2x2 design: compare the increase within two treatments

[p.miller2020]

Hi,
I am currently evaluating a 2x2 experimental design.
Let's say the two independent variables are A and B with the manipulated levels (A1 vs. A2) and (B1 vs. B2). The dependent measure is performance (as a percentage score). I hypothesize that performance is higher in treatment A2 compared to A1. Moreover, i hypothesize that performance in treatment B2 is higher than in B1. However, most importantly, I predict that the increase from A2 to A1 is significantly higher than the increase from B2 to B1.
Is there any way to statistically evaluate whether the increase in performance comparing A2 vs. A1 is significantly higher than the increase from B2 vs. B1? What test should i apply?
Thank you so much in advance! Any keyword/name of a statistical method or whatever would be of great help.
Regards, P.

 

[Karabiner]

You could use a linear regression performance = b0 + b1*A + B2*B + b3*A*B + error where A*B represents
whether the difference between A1 and A2 differs between B1 and B2 (or vice versa). A two-factorial annalysis
of variance including an interaction between A and B would be equivalent to this. Since your dependent
variable is a percentage, there could be problems with the model residuals, but if your sample size is
large and/or the error distribution is not too strange (because of many 0% od 100% performaces, for example),
then this should work.

With kind regards

Karabiner

 

[p.miller2020]

You could use a linear regression performance = b0 + b1*A + B2*B + b3*A*B + error where A*B represents
whether the difference between A1 and A2 differs between B1 and B2 (or vice versa). A two-factorial annalysis
of variance including an interaction between A and B would be equivalent to this. Since your dependent
variable is a percentage, there could be problems with the model residuals, but if your sample size is
large and/or the error distribution is not too strange (because of many 0% od 100% performaces, for example),
then this should work.

With kind regards

Karabiner

Thank you so much, Karabiner!