Mobile phones, GPS receivers, laptops or indeed smart watches have no effect whatsoever on avionic equipment. Most kit is designed and tested for restricted emissions and EMI tolerance in reverse.
The reason this equipment is banned has nothing to do with safety, but financial expedience. There's a lot of electronic equipment in the world. To rigorously prove my assertion in a way that would absolve an airline in a damages court case would take £100Ms. No one wants to pay that, especially if it would have to be passed onto customers. Better just ban the stuff. People will still keep flying as they're a captive market. You'll fly naked sat in a transparent plane if necessary.
Try leaving your phone fully on the next time you fly a long way across Europe. If you survive to land at the other end, you'll find perhaps 10 -15 messages on it welcoming you to various mobile networks that you over flew. No problem.
Edit following comments:
There are approximately 1 million people flying in the air at any one time across the world. If 1 in 1000 people randomly forget to switch off their e devices in flight (plausible), this theory is tested 1000 times/day across all randomly selected airliners in the world. That's 365,000 times a year on every conceivable aircraft type. That's a million hours /year of testing based on a 3hr mean flight time (plausible). That's a pretty extensive systematic experiment. Nothing dangerous happens.