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 which was assigned the key letter "A" 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 the sampling procedure did not automatically insure an exact 25-percent sample of persons or housing units in each locality, the sample design was unbiased if carried through according to instructions; and, generally, for large areas the deviation from 25 percent was found to be quite small. Biases may have arisen however, when the enumerator failed to follow his listing and sampling instructions exactly.

The statistics based on the 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 44 groups of persons in each of the smallest areas for which sample data are published.² (For a more complete discussion of the ratio estimation procedure, see 1960 Census of Population, Volume I, Characteristics of the Population, Part 1, United States Summary.)

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 25-percent sample by a uniform factor of four. The reduction in sampling error is trivial for some items and substantial for others. A by-product of this estimation procedure, in general, is that estimates for this sample are consistent with the complete count with respect to the total population and for the subdivisions used as groups in the estimation procedure.

The figures from the 25-percent sample tabulations are subject to sampling variability, which can be estimated roughly from the standard errors shown in tables A and B. Somewhat more precise estimates of sampling error may be obtained by using the factors shown in table C in conjunction with table B for percentages and table A for absolute numbers. These tables3 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 text books.

Table A. Rough Approximation to Standard Error of Estimated Number
(Range of 2 chances out of 3)

Estimated number	Standard error
50	15
100	20
250	30
500	40
1,000	50
2,500	80
5,000	110
10,000	160
15,000	190
25,000	250
50,000	350

Table A shows rough approximations to standard errors of estimated numbers up to 50,000.⁴ 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 B shows rough standard errors of data in the form of percentages. Linear interpolation in tables A and B will provide approximate results that are satisfactory for most purposes.

Table B. 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	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

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 C provides a factor by which the standard errors shown in table A or 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 C the factor applying to the characteristic. Multiply the standard error given for the size of the estimate as shown in table A by this factor from table C. 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 B by the factor from table C.

Table C. Factor to Be Applied To Standard Errors

Characteristics	Factor
Nativity, place of birth	1.2
Place of residence in 1960	0.8
Color, by place of birth and residence	1.0
Age, by place of birth and residence	1.0

Illustration: Table 4 shows that there are 36,300 nonwhites born in the North Central Region and living in the Northeast Region. Table A shows that the standard error for an estimate of 36,300 is about 295. Table C shows that for characteristics on color by place of birth and residence the standard error from table A should be multiplied by a factor of 1.0. The factor of 1.0 times 295, or 295, means that the chances are approximately 2 out of 3 that the results of a complete census would not differ by more than 295 from this estimated 36,300. It also follows that there is only about 1 chance in 100 that a complete census result would differ by as much as 738, that is, by about 2 ½ times the number estimated from tables A and C.

Table D gives a rough approximation to the standard error of the net migration for an area. The net migration is estimated by subtracting the number of persons born in the area but residing elsewhere on April 1, 1960, from the number of persons residing in the area on April 1, 1960, but born elsewhere. To determine the approximate standard error of this difference, locate the column representing the larger of the two numbers in table D and the row representing the smaller of the two numbers. The figure at the intersection of the row and column represents a rough approximation to the standard error of the difference of the two migration estimates.

Table D. Rough Approximations to Standard Errors of Estimated Net Migration (Range of 2 chances out of 3)

Smaller of two estimates of migration	Larger of two estimates of migration
	100,000	250,000	500,000	1,000,000	2,500,000	5,000,000
50,000	600	850	1,150	1,550	2,300	2,800
100,000	…	900	1,200	1,600	2,350	2,850
250,000	…	…	1,350	1,700	2,400	2,900
500,000	…	…	…	1,850	2,550	3,000
1,000,000	…	…	…	…	2,750	3,200
2,500,000	…	…	…	…	…	3,600