Research design and statistical analysis

Abstract

In writing this book, we had two overriding goals. The first was to provide a textbook from which graduate and advanced undergraduate students could really learn about data analysis. Over the years we have experimented with various organizations of the content and have concluded that bottom-up is better than top-down learning. In view of this, most chapters begin with an informal intuitive discussion of key concepts to be covered, followed by the introduction of a real data set along with some informal discussion about how we propose to analyze the data. At that point, having given the student a foundation on which to build, we provide a more formal justification of the computations that are involved both in exploring and in drawing conclusions about the data, as well as an extensive discussion of the relevant assumptions. The strategy of bottom-up presentation extends to the organization of the chapters. Although it is tempting to begin with an elegant development of the general linear model and then treat topics such as the analysis of variance as special cases, we have found that students learn better when we start with the simpler, less abstract, special cases, and then work up to more general formulations. Therefore, after we develop the basics of statistical inference, we treat the special case of analysis of variance in some detail before developing the general regression approach. Then, the now-familiar analyses of variance, covariance, and trend are reconsidered as special cases. We feel that learning statistics involves many passes; that idea is embodied in our text, with each successive pass at a topic becoming more general.