I don’t know of any studies, and even if it’s a general rule that dealers cost more, there are of course exceptions to that rule, so the best course is always shopping around, getting quotes in writing, getting a second opinion when there’s a lot of money at stake and eventually building a relationship with a place that has shown a history of being honest, reasonably priced and does quality work wether that’s a dealer or an independent place. But as someone who has done an automotive mechanics apprenticeship, worked at two car dealers (one import and one domestic) and an independent shop (although I’m now in a different line of work), as well as plenty of times taking my own vehicles to both dealers and independent shops I can say in my experience a good trustworthy independent shop will cost you 20-50% less for most things than a dealer. Even when dealerships “cut you a deal” and do work “at cost” or whatever it often ends up being about the same you’d pay somewhere else. Again, this is not a universal rule, it’s just my experience (as well as many people I know) and even if it was a rule, there would be exceptions to it.