This chapter covers stratification and sample allocation for one-variable and multi-variable selection schemes. The purpose of sampling is to reduce cost by taking a subset of a population while assuring that the accuracy of one or more estimates are preserved. Stratification and clustering are methods for subdividing a population into subsets in which efficient sampling can be performed. Two implicit assumptions are typically made. The first is that the population file contains all members of the desired population and is free of duplicates. The second is that the quantitative and other variables used in the scientific design are accurately recorded in computer files and represent information that correspond to the desired population estimates. These assumptions can be relaxed in some situations.

The outline of this chapter is as follows. In the first section, we describe univariate methods of stratifying and sampling for one variable. These methods are due to Dalenius and Hodges (1959) and Ekman (1959). Lavallée and Hidiroglou (1988) and Winkler (1998) have given extensions for situations in which the underlying population distribution for continuous variables has significant gaps. The gaps can affect the stratification procedures of Dalenius and Hodges in particular. In the second section, we cover methods of stratification for more than one variable. The stratification ideas begin with independent stratification of two or more variables that are extended to a two or more way stratification of a population. The original ideas are due to Tepping, Hurwitz, and Demming (1943) with extensions by Goodman and Kish (1950) and Bryant, Hartley, and Jessen (1960). Modern extensions using non-trivial computational methods are due to Rao and Nigam (1990, 1992), Sitter and Skinner (1994), and Winkler (2001). In the final section, we give concluding remarks.