Correcting for pre-experiment bias in proportions test? Say I have an obstacle course, which not everyone completes, though, globally, most do. I hypothesize that the treatment, drinking Gatorade, will cause an increase in the obstacle course completion rate (CR).
Due to a fluke in randomization, the test group has a pre-experiment 95% CR but an in-experiment 98% CR. Whereas the control has a pre-experiment 94% CR and a 96% in-experiment CR.
In both time windows, the test group is beating the control group; given that this bias exists, I cannot simply do a Z proportions test on the experimental data. I need to correct for this pre-experiment bias in some way.
My question is: How is this most frequently / easily done?

Edit 1: DAG added (courtesy Excalidraw). The fundamental issue is that I believe that two factors affect Completion Rate, both ability and treatment (gatorade.) Because pre-experiment bias exists in my data (it could be anything from better running shoes, increased stamina, height, etc) which is observed by the CR of test > CR control pre-experiment. I believe that ability is moderating the effect of gatorade such that drawing conclusions from the experimental results alone, might tell an incomplete story.
Edit 2: Perhaps this situation is best solved with a regression model, eg the x=pre-experiment ratios, y=post-experiment ratios and what really matters are the slopes for exposure (yes/no)?

Thanks for the DAG.
As it is written, the intervention has no confounders so you’re free to just compare sample means with an appropriate test.
Ability may modulate the effect of the intervention, and adjusting for pre experiment ability may reduce the variance, but it is not necessary to adjust for. There is no bias here.
Now, this assumes that you have a simple random sample. If your sample consists mostly of people who have innate ability, and this is not reflected in the population, then the inference is troubled. Is this the case you’re trying to describe?
