Chapter 13 Sampling designs, implementation, and analysis
In Chapters 11 and 12 we focused on inference using sample data collected via a simple random sampling design. In this chapter, we introduce several additional probability sampling designs common in forestry applications. Recall, a sampling design is as set of rules for gathering information from a population and using that information to generate statistically valid estimates for parameters of interest. In this chapter we introduce: 1) systematic sampling; 2) stratified sampling; 3) cluster sampling, and; 4) multistage sampling designs. The designs configure and select sampling units in different ways and prescribe the estimators to be applied to sample data. In most cases, a design is selected to improve efficiency from a field effort and statistical standpoint.
As described in Section 12.1, it’s common in forest inventory to rely on an areal sampling frame to select sampling locations identified by placing points, using some random mechanism, within the frame’s areal extent. Under point sampling, a sampling location could be the point from which a forester projects the discerning angle to identify measurement trees, or under plot sampling the sampling location could be used as a circular plot center, corner for rectangular plot, or be used in some other way to position more complex plot shapes and configurations. In this chapter, we introduce the sampling designs using plot sampling; however, the designs can be adapted, often with no modification, to point sampling.
After presenting these sampling designs, we shift our attention to use of auxiliary information in sampling designs, which we refer to as sampling with covariates. In forestry, we’re often interested in estimating parameters that require measurements on variables that are difficult and costly to measure (e.g., timber volume). Sampling with covariates aims to deliver precise estimates for parameters of interest, by measuring variables that are correlated with the variables of interest, but are easier and more cost effective to measure.
The remainder of this chapter is organized as follows. Sections 13.1 through 13.4 cover systematic, stratified, cluster, and multistage sampling designs. We end the chapter with Section 13.5, that details common approaches to using auxiliary information in sampling designs. Application of each design’s estimators will be introduced similar to other mensuration books (Kershaw et al. 2016; Burkhart, Avery, and Bullock 2018). The value added here is using tidyverse and other R tools to apply the various estimators to inventory data. Emphasis is on developing computing toolchains for efficient and routine implementation.