![]() ![]() A collection of 18 participants with moderate to severe depression are recruited for your initial testing. One is a placebo, and the other is an existing antidepressant / anti-anxiety drug called Anxifree. In order to construct a fair test of the drug’s effectiveness, the study involves three separate drugs to be administered. Suppose you’ve become involved in a clinical trial in which you are testing a new antidepressant drug called Joyzepam. At the end of the chapter we’ll talk a little about the relationship between ANOVA and other statistical tools (Section 14.11). We’ll also talk about how to check those assumptions and some of the things you can do if the assumptions are violated (Sections 14.7 to 14.10). The remainder of the chapter discusses a range of important topics that inevitably arise when running an ANOVA, namely how to calculate effect sizes (Section 14.4), post hoc tests and corrections for multiple comparisons (Section 14.5) and the assumptions that ANOVA relies upon (Section 14.6). These two sections are the core of the chapter. After introducing the data, I’ll describe the mechanics of how a one-way ANOVA actually works (Section 14.2) and then focus on how you can run one in R (Section 14.3). The structure of this chapter is as follows: In Section 14.1 I’ll introduce a fictitious data set that we’ll use as a running example throughout the chapter. This is the question that is addressed by a one-way ANOVA. Later on in the book we’ll encounter a range of different ANOVA methods that apply in quite different situations, but for the purposes of this chapter we’ll only consider the simplest form of ANOVA, in which we have several different groups of observations, and we’re interested in finding out whether those groups differ in terms of some outcome variable of interest. Secondly, there are several different things out there that are all referred to as ANOVAs, some of which have only a very tenuous connection to one another. Firstly, although the name of the technique refers to variances, ANOVA is concerned with investigating differences in means. The term ANOVA is a little misleading, in two respects. The basic technique was developed by Sir Ronald Fisher in the early 20th century, and it is to him that we owe the rather unfortunate terminology. This chapter introduces one of the most widely used tools in statistics, known as “the analysis of variance”, which is usually referred to as ANOVA.
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