Analysis of Variance for Balanced Designs

Let’s get a brief overview of the analysis of variance for balanced designs.

We'll cover the following

R packages

We’ll use the following R packages in this chapter.

  • ggplot2
  • Sleuth3
  • arm

Introduction

When we introduced the linear model analysis, we tried to keep things as straightforward as possible. We began with the simplest types of the linear model: one-way ANOVA and its simple linear regression equivalent. However, once we encountered more complex ANOVA and ANCOVA designs, we skipped over some complexities. This chapter explores these complexities of the linear model analysis and some additional ones that show up with unbalanced designs, such as those with unequal numbers of replicates in the different treatment groups.

Analysis of variance of balanced designs

To explore the analysis of balanced designs, let’s return to the example of the factorial ANOVA from the lesson Introduction to Factorial Designs. Let’s call this data frame Balanced. Click the “Run” button in the code widget below to see the first few rows:

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