Basics

This is a book about design, and is typically not concerned with analysis. Most designs, unless they are complete disasters, will result in a reasonably straightforward analysis. However, as the purpose of a good design is to result in an efficient analysis, it is important to be familiar with the types of analysis that will be done. Thus, we will spend some time discussing the important parts of analyses, and how the design can impact them. We will also do many analyses and somewhat address what to do when the design does not go as planned.

Throughout the book analyses will typically be presented in an anova framework, complete with anova tables, sums of squares and degrees of freedom. This is done not because the anova is the best way to analyze data, but rather because the anova is the best way to think about data and plan designs. Fisher (1934) first called the anova “a convenient method of arranging the arithmetic”, but then explained that it is quite a bit more than that, as rigorously demonstrated by Speed (1987). The ideas of partitioning variation, counting degrees of freedom correctly, and identifying the correct error terms, are fundamental to any data analysis. Focusing on the anova helps us focus on these ideas, and ultimately helps us plan a better design.

This first chapter is a collection of “basics”, topics which should seem a bit familiar, but the explanations and interpretations may be somewhat different from what was previously seen. However, since we are assuming some familiarity with these topics, the review will be brief and a little disjointed.