The question of whether to adjust the 1990 census using a capture-recapture model has been hotly argued in statistical journals and courtrooms. Most of the arguments to date concern methodological issues rather than data quality. Following the Post Enumeration Survey, which was designed to provide the basic data for adjustment, the Census Bureau carried out various evaluation studies to try to determine the accuracy of the adjusted counts as compared to the census counts. This resulted in the P-project reports, which totaled over a thousand pages of evaluation descriptions and tables. Careful scrutiny of these studies together with auxiliary sources of information provided by the Census Bureau is used to examine the issue of whether the data gathered in the Post Enumeration Survey can provide reliable undercount estimates.

Current techniques for census adjustment involve the "synthetic assumption" that undercount rates are constant within "post-strata" across geographical areas. A poststratum is a subgroup of people with given demographic characteristics; poststrata are chosen to minimize heterogeneity in undercount rates. This paper will use 1990 census data to assess the synthetic assumption. We find that heterogeneity within poststrata is quite large, with a corresponding impact on local undercount rates estimated by the synthetic method. Thus, any comparison of error rates between the census and adjusted counts should take heterogeneity into account.

Attempting a complete headcount is an imperfect method for carrying out a census, as is modifying an attempted headcount with sample-based adjustments. It is a mistake to assume that one approach enjoys a scientific presumption over the other. There are important details available from evaluation studies of the 1990 decennial census that reflect upon the accuracy of adjusted and unadjusted census figures. Decisions about adjustment might therefore be based on comparing the accuracy of alternative census-taking strategies at some level of aggregation of the population. In any such comparison, the choices of an appropriate level of aggregation, the factors defining the aggregation, and appropriate loss criteria are important issues to decide in advance. After providing context for decisions about census-taking strategy, we comment on the recent literature on census adjustment, including the papers by Freedman and Wachter and by Breiman contained in this issue; we also discuss the Census Bureau's plans for the year 2000. We conclude that the 1990 approach to summarizing the accuracy of an adjusted census can be improved upon, but that many of the criticisms of census adjustment do not reflect a balanced decision-making perspective. We also conclude that the Census Bureau is pursuing constructive research in evaluating a "one-number census," and we suggest that statisticians have a role to play in avoiding the costly legal battles that have plagued recent censuses by assisting in the process of deciding on a design for the 2000 census.

Conducting sample surveys, imputing incomplete observations, and analyzing the resulting data are three indispensable phases of modern practice with public-use data files and with many other statistical applications. Each phase inherits different input, including the information preceding it and the intellectual assessments available, and aims to provide output that is one step closer to arriving at statistical inferences with scientific relevance. However, the role of the imputation phase has often been viewed as merely providing computational convenience for users of data. Although facilitating computation is very important, such a viewpoint ignores the imputer's assessments and information inaccessible to the users. This view underlies the recent controversy over the validity of multiple-imputation inference when a procedure for analyzing multiply imputed data sets cannot be derived from (is "uncongenial" to) the model adopted for multiple imputation. Given sensible imputations and complete-data analysis procedures, inferences from standard multiple-imputation combining rules are typically superior to, and thus different from, users' incomplete-data analyses. The latter may suffer from serious nonresponse biases because such analyses often must rely on convenient but unrealistic assumptions about the nonresponse mechanism. When it is desirable to conduct inferences under models for nonresponse other than the original imputation model, a possible alternative to recreating imputations is to incorporate appropriate importance weights into the standard combining rules. These points are reviewed and explored by simple examples and general theory, from both Bayesian and frequentist perspectives, particularly from the randomization perspective. Some convenient terms are suggested for facilitating communication among researchers from different perspectives when evaluating multiple-imputation inferences with uncongenial sources of input.