For any poststratum, the net undercount rate (UR) is

and the coverage correction factor (CCF) is

where C is the census count, including people requiring imputation and late additions to the count (IIs).

The basic assumption underlying the calculation of the DSE can be stated as follows: Given independence of the P-sample survey from the census, the estimated proportion of P-sample people in a poststratum who match to the census (M/P) is a good estimate of the estimated proportion of all people in the poststratum who were correctly enumerated in the census (CE/DSE). Independence means that the event of being enumerated in the census does not affect the probability of being enumerated in the P-sample (see National Research Council, 1999b:79–80).

Solving for DSE in the following equation,

gives Equation 5.1 above.

Six points are worth noting about dual-systems estimation in the census context. First, the DSE formula (Equation 5.1) includes a factor for IIs; that is, census enumerations that either lacked sufficient information or were added too late to be included in the A.C.E. matching. These enumerations must be assessed to fully understand census coverage estimates (see Section 6-C.1). The total number of IIs in 2000 was about 8.2 million people, including 5.8 million whole-person imputations and 2.4 million people whose records were temporarily removed from the census file as part of the special operation to reduce duplicate Master Address File (MAF) addresses in summer 2000 and reinstated too late to be included in the A.C.E. processing (see Section 4-E). There were no truly late enumerations in 2000. The total number of IIs in 1990 was much smaller—about 2.2 million people, including 1.9 million whole-person imputations and

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