Documentation: Census 1960 (US, County & State)
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Publisher: U.S. Census Bureau
Document: Employment Status and Work Experience(Volume II, Part VI - Subject Reports)
citation:
U.S. Bureau of the Census. U.S. Census of Population: 1960. Subject Reports, Employment Status and Work Experience. Final Report PC(2)-6A. U.S. Government Printing Office, Washington, D.C. 1963.
Employment Status and Work Experience(Volume II, Part VI - Subject Reports)
Sample Design and Sample 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 this report are based on a subsample of one-fifth of the original 25-percent sample schedules. The subsample 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 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 J compares the distribution by employment status, as presented in this report, based upon the 5-percent sample with the corresponding distributionbased upon the 25-percent sample. Table K presents similar comparison for distributions by weeks worked in 1959- Differences shown in each of these tabled reflect primarily sampling error.

Table J. Comparison of 25-Percent and 5-Percent Sample Data on Employment Status, By Sex, For the United States: 1960

Employment status and sex 25-percent sample 5-percent sample Percent distribution Ratio of 25-percent sample number to 5-percent sample number
25-percent sample 5-percent sample
Total, 14 years and over 126,276,548 12,6266,620 100.0 100.0 1.000
Labor force 69,877,481 69,905,256 55.3 55.4 1.000
Armed Forces 1,733,402 1,745,148 1.4 1.4 0.993
Civilian labor force 68,144,079 68,160,108 54.0 54.0 1.000
Employed 64,639,252 64,646,563 51.2 51.2 1.000
Unemployed 3,504,827 3,513,545 2.8 2.8 0.998
Not in labor force 56,399,067 56,361,364 44.7 44.6 1.001
Male, 14 years and over 61,315,294 61,353,999 100.0 100.0 0.999
Labor force 47,467,721 47,506,690 77.4 77.4 0.999
Armed Forces 1,705,052 1,715,924 2.9 2.8 0.994
Civilian labor force 45,762,669 45,790,766 74.6 74.6 0.999
Employed 43,466,951 43,490,888 70.9 70.9 0.999
Unemployed 2,295,718 2,299,878 3.7 3.7 0.998
Not in labor force 13,847,573 13,847,309 22.6 22.6 1.000
Female, 14 years and over 64,961,254 64,912,621 100.0 100.0 1.001
Labor force 22,409,760 22,398,566 34.5 34.5 1.000
Armed Forces 25,350 29,224 … … 0.970
Civilian labor force 22,381,410 22,369,342 34.5 34.5 1.001
Employed 21,172,301 21,155,675 32.6 32.6 1.001
Unemployed 1,209,109 1,213,667 1.9 1.9 0.996
Not in labor force 42,551,494 42,514,055 65.5 65.5 1.001


Table K. Comparison of 25-Percent and 5-Percent Sample Data on Weeks Worked In 1959, By Sex, For the United States: 1960
Weeks worked in 1959 25-percent sample 5-percent sample Percent distribution Ratio of 25-percent sample number to 5-percent sample number
25-percent sample 5-percent sample
Total, 14 years and over 126,276,556 126,266,620 100.0 100.0 1.000
Worked in 1959 77,368,085 77,388,902 61.3 61.3 1.000
50 to 52 weeks 43,972,721 44,018,949 34.8 34.9 0.999
48 to 49 weeks 4,329,913 4,332,436 3.4 3.4 0.999
40 to 47 weeks 6,899,064 6,915,876 5.5 5.5 0.998
27 to 39 weeks 7,189,760 7,169,828 5.7 5.7 1.003
14 to 26 weeks 6,498,414 6,478,103 5.1 5.1 1.003
13 weeks or less 8,478,213 8,473,710 6.7 6.7 1.001
Did not worked in 1959 48,908,471 48,877,718 38.7 38.7 1.001
Male, 14 years and over 61,315,362 61,353,999 100.0 100.0 0.999
Worked in 1959 50,301,864 50,339,915 82.0 82.0 0.999
50 to 52 weeks 32,666,364 32,723,510 53.3 53.3 0.998
48 to 49 weeks 2,941,460 2,943,619 4.8 4.8 0.999
40 to 47 weeks 4,297,265 4,306,101 7.0 7.0 0.998
27 to 39 weeks 3,890,819 3,877,637 6.3 6.3 1.003
14 to 26 weeks 3,034,008 3,019,240 4.9 4.9 1.005
13 weeks or less 3,471,948 3,469,808 5.7 5.7 1.001
Did not worked in 1959 11,013,498 11,014,084 18.0 18.0 1.000
Female, 14 years and over 64,961,194 64,912,621 100.0 100.0 1.001
Worked in 1959 27,066,221 27,048,987 41.7 41.7 1.001
50 to 52 weeks 11,306,357 11,295,439 17.4 17.4 1.001
48 to 49 weeks 1,388,453 1,388,817 2.1 2.1 1.000
40 to 47 weeks 2,601,799 2,609,775 4.0 4.0 0.997
27 to 39 weeks 3,298,941 3,292,191 5.1 5.1 1.002
14 to 26 weeks 3,464,406 3,458,863 5.3 5.3 1.002
13 weeks or less 5,006,265 5,003,902 7.8 7.8 1.000
Did not worked in 1959 37,894,973 37,863,634 58.3 58.3 1.001


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 bk- groups of persons in each of the sample weighting areas: 3

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.4

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 twenty. The reduction in sampling error will be trivial for some items and substantial for others. A byproduct 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:
3 Estimates 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.

4 The estimates of sampling variability are based on partial information on variances calculated from a sample of the 1960 Census results. Further estimates are being calculated and will be made available at a later date.

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 L and M. Somewhat more precise estimates of sampling error may be obtained by using the factors shown In table N in conjunction with table M for percentages and table L for absolute numbers. These tables 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 ½times 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 L 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 M shows rough standard errors of data in the form of percentages. Linear interpolation in tables L and M will provide approximate results that are satisfactory for most purposes.

Table L. 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 M. 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 N provides a factor by which the standard errors shown in table L should be multiplied to adjust for the combined effect of the sample design and the estimation procedure.

Table N. Factor to Be Applied To Standard Errors

Characteristics1 Factor
Nativity and parentage 1.4
Household relationship 0.8
School enrollment, by age 0.8
Residence in 1955 1.8

1All characteristics not appearing in this table have a factor of 1.0 to be applied to the standard errors.

To estimate a somewhat more precise standard error for a given characteristic, locate in table N the factor applying to the characteristic. Multiply the standard error given for the size of the estimate as shown in table L by this factor from table N. 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 M by the factor from table N.

Illustration: Table 3 shows that there are 33,307 unemployed males of foreign or mixed parentage in the age group 30-34 years. Table N shows that for data on parentage the appropriate standard error in table L should be multiplied by a factor of l.4. Table L shows that a rough approximation to the standard error for an estimate of 33,307 is 706. The factor of 1.4 times 706 is 988, which means that the chances are approximately 2 out of 3 that the results of a complete census will not differ by more than 988 from this estimated 33,307. It also follows that there is only about 1 chance in 100 that a complete census result would differ by as much as 2,470, that is, by about 2 ½ times the number estimated from tables L and N.