ANOVA tests using R Worksheet

In this worksheet you will learn how to use R to perform a one way (unpaired) or repeated measures (paired) ANOVA. This test takes 3 or more groups which are unpaired or paired (see suggested video below) and calculates if there is a statistically significant difference between them.

Required prerequisite(s)

You must have R installed on your computer and ideally also RStudio. See https://rstudio-education.github.io/hopr/starting.html for a guide.
You have confirmed your data is suitable for parametric tests by testing normality and homogeny of variance, following the Normality and homogeny of variance testing using R worksheet.
- NOTE: If your data requires a non-parametric tests, the equivalent for the one way (unpaired) ANOVA is the Kruskal-Wallis test. You can see the commands for this and its post hoc tests here: http://www.sthda.com/english/wiki/kruskal-wallis-test-in-r. There is no easy non-parametric test equivalent for the repeat measures (paired) ANOVA.

It is recommended that you have followed the Concepts in Computer Programming and Introduction to R tutorials before starting.
An understanding of tidy data. See https://www.youtube.com/watch?v=KW1laBLEiw0
An understanding of paired vs unpaired samples. See https://www.youtube.com/watch?v=-6vDjGR41YM
An understanding of parametric tests vs non-parametric tests: https://www.youtube.com/watch?v=biXY84hDX5M
An understanding of the melt format in R: https://www.statology.org/melt-in-r/

Open RStudio
Read in the UnpairedDataset1.tsv file. The read.delim will automatically assign row 1 as a header so no extra flags need to be passed to it
```
unpaired <- read.delim(“UnpairedDataset1.tsv")
```
To perform an ANOVA the data must in a ‘melted’ long format. Install the reshape 2 package (if needed) and then load the library
```
install.packages("reshape2")
library("reshape2")
```
Melt the data frame so it is in the right format for the T-test
```
meltedUnpaired=melt(unpaired)
```

Perform the ANOVA and store in a variable

unpairedAnov <- aov(value ~ variable, data=meltedUnpaired)

View the summary of the ANOVA. The Pr(>F) column tells you the p-value
```
summary(unpairedAnov)
```
If there is a significant difference between groups, a post-hoc test must be performed to determine which groups differ. We will use a Tukey HSD test to compare all groups to each other. The ‘p adj’ column tells you the adjusted (corrected) p-value for all pairwise comparisons in the data.
```
TukeyHSD(unpairedAnov, conf.level=.95)
```

Open RStudio
Read in the Paired.Dataset1.tsv file. Although the file has sample names in the first column, we want to keep these as their own column as they are needed for paired data
```
paired <- read.delim("PairedDataset1.tsv")
```
To perform an ANOVA the data must in a ‘melted’ long format. Install the reshape 2 package (if needed) and then load the library
```
install.packages("reshape2")
library("reshape2")
```
Melt the data frame so it is in the right format for the T-test
```
meltedPaired=melt(paired)
```
Perform the ANOVA and store in a variable. We must pass the sample names via the Error method to tell the ANOVA we have paired samples
```
pairedAnov <- aov(value ~factor(variable)+Error(factor(Sample.Name)), data=meltedPaired)
```
View the summary of the ANOVA. The Pr(>F) column tells you the p-value
```
summary(pairedAnov)
```
If there is a significant difference between groups, a post-hoc test must be performed to determine which groups differ. We will use a Tukey HSD test to compare all groups to each other. To do this for repeated measures (paired) ANOVA we have to use the emmeans library. Install (if needed) and load the library
```
install.packages("emmeans")
library("emmeans")
```
Convert the ANOVA result to the right format
```
emm <- emmeans(pairedAnov, ~ variable)
```
Run the Tukey HSD test. The ‘p-value’ column tells you the adjusted (corrected) p-value for all pairwise comparisons in the data.
```
pairs(emm)
```