Two-Way Analysis of Variance

15-1

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CHAPTER OUTLINE

  • 15.1 The Two-Way ANOVA Model
  • 15.2 Inference for Two-Way ANOVA

Introduction

In this chapter, we move from one-way ANOVA, which compares means of several populations, to two-way ANOVA. Two-way ANOVA compares the means of populations that are classified in two ways or the mean responses in two-factor experiments.

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Many of the key concepts are similar to those of one-way ANOVA, but the presence of more than one factor also introduces some new ideas. We once more assume that the data are approximately Normal and that groups may have different means but have the same standard deviation; we again pool to estimate the variance; and we again use statistics for significance tests. The major difference between one-way and two-way ANOVA is in the FIT part of the model. We carefully study this term, finding much that is both new and useful.

We may, of course, have more than two factors. The statistical analysis is then called higher-way ANOVA. Although some details grow more complex, the most important ideas are already present in the two-way setting.

higher-way ANOVA