![]() ![]() The story for unbalanced designs is quite tedious, so we’ll put it to one side for the moment. In this section I’ll talk about how to analyse data from balanced designs, since this is the simplest case. In other words, we have a balanced design. Xtabs( ~ drug + therapy, ial ) # therapyĪs you can see, not only do we have participants corresponding to all possible combinations of the two factors, indicating that our design is completely crossed, it turns out that there are an equal number of people in each group. If we cross-tabulate drug by therapy, using the xtabs() function (see Section 7.1), we get the following table: 230 load("./rbook-master/data/clinicaltrial.rdata") We refer to this as a 3×2 factorial design. For this analysis each person is cross-classified by the drug they were given (a factor with 3 levels) and what therapy they received (a factor with 2 levels). Maybe there actually is an effect of therapy on mood gain, but we couldn’t find it because it was being “hidden” by the effect of drug? In other words, we’re going to want to run a single analysis that includes both drug and therapy as predictors. We didn’t find one, but there’s something a bit worrying about trying to run two separate analyses trying to predict the same outcome. In that chapter we did find a significant effect of drug, but at the end of the chapter we also ran an analysis to see if there was an effect of therapy. ![]() Another example appears in Chapter 14, in which we were looking at the effect of different drugs on the mood.gain experienced by each person. I gave one example of how this kind of design might arise above. In this section, I’ll discuss a broader class of experimental designs, known as factorial designs, in we have more than one grouping variable. When we discussed analysis of variance in Chapter 14, we assumed a fairly simple experimental design: each person falls into one of several groups, and we want to know whether these groups have different means on some outcome variable. ![]()
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