An Essay on the Logical Foundations of Survey Sampling, Part One*

Abstract

In this paper, the statistical model for sample surveys is first put in the conventional set-up of (Ω, α, p ), and it is is shown that a maximal sufficiency reduction is always possible for a sample survey model. The corresponding minimal sufficient statistic is derived. We examine the role of the sufficiency and likelihood principles in the analysis of survey data and arrive at the revolutionary but reasonable conclusion that, once the sample has been drawn, the inference should not depend in any way on the sampling design. This poses the problem of designing a survey which will yield a good (representative) sample. The randomisation principle is examined from this view point and it is noticed that there is very little, if any, use for it in survey designs.