I have a continuous response variable. It is the conversion rate from an AB test.

I noticed that the response variable changes meaningfully based on the experimental group, plus one other variable which is categoric.

category     group         conversion_rate
green        control       0.09
blue         control       0.25
purple       control       0.21 
yellow       control       0.17
green        treatment     0.36 
blue         treatment     0.32
purple       treatment     0.35
yellow       treatment     0.42

We can see that, on the whole, the conversion rate is double for the treatment group, going from .18 to .36. But, the effect changes depending on the category.

For green, the conversion rate goes way up, increasing by 3x. For blue, the conversion rate has a moderate increase, up .07. For purple, it has a strong increase, going up by .14. And, for yellow it has the largest increase in absolute terms, going up by .25.

I was curious if there was a statistical number or tool to describe this interaction effect. I figured I can do a line chart for each category and show the value for the control and the value for treatment.

Is there a more sophisticated way to describe the interaction effect?


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