I am analyzing the WoW change in conversion rate (visitors who booked / visitors).
Let's say the WoW change from week 1 to week 2 was -10% (dropped 10%). Now, I want to know what/where this drop in conversion rate came from. I have a hunch/business knowledge that this drop is coming from northeastern states in the US. So, I remove all northeastern states from the data and check the WoW drop. I see, now the drop is just 1%. That means 90% of the WoW drop is coming from NE states. Does this make sense? Is it mathematically correct?
Second part of my question is, I don't get the same answer if I do the same process as above one state at a time. I don't understand why that is the case.
For example, let's say I remove NY first and see the change, it's 5% (so that's 50% of the drop coming from NY). Second, I remove New Jersey, and I get x%, third I remove Massachusetts and I get x%, and so on… If I repeat this process for all NE states and I add up the effect from each one of them, I get a total of 75% (lower than the 90% I got from the first method, where I removed all NE states at once).
Why this is the case? Any help to make me understand this is much appreciated. Note that visitors in one state is not in any other state. Thanks!