Sample Design on Historical Census Projects at the University of Minnesota

Ron Goeken

Completed historical samples

Census Year Target Population Sample Density Number of Person Records

1850 U.S. Free Population 1-in-100 198,000

1860 U.S. Free Population 1-in-100 274,000

1870 U. S. Population 1-in-100 383,000

1880 U. S. Population 1-in-100 503,000

1900 U. S. Population 1-in-100 755,000

1910 U. S. Population 1-in-100 917,000

1920 U. S. Population 1-in-100 1,050,000

Sample design issues

• Goal is to sample entire households (or dwellings)

• Every individual has an equal probability of being sampled

• Practicality

Basic sample design

• Every household is defined as a cluster

• Samples are also stratified

• Only include in sample if the first person in a household is on a sample line.

• Probability of selection = np(1/n) = p

3 person household: 3*.01(1/3) = .01

8 person household: 8*.01(1/8) = .01

Group Quarters

• Not practical to sample large institutions in their entirety

• A better approach is to apply individual level sampling when household size exceeds a predetermined threshold.

Sampling rules – dwellings/households

• 1. If the dwelling contains 30 or fewer residents: – a) accept the entire dwelling if the sample point falls on the

first listed individual in the dwelling. – b) reject the entire dwelling if the sample point falls on any

other dwelling resident.

• 2. If the dwelling contains 31 or more residents and the household contains 30 or fewer persons: – a) accept the entire household if the sample point falls on

the household head. – b) reject the entire household if the sample point falls on any

other household member.

Sampling rules – group quarters

• 3. If the household contains 31 or more persons :  – accept individuals on sample lines.

Target and Actual Sample Densities for Completed Historical Samples

Census Year Number of Person Records

Target Sample Density

Actual Sample Density

1850 198,000 1 % 0.989 %

1860 274,000 1 % 0.997 %

1870 383,000 1 % 0.998 %

1880 503,000 1 % 1.003 %

1900 755,000 1 % 0.993 %

1910 917,000 1 % 0.994 %

1920 1,050,000 1 % 0.992 %

Sample Confidence Interval

• Estimating the number of sample clusters in the total population

• # of sampled person records = # of sample clusters

Total Population Total # of clusters

Source of under-sampling

• Some enumerator manuscripts were never microfilmed

• Data entry error

• Processing procedures can lead to deleting records, but rarely adding records

• Ambiguity on enumerator manuscripts

Percent of Target Records by Size of Place and Census Year

Population category 1880 1900 1920

100K+ 99.0 98.9 98.7

50K – 99999 97.3 96.3 100.4

25K – 49999 100.5 97.8 99.0

10K – 24999 101.4 98.6 97.5

5K – 9999 93.7 100.1 99.6

2.5K – 4999 97.6 99.3 99.3

Under 2.5K 100.0 98.7 99.6

Assigning Weights

• Each sampled individual represents X number of individuals in the total population.

• We have typically assigned weights at the national level.

County Level or SEA Level Weights

• 1. Weight at the county level if county population exceeds 10,000 and:– A. all other counties in the SEA have populations exceeding

10,000, or– B. the combined populations of the counties with populations

under 10,000 is 10,000 or more.

2. If conditions above are not true, then weight at the SEA level.

Conclusion

• Sample designs are fairly straightforward in theory, but source materials and procedures result in under-sampling bias

• Detailed weights based on county populations or SEA populations theoretically improve precision