ABSTRACT
In Chapter 1, we reviewed several methods regarding making inferences about the means of one or two groups or populations. The methods all involved the use of ttests. The inference about means of more than two groups requires an analytic technique known as analysis of variance (ANOVA). Analysis of variance techniques provide a very general framework for making inferences on mean values. In this chapter, we’ll explore three types of ways that ANOVA can be used to make inferences about means. First, we’ll consider the analysis of variance associated with a one-way design that involves comparing means according to one factor which may have many levels. Because we are interested in comparing means for the many levels, we may run into a problem with falsely declaring the differences to be statistically significant. Accordingly, we will discuss several methods to address this multiple comparisons issue, Next, we consider two-way designs that generalizes making inferences about means according to the levels associated with two factors. Such methods, of course, could be extended to many factors. Finally, we consider a generalization of the regresssion methods introduced in Chapter 4 by considering inferences about means for a factor with many levels while adjusting for a continuous variable. The methods for handlings such data involve the use of analysis of covariance (ANCOVA).
