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In reviewing some market research, I came across a study which decided to weight the results/outcomes of the control group so the distribution of participants in the control sub-groups (0,1,2,3,4,5 - a measure of their pre-experiment activity of a certain activity) would equate with that of the treatment group. The experiment was designed to introduce an incentive to encourage purchase activity.

Both treatment and control groups were supposed to be selected at random (N is in the 1000s for each group) - what would be the proper way(s) to address differences in the pre-distributions across groups when analyzing the results/outcomes of the test?

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