If you're wary about your privacy, you should consider the idea of downloading Pry-Fi for Android. Through your WiFi network, even if switched off, your smartphone can be tracked if the option to connect to WiFi networks is enabled. Pry-Fi is the solution developed by Chainfire, a well-known member of XDA-Developers.
An extra tool to increase your privacy
This app has been designed to prevent any device from being tracked avoiding that the device is noticed on the networks on which it's detected even if it continues to attempt background connections.
It does by transforming our MAC address into a pseudo-random address, preventing any system trying to track down your smartphone from being able to detect it. The latter changes constantly, even if we try to connect to the same WiFi network.
The idea behind this application is still under development and does't offer us a complete solution to our privacy problems in this sense, but for the time being, at least it hinders this kind of tracking. However, you'll need a rooted device to be able to make the most of it.