Chapter 10 - Analysis of Variance

Abstract

Suppose that we are interested in the effect of four different types of chemical fertilizers on the yield of rice, measured in pounds per acre. If there is no difference between the different types of fertilizers, then we would expect all the mean yields to be approximately equal. Otherwise, we would expect the mean yields to differ. The different types of fertilizers are called treatments and their effects are the treatment effects. The yield is called the response. Typically, we have a model with a response variable that is possibly affected by one or more treatments. The study of these types of models falls under the purview of design of experiments, which we discussed in Chapter 9. In this chapter, we concentrate on the analysis aspect of the data obtained from the designed experiments. If the data came from one or two populations, we could use the techniques learned in Chapters 6 and 7. Here, we introduce some tests that are used to analyze the data from more than two populations. These tests are used to deal with treatment effects, including tests that take into account other factors that may affect the response. The hypothesis that the population means are equal is considered equivalent to the hypothesis that there is no difference in treatment effects. The analytical method we will use in such problems is called the analysis of variance (ANOVA). Initial development of this method could be credited to Sir Ronald A. Fisher who introduced this technique for the analysis of agricultural field experiments. The “green revolution” in agriculture would have been impossible without the development of theory of experimental design and the methods of ANOVA.