The subjects of this paper are two relatively unrelated problems in variance estimation. Research into these problems was motivated by their applicability to the demographic surveys conducted by the Census Bureau, but their potential applications are more general. The first problem, which is the subject of Section 2, is the development of a methodology for pairing strata in one PSU per stratum designs, which minimizes the bias of the resulting variance estimator when using a collapsed stratum estimator of variance. The current designs of the Current Population Survey, the National Crime Survey and the American Housing Survey are examples of one PSU per stratum designs.

The second problem, which is the subject of Section 3, is the development of an alternative to the standard unbiased variance estimator for two PSU’s per stratum, without replacement designs, that will have greater precision. The current design of the Survey of Income and Program Participation is essentially this type of design.

Since these two problems are quite different, discussion of them will take place separately in Sections 2 and 3.