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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.

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  • $\begingroup$ Nice question!! $\endgroup$ – user46925 Mar 13 '16 at 18:32
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Some of your problems had been studied in the literatures. Specially on works on ECOLOGY. The song of the dodo by David Quammen is one which is more like stories. But another ones Ecological Diversity and Mathematical Ecology by Pielou had been studied mathematically. Also there is a book by Stephen P. Hubbell name The unified neutral theory of biodiversity and biogeography which had both. Then you may recall those concepts appear in the books and translate to the ones that you asked.

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