ABSTRACT
Statistics is the science that provides the most logical approach to understanding the world around us via the interpretation of our observations. Clearly we need hypotheses derived from knowledge or beliefs about the underlying scienti˜c mechanisms that make the world behave in the way that it does. But it is only by making observations that we are able to differentiate between the scienti˜c beliefs that are close enough to the truth to be useful from those that should be rejected or re˜ned. Statistics provides the methods by which we extract information from the observations we make on the world around us, and just as importantly, guides us when we can choose which observations to make. George Box, one of the most in¯uential statisticians of the last 60 years, frequently discussed how statistics could and should be used as a catalyst to learning (see Box (2000) for numerous examples), and argued that such learning occurs either through “passive observation” or “active experimentation” (as explained in Box and Bisgaard (1987)). It could be argued, and it is certainly my belief, that it is in the area of experimental design that statistics has its biggest impact on the advancement of knowledge in the sciences, engineering, or any other discipline based on logical principles. The twentieth century saw a revolution in the development of methods aimed at improving the way we plan, run, and analyze experiments, starting with the pioneering work of Ronald Fisher (1925) at Rothamsted in England between the two world wars. Although my book only discusses methods of analyzing data once they have been obtained, it is essential that statistical thinking and methods be applied from the very beginning of the experimental process, even before the objectives of the study have been ˜nalized. This is true even in those cases where experiments cannot be designed in the manner of a controlled laboratory experiment, since statistical ideas are still relevant when purely observational studies are being planned. It is unfortunate that much of the scienti˜c research currently being undertaken and reported still does not make use of these powerful ideas ˜rst published nearly 100 years ago. A good introduction to experimental design, explaining the key principles, is provided by the classic text by Cox (1958). Another classic text that covers the most widely used types of designs in more detail is Cochran and Cox (1992). Numerous books exist that cover design for speci˜c application areas such as Wu and Hamada (2000) or Box et al. (1978) for the more technological sciences, Fleiss (1986) or Senn (2002) for medical trials, and Rosenbaum (2009) for observational studies.
