You may want to consider a flip phone but even that has a GPS for 911... A/B testing is the least of your problems. If you are that concerned about privacy get off the cell network, root your phone with AOSP or your own OS and most importantly do not install any apps that you have not built. At that point consider A/B testing as it could greatly improve your user experience ;-).
Joke aside I understand your concern but this is really not the right place to start.
Joke aside I understand your concern but this is really not the right place to start.