Optimal Allocation for Stratified Telephone Survey Designs

1. THE CURRENT STATUS OF TELEPHONE SURVEY DESIGNS The two stage random digit dialing design for sampling telephone households, first proposed by Mitofsky (1970) and more fully developed by Waksberg (1978), has been widely employed in telephone surveys. The Mitofsky-Waksberg technique capitalizes on the fact that working residential numbers (hereafter referred to as WRNs) tend to be highly clustered within banks of consecutive telephone numbers. Currently, only about twenty percent of the possible telephone numbers within the known area code, three digit prefix combinations are WRNs. However, if a bank of 100 consecutive telephone numbers can be identified that has at least one known WRN then, on average, over 50 percent of the numbers in the bank will be WRNs. The Mitofsky-Waksberg technique, which identifies 100-banks containing WRNs in the first stage of sampling, greatly reduces the amount of screening necessary to identify telephone numbers assigned to households. Alternatively, lists of published telephone numbers have been employed as sampling frames. These lists of published numbers are available for the entire country from commercial firms such as Donnelley Marketing Information Systems. A straightforward selection of telephone numbers from such lists provides a very high rate of WRNs (typically at least 85%) but unfortunately does not cover households with unpublished numbers. Comparisons of telephone households with and without published numbers (see, for example, Brunner and Brunner, 1971) indicates that substantial bias may result. The purpose of this paper is to examine stratified designs based on the BellCore Research (BCR) frame as an alternative to list frames and MitofskyWaksberg design. As an example of flame stratification, the BCR frame could be partitioned into two strata: a "high density" stratum consisting of residential numbers in 100-banks with one or more listed numbers and a "low density" stratum consisting of all the remaining numbers in the BCR frame. Direct access to all listed numbers is not required for this stratification scheme. Counts of listed numbers, or any other indicator of the presence of listed telephone numbers in a 100-bank obtained from a reverse directory or a commercial list, would be sufficient. Preliminary work indicates that it is reasonable to expect that approximately 52% of the contrasted to only about 2% in the low density stratum. The obvious cost difference of sampling from the two strata can be exploited through differential sample allocation. The next section examines the question of the appropriate allocation of sample between the strata when simple random sampling is utilized within each stratum. A key feature of the stratified telephone sample approach is that it permits alternative approaches to sample selection within the different strata. Several alternatives are presented and discussed in Section 3. The paper concludes with a general discussion contrasting the Mitofsky-Waksberg procedure and stratified designs.