ABSTRACT
This chapter focuses on significance testing as a fundamental procedure in statistical inference. It presents the theories in general form and reemphasizes fundamental techniques. Some slight modifications of the general theory allow students to construct prediction intervals for future observations from the model. Many of students would argue that the fundamental purpose of science is making accurate predictions of things that can be observed in the future. The results of the chapter apply to more complicated problems such as two-sample problems, regression, and analysis of variance. For these different problems, the only thing that changes is how we model the means of the observations. Models based on two categorical predictors are called two-factor analysis of variance (ANOVA) models. A model based on two or more categorical predictors is called a multifactor ANOVA model. Models with three or more categorical predictors may also be called higher-order ANOVAs.
