Sample Size and Sample Allocation - Sampling Spatial Units for Agricultural Surveys - page 195

Chapter 8
Sample Size and Sample Allocation

8.1 Introduction

Most survey statisticians recognize that determining an appropriate sample size is a
crucial part of the design of a sampling strategy. It has a large impact on the overall
cost and efficiency when producing reliable statistics on a phenomenon. A common
intuition is that the appropriate sample size is a function of the size of the target
population, because we expect that the sample should be larger for an entire country
than for a region. This is not generally true, because in the simplest situation we can
consider the sample size as inversely related to the variance of the survey estimator.
Then, through finite population correction, it is only slightly dependent on N (see
Chap. 6 ) . Indeed, we often choose the sampling rate that achieves a given precision
in the estimates.
In more complex situations, we can aim to choose the sample size and selection
strategy that minimizes the variance given the available budget (Cochran 1977 ).
However, national statistical institutes (NSIs) often prefer the alternative approach
of determining the sample size and selection criteria that minimize costs, while
achieving a desired variance.
In previous chapters, we introduced design-based estimation procedures for both
classical and specific spatial data designs, before discussing the sample size. This is
because we must specify the estimation method before we can evaluate the couple
design-estimator that represents the pillars of a sampling strategy.
The sample size problem can be considered as an optimization problem. We are
interested in minimizing an objective function, for example, the survey cost given
the population characteristics and required efficiency. However, any solution aris-
ing from this deterministic approach may be affected by intrinsic uncertainties in
the population parameters, which are unknown by definition. Furthermore, it is very
difficult to specify all the characteristics of interest at the design stage (Fuller 2009 ),
or to optimize with a large number of constraints.