Two-way ANOVA — post hoc analysis, what is the difference between TukeyHSD and T-test

ANOVA (analysis of the variance) is a statistical method to test the equality of the group means. Furthermore, 2-way anova is used if there are 2 factors.

In this story, we will use in-vivo gene expression data with biological replicates as the example for the 2-way ANOVA analysis.

Data Information

We have a series of gene expression value on 3 different concentration RNA (Low, Medium and High) and 3 mice.

Raw data

It is a 3 X 3 experiment, means 3 factors by 3 factors.

Visualization

Before we jump into the analysis, visualization is always the first thing we need to do.

Here we can see the fold change increase when the concentration is high.

Fit the model

The same as other statistician, I use R for my analysis

First I tried the full model with interaction

two_way_interaction<- aov(Fold_change ~ Mouse * Concentration, data)
summary(two_way_interaction)