Design and power analysis

Abstract

Sampling Fundamental to any statistical analysis, including the regression models we described in the previous two chapters, is the design of the sampling regime. We are assuming that we can clearly define a population of interest, including its spatial and temporal boundaries, and that we have chosen an appropriate type and size of sampling unit. These units may be natural units (e.g. stones, organisms, and lakes) or artificially delineated units of space (e.g. plots or quadrats). Our aim is to design a sampling program that provides the most efficient (in terms of costs) and precise estimates of parameters of the population. It is important to remember that we are talking about a statistical population, all the possible sampling or experimental units about which we wish to make some inference. The term population has another meaning in biology, a group of organisms of the same species (Chapter 2), although this might also represent a statistical population of interest. We will only provide a brief overview of some sampling designs. We recommend Levy & Lemeshow (1991), Manly (2001) and Thompson (1992), the latter two having more of a biological emphasis, as excellent references for more detail on the design of sampling programs and using them to estimate population parameters. Sampling designs Simple random sampling was introduced in Chapter 2 and is where all the possible sampling units in our population have an equal chance of being selected in a sample.