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I have two groups of different sizes (control and test) and I want to measure the impacte of a certain treatment on the test group. Unfortunately, the control group has a different baseline compared to the test group, before the treatment was put in effect. Despite this difference in baseline, I want to be able to determine if the treatment caused a significant change in the test group.

To make it more concrete: let's say I want to measure the impact on order value as a result of treatment X. Treatment X is only applied to customers in the test group. Existing customers are randomly assigned either control (15%) or test group (85%), and the same is done for new customers. Example data might look like this:

Before period (28 days before start of test period)

Group Number of orders Average order value
Control 1500 50
Test 8000 48

Test period (starting treatment X up until today)

Group Number of orders Average order value
Control 2000 52
Test 11000 52

In the before period, the average order value in the test group is significantly lower, as determined by a t-test.

Given this scenario, what would be an applicable method and significance test to determine if treatment X caused a significant higher average order value in the test group?

What I have tried so far


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