampling Variability
The figures from the sample tabulations are subject to sampling variability, which can be estimated roughly from the standard errors shown in tables B and C below. 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 tables4 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 2i 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. Rough Approximation to Standard Error of Estimated Number
(Range of 2 chances out of 3)

Estimated number Standard error
25-percent sample 5-percent sample
50 15 30
100 20 40
250 30 60
500 40 90
1,000 50 120
2,500 80 200
5,000 110 280
10,000 160 390
15,000 190 480
25,000 250 620
50,000 350 880


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
25-percent sample  
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
5-percent sample  
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


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 the Volume I report for the United States.

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.

Table D. Factor to Be Applied To Standard Errors

Characteristic Factor
Mobility status 1.6
By age, sex, and color 1.6
By farm, nonfarm 1.8
By year moved into present house 1.6
By place of residence, 1955 1.6
By all other characteristics 1.2
Year moved into present house 1.6
Place of residence, 1960 0.8
By place of residence, 1955 1.2


Illustration: Table 1 shows that there are 40,101 rural-farm residents 5 years old or over who were living abroad in 1955. Table 1 is based on the 25-percent sample and table B shows that the standard error for an estimate of 40,101, based on the 25-percent sample, is about 310. Table D shows that, for characteristics on mobility status by farm-nonfarm residence, the standard error from table B should be multiplied by a factor of 1.8. The factor of 1.8 times 310, or 558, means that the chances are approximately 2 out of 3 that the results of a complete census would not differ by more than 558 from this estimated 40,101. It also follows that there is only about 1 chance in 100 that a complete census result would differ by as much as 1,395, that is, by about 2 ½ times the number estimated from tables B and D.