Comparative Efficiency of Sampling Plans

PREFACE This publication is regarded by the author as supplementary training material for students who are familiar with, or are studying, elementary theory of sampling including stratification, cluster sampling, ratio and regression estimation, sampling with probability proportional to size, and multiple-stage sampling. After studying sampling methods one at a time, it is important to get a unified view of the several methods and the conditions under which they have about the same or different variances. In sampling various populations we quite often find two or more techniques that are roughly equal in efficiency and reduce sampling variance about as much as possible. Administrative feasibility, costs, and freedom from potential bias are important criteria for selecting a sampling plan and become primary criteria when the choice ~s among plans having small differences In sampling variance. Ability to prejudge accurately the efficiency of alternative sample designs with reference to various survey objectives and populations is important. Such ability comes from experience and detailed study of alternative techniques of sampling a population and of making estimates. Quite often only two or three alternatives are compared in an analysis because of limitations of data or only a few alternatives are of interest. In this publication many alternative I sampling and estimation plans are applied to a small population of apple trees and the results are recorded in tables for comparative purposes. The focus of attention is on the magnitude of the differences in efficiency in relation to the patterns of variation that exist. For some readers, parts of the presentation are probably too detailed. However, it is important to understand fully the alternatives and to put mathematical expressions for estimators and their variances in forms that are most meaningful for comparative purposes. Exercises are distributed through the text. Chapter I makes use of graphical, or geometrical, interpretations in the comparison of four alternative ways of using an auxiliary variable. There is a brief presentation of the relevant theory for each plan which is followed by a discussion of the plans including a numerical example. Sampling with probability proportional to size in comparison to other methods is of special interest. For comparison, a part of each variance formula IS written as the sum of squares of deviations from a line. Chapter II expands the comparisons made in Chapter I to include interactions in efficiency. For example, the comparative efficiency of sampling units of various size …