This paper provides an overview of the probability sample designs and sampling methods for the Collaborative Psychiatric Epidemiology Studies (CPES): the National Comorbidity Survey Replication (NCS-R), the National Study of American Life (NSAL) and the National Latino and Asian American Study of Mental Health (NLAAS). The multi-stage sample design and respondent selection procedures used in these three studies are based on the University of Michigan Survey Research Center's National Sample designs and operations. The paper begins with a general overview of these designs and procedures and then turns to a more detailed discussion of the adaptation of these general methods to the three specific study designs. The detailed discussions of the individual study samples focus on design characteristics and outcomes that are important to analysts of the CPES data sets and to researchers and statisticians who are planning future studies. The paper describes how the expected survey cost and error structure for each of these surveys influenced the original design of the samples and how actual field experience led to changes and adaptations to arrive at the final samples of each survey population.

Abstract. We prove Smorodinsky's conjecture: the rank-one transformation, obtained by adding staircases whose heights increase consecutively by one, is mixing. IntroductionThe first rank-one mixing transformation was constructed by Ornstein [O] using "random" spacers on each column. We refer to [F1] for a description of rank-one constructions. Recently, the first rank-one mixing transformation was constructed with an explicit formula for adding spacers [AF]. In [AF] a method for adding staircases was given which produced mixing. However, Smorodinsky's conjecture remained open. M. Smorodinsky conjectured that by adding staircases whose heights increase consecutively by one, the resulting transformation (classical staircase construction) is mixing.In this paper, we will prove that an infinite staircase construction, whose sequence r n of cuts and h n of heights satisfy the condition lim n→∞ r 2 n hn = 0, is mixing. Thus Smorodinsky's conjecture follows as a corollary. Staircase constructionsA rank-one transformation T is called a staircase construction if there exists a sequence (r n ) ∞ n=1 of natural numbers such that each column C n+1 is obtained by cutting C n into r n subcolumns of equal width, placing i − 1 spacers on the i th subcolumn for 1 ≤ i ≤ r n , and then stacking the (i + 1) st subcolumn on top of the i th subcolumn for 1 ≤ i ≤ r n . Denote T = T (rn) . Let h n be the height of column C n for n ≥ 1. From now on, we assume the sequence (h n ) is derived from the sequence (r n ) in this manner. If the sequence r n is bounded then T is called a finite staircase construction. The classical staircase construction is given by r n = n. If r n → ∞, we call T an infinite staircase construction. In this case T may not be finite measure preserving since we may be adding measure too quickly. Assume T is finite measure preserving. The following question remains open:Question. Is every infinite staircase construction mixing?

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