Fundamentals of Statistical Experimental Design and Analysis

2Fundamentals of Experimental Design

Introduction

The experiments dealt within this book are comparative: the purpose of doing the experiments is to compare two or more ways of doing something. In this context, an experimental design defines a suite, or set, of experiments. In this suite of experiments, different experimental units are subjected to different treatments. Responses of the experimental units to the different treatments are measured and compared (statistically analyzed) to assess the extent to which different treatments lead to different responses and to characterize the relationship of responses to treatments. This process will be illustrated numerous ways throughout this book.

Agricultural experimentation, which gave rise to much of the early research on statistical experimental design (see, e.g., Fisher 1947), provides a simple conceptual example. An experimenter wants to compare the crop yield and environmental effects for two different fertilizers. The experimental units are separate plots of land. Some of these plots will be treated with Fertilizer A, and some with Fertilizer B. For example, Fertilizer A may be the currently used fertilizer; Fertilizer B is a newly developed alternative, perhaps one designed to have the same or better crop growth yields but with reduced environmental side effects. Better food production with reduced environmental impact is clearly something a research scientist and the public could be passionate, or at least enthusiastic, about. ...