I am looking for resources (doesn't have to be a single book) that would cover some of the more challenging cases of experimental design and statistical analysis. Some of the cases I would like to be covered:
1. Cases where units of randomization are different from units of analysis
Example: I run an ecommerce platform with M sellers and N buyers I want to introduce a treatment on seller level, but interested in the probability of a buyer making a purchase. A typical buyer will visit several stores in a session.
2. The outcome variable is highly skewed
Example: I run a call center and I want to try prompting the customer to enter their customer ID before reaching the agent. I hope to reduce the average duration of a phone calls. The phone calls distribution is extremely skewed.
3. A treatment group has differently shaped distribution
Example: Same call center, but now my treatment works much better for shorter calls and slightly worse for longer calls. What's the correct way of analyzing this?
4. The treatment itself makes my groups unbalanced
Example: The same ecommerce platform as in 1. but now I want to experiment with different ranking mechanisms. By being assigned to a more favorable ranking position a seller might want to raise prices, increase its inventory, change marketing strategies, etc. in a way that will make some of those variables systematically different for different treatments.