Probability Sampling under Imperfect Frame

INTRODUCTION Availability of a sampling frame is a basic requirement for application of a probability sampling technique. In order that each and every element in a population has a known and non-zero chance of being included in a sample, an ideal frame should consist of all elements occurring only once and it should exclude any other element that is irrelevant for the study. The basic techniques, such as SRS, stratified sampling and systematic sampling, discussed in Chapter 2, presume availability of such a list of elements if elements are being selected directly. In cluster and multistage sampling, a list of all areal units comprising a population is required initially. They are often selected using a PPS sampling (also discussed in Chapter 2), which assumes an availability of size or at least an estimated size of each cluster. For selection of elements in the final stage of a multistage design, a frame consisting of elements in selected areas would be required. This is generally obtained through listing of dwellings or households in a population-based survey. It is indeed difficult to have a perfect frame in every situation. Let us consider, for example, a common situation of studying a population having certain characteristics, say, suffering from a particular disease. A usual available list will consist of both the elements, households having a member suffering from the disease and those without anyone suffering. The latter element may be irrelevant and, therefore, considered as a blank. The present chapter discusses a few applications of probability sampling in the absence of an ideal frame, following three broad situations that are generally encountered: (a) Sampling populations having specific attributes, that is, a frame consisting of elements as well as blanks. (b) Sampling populations using a defective frame, that is, a frame which is either incomplete or consists of duplications (same element occurring more than once). (c) Sampling populations in the absence of any frame. In addition, the chapter also includes a discussion on household listing that is advisable in implementing a cluster sampling. SAMPLING POPULATIONS HAVING SPECIFIC ATTRIBUTES This situation arises when a survey objective refers to not all the elements in a population but to a section of it.