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I am trying to calculate effect sizes, but all I can find on the web relates only to the effect size of the difference between two groups. What I am interested in, is the effect size of the difference between group differences.

Not a very clear explanation, I know... I will use the IRIS dataset as example:

I would like to know if

the difference between the Petal.Length of Species setosa and the Petal.Length of Species versicolor (Δsetosa-versicolor)

is larger or smaller than

the difference between the Petal.Length of Species setosa and the Petal.Length of Species viriginica (Δsetosa-virginica).

Therefore I would like to calculate the effect size between Δsetosa-versicolor and Δsetosa-virginica.

For my dataset, I already performed GLM and a subsequent post-hoc test using custom costrasts to assess that there is indeed a difference between groups (corresponding to a significant difference between setosa and versicolor petal length, and between setosa and virginica petal length in the IRIS dataset).

Some attempts that I made:

use the dist() function to calculate the difference matrix of Petal.Length between two species. But I lose the information on species, so not very useful. Moreover, I am not sure what I get... all possible pairwise comparisons? Only those between groups? subsequent comparisons? Anyway, how can then use this matrix to calculate the effect size?

as.numeric(dist(iris$Petal.Length))
abs(apply(combn(iris$Petal.Length,2), 2, diff))

Use the mes() function from compute.es package. But in this way I am only able to get the effect size between eg setosa and versicolor, not what I am interested in.

mes(mean(iris$Petal.Length[iris$Species=="setosa"],na.rm=T), mean(iris$Petal.Length[iris$Species=="versicolor"],na.rm=T),
    sd(iris$Petal.Length[iris$Species=="setosa"],na.rm=T), sd(iris$Petal.Length[iris$Species=="versicolor"],na.rm=T),
    length(iris$Petal.Length[iris$Species=="setosa"]), length(iris$Petal.Length[iris$Species=="versicolor"]))

What can I do? I am really blocked here

Thank you very much for your help! =)

PS: question re-directed from StackOverflow

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