Chapter 12 - Introduction to Analysis of Variance: This chapter requires an understanding of the material in sections 3.1, 3.2, 3.4, and 10.1.2

Abstract

This chapter introduces the analysis of variance, one of the main methods of analyzing data from factorial designs. With both quantitative and qualitative data, the function of the analysis of variance is to find whether each input has a significant effect on the system's response. Thus, an analysis of variance is often used at an early stage in the analysis of quantitative data. The chapter discusses in detail the one-way analysis of variance and explains the basic relations, assumptions, diagnostic plots, and table for the analysis of variance. In the two-way analysis of variance, the effects of more than one factor are considered in a factorial design. The possibility of interaction must be taken into account. This chapter also explains the analysis of randomized block design. In randomized block designs, there is no replication within a block, and interactions between treatments and blocks are assumed to be negligible (subject to checking). The analysis of variance does not give us all the information wanted in many practical cases. The analysis of variance in the form may tell us that a certain independent variable has a significant effect on the dependent variable, but it cannot give a quantitative functional relationship between the variables. To obtain a functional relationship, a different mathematical model and a different analysis must be used.