Though a nice starting point, you reject #1 as too simplistic. With just single pre and post observations, it's too difficult to interpret change, to separate price responsiveness from history or maturation. And if the testing commences in a down market, there's always the possibility that business improves because of an uplifting economy that performance regresses to the mean independent of pricing changes. #2 is a better design, the multiple pre and post measures providing some protection against alternative explanations. #3 is better yet, especially if noted changes disappear when price changes are rescinded.
#4 introduces multiple group and is generally considered a desirable quasi-experiment. The challenge with this design is one of selection. The groups might represent stores in Massachusetts and Mississippi that serve fundamentally different populations. #5 promotes different flavors of intervention perhaps multiple pricing variations. #6 is a design that might best align with business needs, testing and learning in sequence. Finally, #7 is a personal favorite, combining multiple interventions with several groups, including a control. In our example, X1 and X2 might be two competing pricing models, with the first group a Massachusetts store, the second from Mississippi, and the control a store from each state. The multiple groups with control, in addition to multiple, sequenced interventions, should be able to handle many of the alternative explanations related to history, maturation, selection and regression to the mean.
I've presented just a sampling of the possibilities. Clever BI analysts can explore even more sophisticated designs that map to the climate of their enterprise. Two excellent sources on designs in general and Interrupted Time Series in particular are the comprehensive text by Shadish, Cook and Campbell
, and the clearly-written introductory article by Glass
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