Lecture 5: Factorial ANOVA part 2

January 24, 2023 (3rd week of classes)

Multifactorial Analysis of Variance (ANOVA)

In this lecture we will continue covering factorial ANOVAs. We will cover how to use interaction plots to gain insights about the nature of the results involving factorial designs. We will also cover testing the assumptions underlying multifactorial ANOVAs.

The ANOVA fictional example in lectures 4 and this lecture 5 are based on equal number of observations per combination of groups (levels or treatments; remember we use these terms interchangeably). In the fictional diet example, there were 5 individuals in each of the 4 combinations of diet (yes/no) and exercise (yes/no). In the gene expression study, there were 2 individuals in each of the 12 combinations of strain (2 strains) and brain region (6 regions). For balanced designs, we say that the design is fully orthogonal because there is no variation that is shared between factors (a concept we will see in a few lectures; under ANCOVA). For fully orthogonal designs, we use what is called a Type I Sum-of-Squares (Type I SS). When factors are not fully orthogonal, then we use the Type III SS (Sum-of-Squares). We will learn about Type III in the ANCOVA module; the concepts there will be applicable to multifactorial ANOVAs that are not balanced, i.e., non-orthogonal).

A board overview on interaction main effect graphs
Although interaction plots are covered in our lecture (as everything we watch in videos from others that I post), I find it important to understand these concepts from different perspectives as there are many ways to learn and better understand the same concept. Remember that our learning styles are diverse and different ways to understand the same concept is relevant.

Normal QQ plots to assess the normality assumption

This video is also covered in Tutorial 3 and provides a good explanation of QQ plots to assess whether we can assume normality (important assumption for ANOVA) for our observed data. QQ plots were covered in BIOL322 but if they haven’t been covered in your stats course or don’t remember them well, here is a refresher. They are widely used to assess normality based on data visualization.


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