| Toothaker’s Two Factor Design 528 Setting Linear Combinations of Effects 530 Textbook Parameterization 531 Over-Parameterized Models 532 (2009) | |||||||||||||||
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| This chapter describes the use of the function multicomp in the analysis of multiple comparisons. Section 17.1 describes simple calls to multicomp for standard comparisons in one-way layouts. Section 17.2 tells how to use multicomp for nonstandard designs and comparisons. In section 17.3, the capabilities and limitations of this function are summarized. 17.1 OVERVIEW When an experiment has been carried out in order to compare effects of several treatments, a classical analytical approach is to begin with a test for equality of those effects. Regardless of whether one embraces this classical strategy, and regardless of the outcome of this test, one is usually not finished with the analysis until determining where any differences exist, and how large the differences are (or might be); that is, until one does multiple comparisons of the treatment effects. As a simple start, consider the built-in S-PLUS data frame on fuel consumption of vehicles, fuel.frame. Each row provides the fuel consumption (Fuel) in 100*gallons/mile for a vehicle model, as well as the Type group of the model: Compact, Large, Medium, Small, Sporty, or Van. There is also information available on the Weight and Displacement of the vehicle. Figure 17.1 shows a boxplot of fuel consumption, the result of the following commands.> attach(fuel.frame)> boxplot(split(Fuel,Type)) Not surprisingly, the plot suggests that there are differences between vehicle types in terms of mean fuel consumption. This is confirmed by a one-factor analysis of variance test of equality obtained by a call to aov.> aovout.fuel <- aov ( Fuel ~ Type, data = fuel.frame)> anova(aovout.fuel) | |||||||||||||||
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