This book should help you get familiar with analysis of variance (ANOVA)
and mixed models in
R. From a methodological point of view, we build upon
the knowledge of an introductory course to probability and statistics covering
the basic concepts of statistical inference (estimation, hypothesis tests,
confidence intervals) up to the two-sample \(t\)-test.
There are of course already excellent textbooks covering ANOVA
(including experimental design) in great detail. Examples are
Oehlert (2010), Kuehl (2000), Montgomery (2019) and many more. We build upon
these great books. From a mathematical point of view, we use similar notation
as Oehlert (2010). We try to provide a compact overview of the most important
topics including the corresponding applications in
R (R Core Team 2021) using
flexible mixed model approaches. We also use examples from the classical text
books and will redo the analysis in
R. This means you will see a lot
R code and
R output having the following form.
text <- "Let's get started ..." paste(text, "now!", sep = " ")
##  "Let's get started ... now!"
For better readability, we sometimes shorten the
R output a bit. This is
indicated with the symbol “
## ...” If you are completely new to
R you can get
an overview of online courses for example at
In addition, we try to give you an intuition when and how things can go wrong. This is useful not only when planning an experiment on your own but also when analyzing data from other sources or when reading a research paper.