I am having difficulties with wrapping my head around an idea. Can difference-in-differences be used to remove bias from the data? I found a mention here: "Difference in differences is a well-accepted method in quantitative research and we use it to correct pre-experiment bias between groups so as to produce reliable treatment effects estimation."
Let's assume I have two variables at user level, and I have information collected before and after the experiment. Can I use diff-in-diff as a preprocessing step and then test the effect caused by a treatment by using a regular t-test?
The idea is as follows. Before introducing the treatment, there are two groups A and B (each with 1000 observations). The properties of the groups can change with time (increasing/decreasing pattern). I introduce a new feature to group B (part of the experiment, it is the test group), A is left unchanged. This creates group A -> C and and B -> D. In the end I want to carry out a statistical test, but account for the fact that some changes happened due to trend.
As in the picture below:
Looking at Dimitriy V. Masterov's answer here I see how to get the DiD coefficient (or simply value). He suggests that one of the possibilities is to carry out a hypothesis test to see if it is different from 0. But coming back to the original article I mentioned, I do not see how to use it as a pre-processing step and then later carry out different kind of hypothesis test (bootstrap/delta + t-test).