```
rm(list=ls())
library(ggplot2)
library(effects)
library(effsize)
rnd = function(x,digits=2){ return(format(round(x,digits),nsmall=digits)) }
load("interaction_datasets.RData")
tsz=25
```

Fully open code at: https://github.com/psicostat/workshops/tree/main/Interaction%20introduction%202024

Cohen’s *f* is often used for expressing effect size in
interactions. General formula for Cohen’s *f* is like this:

\[Cohen's f = \sqrt{\frac{R^2}{1 - R^2}}\]

However, for interactions we should consider what is *added*
by the interaction alone (above and beyond the main effects):

\[Cohen's f = \sqrt{\frac{R^2_1 - R^2_0}{1 - R^2_1}}\]

Cohen’s *f* = 0.25 (about Cohen’s *f* ^{2} =
0.06) is often taken as “medium” effect size. In fact, Cohen’s
*f* = 0.40 (about Cohen’s *f* ^{2} = 0.15) is also
taken as “medium” sometimes. Note that Cohen’s *f* = 0.25
requires R^{2} = 0.06, corresponding to about *r* = 0.24,
while Cohen’s *f* = 0.40 requires R^{2} = 0.15,
corresponding to about *r* = 0.39. **So, it makes more
sense to say that Cohen’s f = 0.25 is “medium”.**

Anyways… what does that mean in actual interactions? The problem is
that there are infinite cases that lead to the same effect size (e.g.,
Cohen’s *f*) in interactions.

All examples below will present about Cohen’s *f* ≈ 0.25
(Cohen’s *f* ^{2} ≈ 0.06).

This is also a useful resource: https://lakens.github.io/statistical_inferences/06-effectsize.html#effect-sizes-for-interactions